1.
Orders of magnitude (numbers)
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This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantity and probabilities. Mathematics – Writing, Approximately 10−183,800 is a rough first estimate of the probability that a monkey, however, taking punctuation, capitalization, and spacing into account, the actual probability is far lower, around 10−360,783. Computing, The number 1×10−6176 is equal to the smallest positive non-zero value that can be represented by a quadruple-precision IEEE decimal floating-point value, Computing, The number 6. 5×10−4966 is approximately equal to the smallest positive non-zero value that can be represented by a quadruple-precision IEEE floating-point value. Computing, The number 3. 6×10−4951 is approximately equal to the smallest positive non-zero value that can be represented by a 80-bit x86 double-extended IEEE floating-point value. Computing, The number 1×10−398 is equal to the smallest positive non-zero value that can be represented by a double-precision IEEE decimal floating-point value, Computing, The number 4. 9×10−324 is approximately equal to the smallest positive non-zero value that can be represented by a double-precision IEEE floating-point value. Computing, The number 1×10−101 is equal to the smallest positive non-zero value that can be represented by a single-precision IEEE decimal floating-point value, Mathematics, The probability in a game of bridge of all four players getting a complete suit is approximately 4. 47×10−28. ISO, yocto- ISO, zepto- Mathematics, The probability of matching 20 numbers for 20 in a game of keno is approximately 2.83 × 10−19. ISO, atto- Mathematics, The probability of rolling snake eyes 10 times in a row on a pair of dice is about 2. 74×10−16. ISO, micro- Mathematics – Poker, The odds of being dealt a flush in poker are 649,739 to 1 against. Mathematics – Poker, The odds of being dealt a flush in poker are 72,192 to 1 against. Mathematics – Poker, The odds of being dealt a four of a kind in poker are 4,164 to 1 against, for a probability of 2.4 × 10−4. ISO, milli- Mathematics – Poker, The odds of being dealt a full house in poker are 693 to 1 against, for a probability of 1.4 × 10−3. Mathematics – Poker, The odds of being dealt a flush in poker are 507.8 to 1 against, Mathematics – Poker, The odds of being dealt a straight in poker are 253.8 to 1 against, for a probability of 4 × 10−3. Physics, α =0.007297352570, the fine-structure constant, ISO, deci- Mathematics – Poker, The odds of being dealt only one pair in poker are about 5 to 2 against, for a probability of 0.42. Demography, The population of Monowi, a village in Nebraska. Mathematics, √2 ≈1.414213562373095489, the ratio of the diagonal of a square to its side length. Mathematics, φ ≈1.618033988749895848, the golden ratio Mathematics, the number system understood by most computers, human scale, There are 10 digits on a pair of human hands, and 10 toes on a pair of human feet. Mathematics, The number system used in life, the decimal system, has 10 digits,0,1,2,3,4,5,6,7,8,9
2.
Long and short scales
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Thus, billion means a million millions, trillion means a million billions, and so on. Short scale Every new term greater than million is one thousand times larger than the previous term, thus, billion means a thousand millions, trillion means a thousand billions, and so on. For whole numbers less than a million the two scales are identical. From a thousand million up the two scales diverge, using the words for different numbers, this can cause misunderstanding. Countries where the scale is currently used include most countries in continental Europe and most French-speaking, Spanish-speaking. The short scale is now used in most English-speaking and Arabic-speaking countries, in Brazil, in former Soviet Union, number names are rendered in the language of the country, but are similar everywhere due to shared etymology. Some languages, particularly in East Asia and South Asia, have large number naming systems that are different from both the long and short scales, for example the Indian numbering system. After several decades of increasing informal British usage of the scale, in 1974 the government of the UK adopted it. With very few exceptions, the British usage and American usage are now identical, the first recorded use of the terms short scale and long scale was by the French mathematician Geneviève Guitel in 1975. At and above a million the same names are used to refer to numbers differing by a factor of an integer power of 1,000. Each scale has a justification to explain the use of each such differing numerical name. The short-scale logic is based on powers of one thousand, whereas the long-scale logic is based on powers of one million, in both scales, the prefix bi- refers to 2 and tri- refers to 3, etc. However only in the scale do the prefixes beyond one million indicate the actual power or exponent. In the short scale, the prefixes refer to one less than the exponent, the word, million, derives from the Old French, milion, from the earlier Old Italian, milione, an intensification of the Latin word, mille, a thousand. That is, a million is a big thousand, much as a great gross is a dozen gross or 12×144 =1728, the word, milliard, or its translation, is found in many European languages and is used in those languages for 109. However, it is unknown in American English, which uses billion, and not used in British English, which preferred to use thousand million before the current usage of billion. The financial term, yard, which derives from milliard, is used on financial markets, as, unlike the term, billion, it is internationally unambiguous and phonetically distinct from million. Likewise, many long scale use the word billiard for one thousand long scale billions
3.
Integer
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An integer is a number that can be written without a fractional component. For example,21,4,0, and −2048 are integers, while 9.75, 5 1⁄2, the set of integers consists of zero, the positive natural numbers, also called whole numbers or counting numbers, and their additive inverses. This is often denoted by a boldface Z or blackboard bold Z standing for the German word Zahlen, ℤ is a subset of the sets of rational and real numbers and, like the natural numbers, is countably infinite. The integers form the smallest group and the smallest ring containing the natural numbers, in algebraic number theory, the integers are sometimes called rational integers to distinguish them from the more general algebraic integers. In fact, the integers are the integers that are also rational numbers. Like the natural numbers, Z is closed under the operations of addition and multiplication, that is, however, with the inclusion of the negative natural numbers, and, importantly,0, Z is also closed under subtraction. The integers form a ring which is the most basic one, in the following sense, for any unital ring. This universal property, namely to be an object in the category of rings. Z is not closed under division, since the quotient of two integers, need not be an integer, although the natural numbers are closed under exponentiation, the integers are not. The following lists some of the properties of addition and multiplication for any integers a, b and c. In the language of algebra, the first five properties listed above for addition say that Z under addition is an abelian group. As a group under addition, Z is a cyclic group, in fact, Z under addition is the only infinite cyclic group, in the sense that any infinite cyclic group is isomorphic to Z. The first four properties listed above for multiplication say that Z under multiplication is a commutative monoid. However, not every integer has an inverse, e. g. there is no integer x such that 2x =1, because the left hand side is even. This means that Z under multiplication is not a group, all the rules from the above property table, except for the last, taken together say that Z together with addition and multiplication is a commutative ring with unity. It is the prototype of all objects of algebraic structure. Only those equalities of expressions are true in Z for all values of variables, note that certain non-zero integers map to zero in certain rings. The lack of zero-divisors in the means that the commutative ring Z is an integral domain
4.
100 (number)
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100 or one hundred is the natural number following 99 and preceding 101. In medieval contexts, it may be described as the hundred or five score in order to differentiate the English. The standard SI prefix for a hundred is hecto-,100 is the basis of percentages, with 100% being a full amount. 100 is the sum of the first nine prime numbers, as well as the sum of pairs of prime numbers e. g.3 +97,11 +89,17 +83,29 +71,41 +59. 100 is the sum of the cubes of the first four integers and this is related by Nicomachuss theorem to the fact that 100 also equals the square of the sum of the first four integers,100 =102 =2. 26 +62 =100, thus 100 is a Leyland number and it is divisible by the number of primes below it,25 in this case. It can not be expressed as the difference between any integer and the total of coprimes below it, making it a noncototient and it can be expressed as a sum of some of its divisors, making it a semiperfect number. 100 is a Harshad number in base 10, and also in base 4, there are exactly 100 prime numbers whose digits are in strictly ascending order. 100 is the smallest number whose common logarithm is a prime number,100 senators are in the U. S One hundred is the atomic number of fermium, an actinide. On the Celsius scale,100 degrees is the temperature of pure water at sea level. The Kármán line lies at an altitude of 100 kilometres above the Earths sea level and is used to define the boundary between Earths atmosphere and outer space. There are 100 blasts of the Shofar heard in the service of Rosh Hashana, a religious Jew is expected to utter at least 100 blessings daily. In Hindu Religion - Mythology Book Mahabharata - Dhritarashtra had 100 sons known as kauravas, the United States Senate has 100 Senators. Most of the currencies are divided into 100 subunits, for example, one euro is one hundred cents. The 100 Euro banknotes feature a picture of a Rococo gateway on the obverse, the U. S. hundred-dollar bill has Benjamin Franklins portrait, the Benjamin is the largest U. S. bill in print. American savings bonds of $100 have Thomas Jeffersons portrait, while American $100 treasury bonds have Andrew Jacksons portrait, One hundred is also, The number of years in a century. The number of pounds in an American short hundredweight, in Greece, India, Israel and Nepal,100 is the police telephone number. In Belgium,100 is the ambulance and firefighter telephone number, in United Kingdom,100 is the operator telephone number
5.
1,000,000
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One million or one thousand thousand is the natural number following 999,999 and preceding 1,000,001. The word is derived from the early Italian millione, from mille, thousand and it is commonly abbreviated as m or M, further MM, mm, or mn in financial contexts. In scientific notation, it is written as 1×106 or 106, physical quantities can also be expressed using the SI prefix mega, when dealing with SI units, for example,1 megawatt equals 1,000,000 watts. The meaning of the word million is common to the scale and long scale numbering systems, unlike the larger numbers. Information, Not counting spaces, the text printed on 136 pages of an Encyclopædia Britannica, length, There are one million millimeters in a kilometer, and roughly a million sixteenths of an inch in a mile. A typical car tire might rotate a million times in a 1, 200-mile trip, fingers, If the width of a human finger is 2.2 cm, then a million fingers lined up would cover a distance of 22 km. If a person walks at a speed of 4 km/h, it would take approximately five. A city lot 70 by 100 feet is about a million square inches, volume, The cube root of one million is only one hundred, so a million objects or cubic units is contained in a cube only a hundred objects or linear units on a side. A million grains of salt or granulated sugar occupies only about 64 ml. One million cubic inches would be the volume of a room only 8 1⁄3 feet long by 8 1⁄3 feet wide by 8 1⁄3 feet high. Mass, A million cubic millimeters of water would have a volume of one litre, a million millilitres or cubic centimetres of water has a mass of a million grams or one tonne. Weight, A million 80-milligram honey bees would weigh the same as an 80 kg person, landscape, A pyramidal hill 600 feet wide at the base and 100 feet high would weigh about a million tons. Computer, A display resolution of 1,280 by 800 pixels contains 1,024,000 pixels, money, A USD bill of any denomination weighs 1 gram. There are 454 grams in a pound, one million $1 bills would weigh 2,204.62 pounds, or just over 1 ton. Time, A million seconds is 11.57 days, in Indian English and Pakistani English, it is also expressed as 10 lakh or 10 Lac. Lakh is derived from laksh for 100,000 in Sanskrit
6.
Factorization
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In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 ×5, in all cases, a product of simpler objects is obtained. The aim of factoring is usually to reduce something to “basic building blocks”, such as numbers to prime numbers, factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra. Viètes formulas relate the coefficients of a polynomial to its roots, the opposite of polynomial factorization is expansion, the multiplying together of polynomial factors to an “expanded” polynomial, written as just a sum of terms. Integer factorization for large integers appears to be a difficult problem, there is no known method to carry it out quickly. Its complexity is the basis of the security of some public key cryptography algorithms. A matrix can also be factorized into a product of matrices of special types, One major example of this uses an orthogonal or unitary matrix, and a triangular matrix. There are different types, QR decomposition, LQ, QL, RQ and this situation is generalized by factorization systems. By the fundamental theorem of arithmetic, every integer greater than 1 has a unique prime factorization. Given an algorithm for integer factorization, one can factor any integer down to its constituent primes by repeated application of this algorithm, for very large numbers, no efficient classical algorithm is known. Modern techniques for factoring polynomials are fast and efficient, but use sophisticated mathematical ideas and these techniques are used in the construction of computer routines for carrying out polynomial factorization in Computer algebra systems. This article is concerned with classical techniques. While the general notion of factoring just means writing an expression as a product of simpler expressions, when factoring polynomials this means that the factors are to be polynomials of smaller degree. Thus, while x 2 − y = is a factorization of the expression, another issue concerns the coefficients of the factors. It is not always possible to do this, and a polynomial that can not be factored in this way is said to be irreducible over this type of coefficient, thus, x2 -2 is irreducible over the integers and x2 +4 is irreducible over the reals. In the first example, the integers 1 and -2 can also be thought of as real numbers, and if they are, then x 2 −2 = shows that this polynomial factors over the reals. Similarly, since the integers 1 and 4 can be thought of as real and hence complex numbers, x2 +4 splits over the complex numbers, i. e. x 2 +4 =. The fundamental theorem of algebra can be stated as, Every polynomial of n with complex number coefficients splits completely into n linear factors
7.
Greek numerals
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Greek numerals are a system of writing numbers using the letters of the Greek alphabet. These alphabetic numerals are known as Ionic or Ionian numerals, Milesian numerals. In modern Greece, they are used for ordinal numbers. For ordinary cardinal numbers, however, Greece uses Arabic numerals, attic numerals, which were later adopted as the basis for Roman numerals, were the first alphabetic set. They were acrophonic, derived from the first letters of the names of the numbers represented and they ran =1, =5, =10, =100, =1000, and =10000. 50,500,5000, and 50000 were represented by the letter with minuscule powers of ten written in the top right corner, the same system was used outside of Attica, but the symbols varied with the local alphabets, in Boeotia, was 1000. The present system probably developed around Miletus in Ionia, 19th-century classicists placed its development in the 3rd century BC, the occasion of its first widespread use. The present system uses the 24 letters adopted by Euclid as well as three Phoenician and Ionic ones that were not carried over, digamma, koppa, and sampi. The position of characters within the numbering system imply that the first two were still in use while the third was not. Greek numerals are decimal, based on powers of 10, the units from 1 to 9 are assigned to the first nine letters of the old Ionic alphabet from alpha to theta. Each multiple of one hundred from 100 to 900 was then assigned its own separate letter as well and this alphabetic system operates on the additive principle in which the numeric values of the letters are added together to obtain the total. For example,241 was represented as, in ancient and medieval manuscripts, these numerals were eventually distinguished from letters using overbars, α, β, γ, etc. In medieval manuscripts of the Book of Revelation, the number of the Beast 666 is written as χξϛ, although the Greek alphabet began with only majuscule forms, surviving papyrus manuscripts from Egypt show that uncial and cursive minuscule forms began early. These new letter forms sometimes replaced the ones, especially in the case of the obscure numerals. The old Q-shaped koppa began to be broken up and simplified, the numeral for 6 changed several times. During antiquity, the letter form of digamma came to be avoided in favor of a special numerical one. By the Byzantine era, the letter was known as episemon and this eventually merged with the sigma-tau ligature stigma. In modern Greek, a number of changes have been made
8.
Roman numerals
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The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet, Roman numerals, as used today, are based on seven symbols, The use of Roman numerals continued long after the decline of the Roman Empire. The numbers 1 to 10 are usually expressed in Roman numerals as follows, I, II, III, IV, V, VI, VII, VIII, IX, Numbers are formed by combining symbols and adding the values, so II is two and XIII is thirteen. Symbols are placed left to right in order of value. Named after the year of its release,2014 as MMXIV, the year of the games of the XXII Olympic Winter Games The standard forms described above reflect typical modern usage rather than a universally accepted convention. Usage in ancient Rome varied greatly and remained inconsistent in medieval, Roman inscriptions, especially in official contexts, seem to show a preference for additive forms such as IIII and VIIII instead of subtractive forms such as IV and IX. Both methods appear in documents from the Roman era, even within the same document, double subtractives also occur, such as XIIX or even IIXX instead of XVIII. Sometimes V and L are not used, with such as IIIIII. Such variation and inconsistency continued through the period and into modern times. Clock faces that use Roman numerals normally show IIII for four o’clock but IX for nine o’clock, however, this is far from universal, for example, the clock on the Palace of Westminster in London uses IV. Similarly, at the beginning of the 20th century, different representations of 900 appeared in several inscribed dates. For instance,1910 is shown on Admiralty Arch, London, as MDCCCCX rather than MCMX, although Roman numerals came to be written with letters of the Roman alphabet, they were originally independent symbols. The Etruscans, for example, used
9.
Binary number
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The base-2 system is a positional notation with a radix of 2. Because of its implementation in digital electronic circuitry using logic gates. Each digit is referred to as a bit, the modern binary number system was devised by Gottfried Leibniz in 1679 and appears in his article Explication de lArithmétique Binaire. Systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, Leibniz was specifically inspired by the Chinese I Ching. The scribes of ancient Egypt used two different systems for their fractions, Egyptian fractions and Horus-Eye fractions, the method used for ancient Egyptian multiplication is also closely related to binary numbers. This method can be seen in use, for instance, in the Rhind Mathematical Papyrus, the I Ching dates from the 9th century BC in China. The binary notation in the I Ching is used to interpret its quaternary divination technique and it is based on taoistic duality of yin and yang. Eight trigrams and a set of 64 hexagrams, analogous to the three-bit and six-bit binary numerals, were in use at least as early as the Zhou Dynasty of ancient China. The Song Dynasty scholar Shao Yong rearranged the hexagrams in a format that resembles modern binary numbers, the Indian scholar Pingala developed a binary system for describing prosody. He used binary numbers in the form of short and long syllables, Pingalas Hindu classic titled Chandaḥśāstra describes the formation of a matrix in order to give a unique value to each meter. The binary representations in Pingalas system increases towards the right, the residents of the island of Mangareva in French Polynesia were using a hybrid binary-decimal system before 1450. Slit drums with binary tones are used to encode messages across Africa, sets of binary combinations similar to the I Ching have also been used in traditional African divination systems such as Ifá as well as in medieval Western geomancy. The base-2 system utilized in geomancy had long been applied in sub-Saharan Africa. Leibnizs system uses 0 and 1, like the modern binary numeral system, Leibniz was first introduced to the I Ching through his contact with the French Jesuit Joachim Bouvet, who visited China in 1685 as a missionary. Leibniz saw the I Ching hexagrams as an affirmation of the universality of his own beliefs as a Christian. Binary numerals were central to Leibnizs theology and he believed that binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing. Is not easy to impart to the pagans, is the ex nihilo through Gods almighty power. In 1854, British mathematician George Boole published a paper detailing an algebraic system of logic that would become known as Boolean algebra
10.
Ternary numeral system
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The ternary numeral system has three as its base. Analogous to a bit, a digit is a trit. One trit is equivalent to bits of information. Representations of integer numbers in ternary do not get uncomfortably lengthy as quickly as in binary, for example, decimal 365 corresponds to binary 101101101 and to ternary 111112. However, they are far less compact than the corresponding representations in bases such as decimal – see below for a compact way to codify ternary using nonary. The value of a number with n bits that are all 1 is 2n −1. Then N = M, N = /, and N = bd −1, for a three-digit ternary number, N =33 −1 =26 =2 ×32 +2 ×31 +2 ×30 =18 +6 +2. Nonary or septemvigesimal can be used for representation of ternary. A base-three system is used in Islam to keep track of counting Tasbih to 99 or to 100 on a hand for counting prayers. In certain analog logic, the state of the circuit is often expressed ternary and this is most commonly seen in Transistor–transistor logic using 7406 open collector logic. The output is said to either be low, high, or open, in this configuration the output of the circuit is actually not connected to any voltage reference at all. Where the signal is usually grounded to a reference, or at a certain voltage level. Thus, the voltage level is sometimes unpredictable. A rare ternary point is used to denote fractional parts of an inning in baseball, since each inning consists of three outs, each out is considered one third of an inning and is denoted as.1. For example, if a player pitched all of the 4th, 5th and 6th innings, plus 2 outs of the 7th inning, his Innings pitched column for that game would be listed as 3.2, meaning 3⅔. In this usage, only the part of the number is written in ternary form. Ternary numbers can be used to convey self-similar structures like the Sierpinski triangle or the Cantor set conveniently, additionally, it turns out that the ternary representation is useful for defining the Cantor set and related point sets, because of the way the Cantor set is constructed. The Cantor set consists of the points from 0 to 1 that have an expression that does not contain any instance of the digit 1
11.
Quaternary numeral system
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Quaternary is the base-4 numeral system. It uses the digits 0,1,2 and 3 to represent any real number. Four is the largest number within the range and one of two numbers that is both a square and a highly composite number, making quaternary a convenient choice for a base at this scale. Despite being twice as large, its economy is equal to that of binary. However, it no better in the localization of prime numbers. See decimal and binary for a discussion of these properties, as with the octal and hexadecimal numeral systems, quaternary has a special relation to the binary numeral system. Each radix 4,8 and 16 is a power of 2, so the conversion to and from binary is implemented by matching each digit with 2,3 or 4 binary digits, for example, in base 4,302104 =11001001002. Although octal and hexadecimal are widely used in computing and computer programming in the discussion and analysis of binary arithmetic and logic, by analogy with byte and nybble, a quaternary digit is sometimes called a crumb. There is a surviving list of Ventureño language number words up to 32 written down by a Spanish priest ca, the Kharosthi numerals have a partial base 4 counting system from 1 to decimal 10. Quaternary numbers are used in the representation of 2D Hilbert curves, here a real number between 0 and 1 is converted into the quaternary system. Every single digit now indicates in which of the respective 4 sub-quadrants the number will be projected, parallels can be drawn between quaternary numerals and the way genetic code is represented by DNA. The four DNA nucleotides in order, abbreviated A, C, G and T, can be taken to represent the quaternary digits in numerical order 0,1,2. With this encoding, the complementary digit pairs 0↔3, and 1↔2 match the complementation of the pairs, A↔T and C↔G. For example, the nucleotide sequence GATTACA can be represented by the quaternary number 2033010, quaternary line codes have been used for transmission, from the invention of the telegraph to the 2B1Q code used in modern ISDN circuits
12.
Quinary
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Quinary is a numeral system with five as the base. A possible origination of a system is that there are five fingers on either hand. The base five is stated from 0–4, in the quinary place system, five numerals, from 0 to 4, are used to represent any real number. According to this method, five is written as 10, twenty-five is written as 100, today, the main usage of base 5 is as a biquinary system, which is decimal using five as a sub-base. Another example of a system, is sexagesimal, base 60. Each quinary digit has log25 bits of information, many languages use quinary number systems, including Gumatj, Nunggubuyu, Kuurn Kopan Noot, Luiseño and Saraveca. Gumatj is a true 5–25 language, in which 25 is the group of 5. The Gumatj numerals are shown below, In the video game Riven and subsequent games of the Myst franchise, a decimal system with 2 and 5 as a sub-bases is called biquinary, and is found in Wolof and Khmer. Roman numerals are a biquinary system, the numbers 1,5,10, and 50 are written as I, V, X, and L respectively. Eight is VIII and seventy is LXX, most versions of the abacus use a biquinary system to simulate a decimal system for ease of calculation. Urnfield culture numerals and some tally mark systems are also biquinary, units of currencies are commonly partially or wholly biquinary. A vigesimal system with 4 and 5 as a sub-bases is found in Nahuatl, pentimal system Quibinary Yan Tan Tethera References, Quinary Base Conversion, includes fractional part, from Math Is Fun Media related to Quinary numeral system at Wikimedia Commons
13.
Senary
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The senary numeral system has six as its base. It has been adopted independently by a number of cultures. Like decimal, it is a semiprime, though being the product of the two consecutive numbers that are both prime it has a high degree of mathematical properties for its size. As six is a highly composite number, many of the arguments made in favor of the duodecimal system also apply to this base-6. Senary may be considered interesting in the study of numbers, since all primes other than 2 and 3. That is, for every number p greater than 3, one has the modular arithmetic relations that either p ≡1 or 5. This property maximizes the probability that the result of an integer multiplication will end in zero, E. g. if three fingers are extended on the left hand and four on the right, 34senary is represented. This is equivalent to 3 ×6 +4 which is 22decimal, flipping the sixes hand around to its backside may help to further disambiguate which hand represents the sixes and which represents the units. While most developed cultures count by fingers up to 5 in very similar ways, beyond 5 non-Western cultures deviate from Western methods, such as with Chinese number gestures. More abstract finger counting systems, such as chisanbop or finger binary, allow counting to 99,1,023, or even higher depending on the method. The English monk and historian Bede, in the first chapter of De temporum ratione, titled Tractatus de computo, vel loquela per gestum digitorum, the Ndom language of Papua New Guinea is reported to have senary numerals. Mer means 6, mer an thef means 6 ×2 =12, nif means 36, another example from Papua New Guinea are the Morehead-Maro languages. In these languages, counting is connected to ritualized yam-counting and these languages count from a base six, employing words for the powers of six, running up to 66 for some of the languages. One example is Kómnzo with the numerals, nimbo, féta, tarumba, ntamno, wärämäkä. Some Niger-Congo languages have been reported to use a number system, usually in addition to another. For some purposes, base 6 might be too small a base for convenience. The choice of 36 as a radix is convenient in that the digits can be represented using the Arabic numerals 0–9 and the Latin letters A–Z, this choice is the basis of the base36 encoding scheme. Base36 encoding scheme Binary Ternary Duodecimal Sexagesimal Shacks Base Six Dialectic Digital base 6 clock Analog Clock Designer capable of rendering a base 6 clock Senary base conversion
14.
Octal
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The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping binary digits into groups of three. For example, the representation for decimal 74 is 1001010. Two zeroes can be added at the left,1001010, corresponding the octal digits 112, in the decimal system each decimal place is a power of ten. For example,7410 =7 ×101 +4 ×100 In the octal system each place is a power of eight. The Yuki language in California and the Pamean languages in Mexico have octal systems because the speakers count using the spaces between their fingers rather than the fingers themselves and it has been suggested that the reconstructed Proto-Indo-European word for nine might be related to the PIE word for new. Based on this, some have speculated that proto-Indo-Europeans used a number system. In 1716 King Charles XII of Sweden asked Emanuel Swedenborg to elaborate a number based on 64 instead of 10. Swedenborg however argued that for people with less intelligence than the king such a big base would be too difficult, in 1718 Swedenborg wrote a manuscript, En ny rekenkonst som om vexlas wid Thalet 8 i stelle then wanliga wid Thalet 10. The numbers 1-7 are there denoted by the l, s, n, m, t, f, u. Thus 8 = lo,16 = so,24 = no,64 = loo,512 = looo etc, numbers with consecutive consonants are pronounced with vowel sounds between in accordance with a special rule. Writing under the pseudonym Hirossa Ap-Iccim in The Gentlemans Magazine, July 1745, Hugh Jones proposed a system for British coins, weights. In 1801, James Anderson criticized the French for basing the Metric system on decimal arithmetic and he suggested base 8 for which he coined the term octal. In the mid 19th century, Alfred B. Taylor concluded that Our octonary radix is, therefore, so, for example, the number 65 would be spoken in octonary as under-un. Taylor also republished some of Swedenborgs work on octonary as an appendix to the above-cited publications, in the 2009 film Avatar, the language of the extraterrestrial Navi race employs an octal numeral system, probably due to the fact that they have four fingers on each hand. In the TV series Stargate SG-1, the Ancients, a race of beings responsible for the invention of the Stargates, in the tabletop game series Warhammer 40,000, the Tau race use an octal number system. Octal became widely used in computing systems such as the PDP-8, ICL1900. Octal was an abbreviation of binary for these machines because their word size is divisible by three
15.
Duodecimal
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The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written by a rotated 2 and this notation was introduced by Sir Isaac Pitman. These digit forms are available as Unicode characters on computerized systems since June 2015 as ↊ and ↋, other notations use A, T, or X for ten and B or E for eleven. The number twelve is written as 10 in duodecimal, whereas the digit string 12 means 1 dozen and 2 units. Similarly, in duodecimal 100 means 1 gross,1000 means 1 great gross, the number twelve, a superior highly composite number, is the smallest number with four non-trivial factors, and the smallest to include as factors all four numbers within the subitizing range. As a result, duodecimal has been described as the number system. Of its factors,2 and 3 are prime, which means the reciprocals of all 3-smooth numbers have a representation in duodecimal. In particular, the five most elementary fractions all have a terminating representation in duodecimal. This all makes it a convenient number system for computing fractions than most other number systems in common use, such as the decimal, vigesimal, binary. Although the trigesimal and sexagesimal systems do even better in respect, this is at the cost of unwieldy multiplication tables. In this section, numerals are based on decimal places, for example,10 means ten,12 means twelve. Languages using duodecimal number systems are uncommon, germanic languages have special words for 11 and 12, such as eleven and twelve in English. However, they are considered to come from Proto-Germanic *ainlif and *twalif, historically, units of time in many civilizations are duodecimal. There are twelve signs of the zodiac, twelve months in a year, traditional Chinese calendars, clocks, and compasses are based on the twelve Earthly Branches. There are 12 inches in a foot,12 troy ounces in a troy pound,12 old British pence in a shilling,24 hours in a day. The Romans used a system based on 12, including the uncia which became both the English words ounce and inch. The importance of 12 has been attributed to the number of cycles in a year. It is possible to count to 12 with the acting as a pointer
16.
Hexadecimal
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In mathematics and computing, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, Hexadecimal numerals are widely used by computer system designers and programmers. As each hexadecimal digit represents four binary digits, it allows a more human-friendly representation of binary-coded values, one hexadecimal digit represents a nibble, which is half of an octet or byte. For example, a byte can have values ranging from 00000000 to 11111111 in binary form. In a non-programming context, a subscript is typically used to give the radix, several notations are used to support hexadecimal representation of constants in programming languages, usually involving a prefix or suffix. The prefix 0x is used in C and related languages, where this value might be denoted as 0x2AF3, in contexts where the base is not clear, hexadecimal numbers can be ambiguous and confused with numbers expressed in other bases. There are several conventions for expressing values unambiguously, a numerical subscript can give the base explicitly,15910 is decimal 159,15916 is hexadecimal 159, which is equal to 34510. Some authors prefer a text subscript, such as 159decimal and 159hex, or 159d and 159h. example. com/name%20with%20spaces where %20 is the space character, thus ’, represents the right single quotation mark, Unicode code point number 2019 in hex,8217. In the Unicode standard, a value is represented with U+ followed by the hex value. Color references in HTML, CSS and X Window can be expressed with six hexadecimal digits prefixed with #, white, CSS allows 3-hexdigit abbreviations with one hexdigit per component, #FA3 abbreviates #FFAA33. *nix shells, AT&T assembly language and likewise the C programming language, to output an integer as hexadecimal with the printf function family, the format conversion code %X or %x is used. In Intel-derived assembly languages and Modula-2, hexadecimal is denoted with a suffixed H or h, some assembly languages use the notation HABCD. Ada and VHDL enclose hexadecimal numerals in based numeric quotes, 16#5A3#, for bit vector constants VHDL uses the notation x5A3. Verilog represents hexadecimal constants in the form 8hFF, where 8 is the number of bits in the value, the Smalltalk language uses the prefix 16r, 16r5A3 PostScript and the Bourne shell and its derivatives denote hex with prefix 16#, 16#5A3. For PostScript, binary data can be expressed as unprefixed consecutive hexadecimal pairs, in early systems when a Macintosh crashed, one or two lines of hexadecimal code would be displayed under the Sad Mac to tell the user what went wrong. Common Lisp uses the prefixes #x and #16r, setting the variables *read-base* and *print-base* to 16 can also used to switch the reader and printer of a Common Lisp system to Hexadecimal number representation for reading and printing numbers. Thus Hexadecimal numbers can be represented without the #x or #16r prefix code, MSX BASIC, QuickBASIC, FreeBASIC and Visual Basic prefix hexadecimal numbers with &H, &H5A3 BBC BASIC and Locomotive BASIC use & for hex. TI-89 and 92 series uses a 0h prefix, 0h5A3 ALGOL68 uses the prefix 16r to denote hexadecimal numbers, binary, quaternary and octal numbers can be specified similarly
17.
Vigesimal
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The vigesimal or base 20 numeral system is based on twenty. In a vigesimal system, twenty individual numerals are used. One modern method of finding the extra needed symbols is to write ten as the letter A20, to write nineteen as J20, and this is similar to the common computer-science practice of writing hexadecimal numerals over 9 with the letters A–F. Another method skips over the letter I, in order to avoid confusion between I20 as eighteen and one, so that the number eighteen is written as J20, the number twenty is written as 1020. According to this notation,2020 means forty in decimal = + D020 means two hundred and sixty in decimal = +10020 means four hundred in decimal = + +, in the rest of this article below, numbers are expressed in decimal notation, unless specified otherwise. For example,10 means ten,20 means twenty, in decimal, dividing by three twice only gives one digit periods because 9 is the number below ten. 21, however, the adjacent to 20 that is divisible by 3, is not divisible by 9. Ninths in vigesimal have six-digit periods, the prime factorization of twenty is 22 ×5, so it is not a perfect power. However, its part,5, is congruent to 1. Thus, according to Artins conjecture on primitive roots, vigesimal has infinitely many cyclic primes, but the fraction of primes that are cyclic is not necessarily ~37. 395%. An UnrealScript program that computes the lengths of recurring periods of various fractions in a set of bases found that, of the first 15,456 primes. In many European languages,20 is used as a base, vigesimal systems are common in Africa, for example in Yoruba. Ogún,20, is the basic numeric block, ogójì,40, =20 multiplied by 2. Ogota,60, =20 multiplied by 3, ogorin,80, =20 multiplied by 4. Ogorun,100, =20 multiplied by 5, twenty was a base in the Maya and Aztec number systems. The Maya used the names for the powers of twenty, kal, bak, pic, calab, kinchil. See also Maya numerals and Maya calendar, Mayan languages, Yucatec, the Aztec called them, cempoalli, centzontli, cenxiquipilli, cempoalxiquipilli, centzonxiquipilli and cempoaltzonxiquipilli. Note that the ce prefix at the beginning means one and is replaced with the number to get the names of other multiples of the power
18.
Natural number
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In mathematics, the natural numbers are those used for counting and ordering. In common language, words used for counting are cardinal numbers, texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, but in other writings, that term is used instead for the integers. These chains of extensions make the natural numbers canonically embedded in the number systems. Properties of the numbers, such as divisibility and the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partitioning and enumerations, are studied in combinatorics, the most primitive method of representing a natural number is to put down a mark for each object. Later, a set of objects could be tested for equality, excess or shortage, by striking out a mark, the first major advance in abstraction was the use of numerals to represent numbers. This allowed systems to be developed for recording large numbers, the ancient Egyptians developed a powerful system of numerals with distinct hieroglyphs for 1,10, and all the powers of 10 up to over 1 million. A stone carving from Karnak, dating from around 1500 BC and now at the Louvre in Paris, depicts 276 as 2 hundreds,7 tens, and 6 ones, and similarly for the number 4,622. A much later advance was the development of the idea that 0 can be considered as a number, with its own numeral. The use of a 0 digit in place-value notation dates back as early as 700 BC by the Babylonians, the Olmec and Maya civilizations used 0 as a separate number as early as the 1st century BC, but this usage did not spread beyond Mesoamerica. The use of a numeral 0 in modern times originated with the Indian mathematician Brahmagupta in 628, the first systematic study of numbers as abstractions is usually credited to the Greek philosophers Pythagoras and Archimedes. Some Greek mathematicians treated the number 1 differently than larger numbers, independent studies also occurred at around the same time in India, China, and Mesoamerica. In 19th century Europe, there was mathematical and philosophical discussion about the nature of the natural numbers. A school of Naturalism stated that the numbers were a direct consequence of the human psyche. Henri Poincaré was one of its advocates, as was Leopold Kronecker who summarized God made the integers, in opposition to the Naturalists, the constructivists saw a need to improve the logical rigor in the foundations of mathematics. In the 1860s, Hermann Grassmann suggested a recursive definition for natural numbers thus stating they were not really natural, later, two classes of such formal definitions were constructed, later, they were shown to be equivalent in most practical applications. The second class of definitions was introduced by Giuseppe Peano and is now called Peano arithmetic and it is based on an axiomatization of the properties of ordinal numbers, each natural number has a successor and every non-zero natural number has a unique predecessor. Peano arithmetic is equiconsistent with several systems of set theory
19.
Scientific notation
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Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. It is commonly used by scientists, mathematicians and engineers, in part because it can simplify certain arithmetic operations, on scientific calculators it is known as SCI display mode. In scientific notation all numbers are written in the form m × 10n, where the exponent n is an integer, however, the term mantissa may cause confusion because it is the name of the fractional part of the common logarithm. If the number is then a minus sign precedes m. In normalized notation, the exponent is chosen so that the value of the coefficient is at least one. Decimal floating point is an arithmetic system closely related to scientific notation. Any given integer can be written in the form m×10^n in many ways, in normalized scientific notation, the exponent n is chosen so that the absolute value of m remains at least one but less than ten. Thus 350 is written as 3. 5×102 and this form allows easy comparison of numbers, as the exponent n gives the numbers order of magnitude. In normalized notation, the exponent n is negative for a number with absolute value between 0 and 1, the 10 and exponent are often omitted when the exponent is 0. Normalized scientific form is the form of expression of large numbers in many fields, unless an unnormalized form. Normalized scientific notation is often called exponential notation—although the latter term is general and also applies when m is not restricted to the range 1 to 10. Engineering notation differs from normalized scientific notation in that the exponent n is restricted to multiples of 3, consequently, the absolute value of m is in the range 1 ≤ |m| <1000, rather than 1 ≤ |m| <10. Though similar in concept, engineering notation is rarely called scientific notation, engineering notation allows the numbers to explicitly match their corresponding SI prefixes, which facilitates reading and oral communication. A significant figure is a digit in a number that adds to its precision and this includes all nonzero numbers, zeroes between significant digits, and zeroes indicated to be significant. Leading and trailing zeroes are not significant because they exist only to show the scale of the number. Therefore,1,230,400 usually has five significant figures,1,2,3,0, and 4, when a number is converted into normalized scientific notation, it is scaled down to a number between 1 and 10. All of the significant digits remain, but the place holding zeroes are no longer required, thus 1,230,400 would become 1.2304 ×106. However, there is also the possibility that the number may be known to six or more significant figures, thus, an additional advantage of scientific notation is that the number of significant figures is clearer
20.
Metric prefix
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A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit. While all metric prefixes in use today are decadic, historically there have been a number of binary metric prefixes as well. Each prefix has a symbol that is prepended to the unit symbol. The prefix kilo-, for example, may be added to gram to indicate multiplication by one thousand, the prefix milli-, likewise, may be added to metre to indicate division by one thousand, one millimetre is equal to one thousandth of a metre. Decimal multiplicative prefixes have been a feature of all forms of the system with six dating back to the systems introduction in the 1790s. Metric prefixes have even been prepended to non-metric units, the SI prefixes are standardized for use in the International System of Units by the International Bureau of Weights and Measures in resolutions dating from 1960 to 1991. Since 2009, they have formed part of the International System of Quantities, the BIPM specifies twenty prefixes for the International System of Units. Each prefix name has a symbol which is used in combination with the symbols for units of measure. For example, the symbol for kilo- is k, and is used to produce km, kg, and kW, which are the SI symbols for kilometre, kilogram, prefixes corresponding to an integer power of one thousand are generally preferred. Hence 100 m is preferred over 1 hm or 10 dam, the prefixes hecto, deca, deci, and centi are commonly used for everyday purposes, and the centimetre is especially common. However, some building codes require that the millimetre be used in preference to the centimetre, because use of centimetres leads to extensive usage of decimal points. Prefixes may not be used in combination and this also applies to mass, for which the SI base unit already contains a prefix. For example, milligram is used instead of microkilogram, in the arithmetic of measurements having units, the units are treated as multiplicative factors to values. If they have prefixes, all but one of the prefixes must be expanded to their numeric multiplier,1 km2 means one square kilometre, or the area of a square of 1000 m by 1000 m and not 1000 square metres. 2 Mm3 means two cubic megametres, or the volume of two cubes of 1000000 m by 1000000 m by 1000000 m or 2×1018 m3, and not 2000000 cubic metres, examples 5 cm = 5×10−2 m =5 ×0.01 m =0. The prefixes, including those introduced after 1960, are used with any metric unit, metric prefixes may also be used with non-metric units. The choice of prefixes with a unit is usually dictated by convenience of use. Unit prefixes for amounts that are larger or smaller than those actually encountered are seldom used
21.
Crore
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A crore denotes ten million and is equal to 100 lakh in the Indian numbering system. It is widely used in South Asia, and is written in Indian numbering system as 1,00,00,000 with the style of digit group separators. Large amounts of money in India are often written in terms of crores, for example,150,000,000 Indian rupees is written as fifteen crore rupees, ₹15 crore or Rs 15 crore. Trillions of ₹ are often written or spoken of in terms of lakh crore, the crore is known by various regional names. Kapampangan, katâ / kata-katâ Persian, کرور Krur / Korur Tagalog, thai, โกฏิ kot or kot̩i Myriad Names of large numbers Names of numbers in English Chisholm, Hugh, ed. Crore
22.
Roman Empire
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Civil wars and executions continued, culminating in the victory of Octavian, Caesars adopted son, over Mark Antony and Cleopatra at the Battle of Actium in 31 BC and the annexation of Egypt. Octavians power was then unassailable and in 27 BC the Roman Senate formally granted him overarching power, the imperial period of Rome lasted approximately 1,500 years compared to the 500 years of the Republican era. The first two centuries of the empires existence were a period of unprecedented political stability and prosperity known as the Pax Romana, following Octavians victory, the size of the empire was dramatically increased. After the assassination of Caligula in 41, the senate briefly considered restoring the republic, under Claudius, the empire invaded Britannia, its first major expansion since Augustus. Vespasian emerged triumphant in 69, establishing the Flavian dynasty, before being succeeded by his son Titus and his short reign was followed by the long reign of his brother Domitian, who was eventually assassinated. The senate then appointed the first of the Five Good Emperors, the empire reached its greatest extent under Trajan, the second in this line. A period of increasing trouble and decline began with the reign of Commodus, Commodus assassination in 192 triggered the Year of the Five Emperors, of which Septimius Severus emerged victorious. The assassination of Alexander Severus in 235 led to the Crisis of the Third Century in which 26 men were declared emperor by the Roman Senate over a time span. It was not until the reign of Diocletian that the empire was fully stabilized with the introduction of the Tetrarchy, which saw four emperors rule the empire at once. This arrangement was unsuccessful, leading to a civil war that was finally ended by Constantine I. Constantine subsequently shifted the capital to Byzantium, which was renamed Constantinople in his honour and it remained the capital of the east until its demise. Constantine also adopted Christianity which later became the state religion of the empire. However, Augustulus was never recognized by his Eastern colleague, and separate rule in the Western part of the empire ceased to exist upon the death of Julius Nepos. The Eastern Roman Empire endured for another millennium, eventually falling to the Ottoman Turks in 1453, the Roman Empire was among the most powerful economic, cultural, political and military forces in the world of its time. It was one of the largest empires in world history, at its height under Trajan, it covered 5 million square kilometres. It held sway over an estimated 70 million people, at that time 21% of the entire population. Throughout the European medieval period, attempts were made to establish successors to the Roman Empire, including the Empire of Romania, a Crusader state. Rome had begun expanding shortly after the founding of the republic in the 6th century BC, then, it was an empire long before it had an emperor
23.
Stone Age
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The Stone Age was a broad prehistoric period during which stone was widely used to make implements with an edge, a point, or a percussion surface. The period lasted roughly 3.4 million years, and ended between 8700 BCE and 2000 BCE with the advent of metalworking, bone tools were used during this period as well but are rarely preserved in the archaeological record. The Stone Age is further subdivided by the types of tools in use. According to the age and location of the current evidence, the cradle of the genus is the East African Rift System, especially toward the north in Ethiopia, where it is bordered by grasslands. The closest relative among the living primates, the genus Pan, represents a branch that continued on in the deep forest. The rift served as a conduit for movement into southern Africa and also north down the Nile into North Africa and through the continuation of the rift in the Levant to the vast grasslands of Asia. The oldest indirect evidence found of stone tool use is fossilised animal bones with tool marks, the oldest stone tools were excavated from the site of Lomekwi 3 in West Turkana, northwestern Kenya, and date to 3.3 million years old. Prior to the discovery of these Lomekwian tools, the oldest known stone tools had been found at sites at Gona, Ethiopia, on the sediments of the paleo-Awash River. All the tools come from the Busidama Formation, which lies above a disconformity, or missing layer, the oldest sites containing tools are dated to 2. 6–2.55 mya. One of the most striking circumstances about these sites is that they are from the Late Pliocene, excavators at the locality point out that. the earliest stone tool makers were skilled flintknappers. The possible reasons behind this seeming abrupt transition from the absence of tools to the presence thereof include. The species who made the Pliocene tools remains unknown, fragments of Australopithecus garhi, Australopithecus aethiopicus and Homo, possibly Homo habilis, have been found in sites near the age of the Gona tools. Innovation of the technique of smelting ore ended the Stone Age, the first most significant metal manufactured was bronze, an alloy of copper and tin, each of which was smelted separately. The Chalcolithic by convention is the period of the Bronze Age. The Bronze Age was followed by the Iron Age, the transition out of the Stone Age occurred between 6000 BCE and 2500 BCE for much of humanity living in North Africa and Eurasia. Note the Rudna Glava mine in Serbia, Ötzi the Iceman, a mummy from about 3300 BCE carried with him a copper axe and a flint knife. In regions such as Sub-Saharan Africa, the Stone Age was followed directly by the Iron Age, the Middle East and southeastern Asian regions progressed past Stone Age technology around 6000 BCE. Europe, and the rest of Asia became post–Stone Age societies by about 4000 BCE, the proto-Inca cultures of South America continued at a Stone Age level until around 2000 BCE, when gold, copper and silver made their entrance
24.
Middle Paleolithic
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The Middle Paleolithic is the second subdivision of the Paleolithic or Old Stone Age as it is understood in Europe, Africa and Asia. The term Middle Stone Age is used as an equivalent or a synonym for the Middle Paleolithic in African archeology, the Middle Paleolithic broadly spanned from 300,000 to 30,000 years ago. There are considerable dating differences between regions, the Middle Paleolithic was succeeded by the Upper Paleolithic subdivision which first began between 50,000 and 40,000 years ago. Activities such as catching fish and hunting large game animals with specialized tools connote increased group-wide cooperation. Both Neandertal and modern human societies took care of the members of their societies during the Middle Paleolithic. Typically, it has assumed that women gathered plants and firewood. Anthropologists such as Tim D. Cannibalism in the Middle Paleolithic may have occurred because of food shortages, around 200,000 BP Middle Paleolithic Stone tool manufacturing spawned a tool-making technique known as the prepared-core technique, that was more elaborate than previous Acheulean techniques. Wallace and Shea split the core artifacts into two different types, formal cores and expedient cores, formal cores are designed to extract the maximum amount from the raw material while expedient cores are more based on function need. This method increased efficiency by permitting the creation of more controlled and this method allowed Middle Paleolithic humans correspondingly to create stone-tipped spears, which were the earliest composite tools, by hafting sharp, pointy stone flakes onto wooden shafts. The use of fire became widespread for the first time in human prehistory during the Middle Paleolithic, some scientists have hypothesized that hominids began cooking food to defrost frozen meat which would help ensure their survival in cold regions
25.
Australopithecus
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Australopithecus is an extinct genus of hominins. During that time, a number of australopithecine species emerged, including Australopithecus afarensis, A. africanus, A. anamensis, A. bahrelghazali, A. deyiremeda, A. garhi, and A. sediba. For some hominid species of time, such as A. robustus and A. boisei. If so, they would be considered robust australopiths, while the others would be gracile australopiths, however, if these species do constitute their own genus, they may be given their own name, Paranthropus. Australopithecus species played a significant part in human evolution, the genus Homo being derived from Australopithecus at some time after three years ago. Among other things, they were the first hominids to show the presence of a gene that causes increased length and ability of neurons in the brain, the duplicated SRGAP2 gene. One of the species eventually became the Homo genus in Africa around two million years ago, and eventually modern humans, H. sapiens sapiens. Gracile australopiths shared several traits with modern apes and humans, and were widespread throughout Eastern and Northern Africa around 3.5 million years ago, the earliest evidence of fundamentally bipedal hominids can be observed at the site of Laetoli in Tanzania. This site contains hominid footprints that are similar to those of modern humans and have been dated to as old as 3.6 million years. The footprints have generally classified as australopith because that is the only form of prehuman known to have existed in that region at that time. Australopithecus anamensis, A. afarensis, and A. africanus are among the most famous of the extinct hominins, a. africanus was once considered to be ancestral to the genus Homo. However, fossils assigned to the genus Homo have been found that are older than A. africanus, thus, the genus Homo either split off from the genus Australopithecus at an earlier date, or both developed from a yet possibly unknown common ancestor independently. According to the Chimpanzee Genome Project, the human and chimpanzee lineages diverged from a common ancestor about five to six years ago. Sahelanthropus tchadensis, commonly called Toumai, is seven million years old. One theory suggests that the human and chimpanzee lineages diverged somewhat at first, the brains of most species of Australopithecus were roughly 35% of the size of a modern human brain. Most species of Australopithecus were diminutive and gracile, usually standing 1.2 to 1.4 m tall, in several variations is a considerable degree of sexual dimorphism, males being larger than females. According to one scholar, A. Furthermore, thermoregulatory models suggest that Australopithecus species were fully covered, more like chimpanzees and bonobos. Modern humans do not appear to display the same degree of sexual dimorphism as Australopithecus did, in modern populations, males are on average a mere 15% larger than females, while in Australopithecus, males could be up to 50% larger than females
26.
Savanna
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A savanna or savannah is a mixed woodland grassland ecosystem characterised by the trees being sufficiently widely spaced so that the canopy does not close. The open canopy allows sufficient light to reach the ground to support a herbaceous layer consisting primarily of grasses. Savannas maintain an open canopy despite a high tree density and it is often believed that savannas feature widely spaced, scattered trees. However, in savannas, tree densities are higher and trees are more regularly spaced than in forests. Savanna covers approximately 20% of the Earths land area, the word originally entered English in 1555 as the Latin Zauana, equivalent in the orthography of the times to zavana. Peter Martyr reported it as the name for the plain around Comagre. The accounts are inexact, but this is placed in present-day Madugandí or at points on the nearby Guna Yala coast opposite Ustupo or on Point Mosquitos. These areas are now given over to modern cropland or jungle. The common usage meaning to describe vegetation now conflicts with a simplified yet widespread climatic concept meaning, the divergence has sometimes caused areas such as extensive savannas north and south of the Congo and Amazon Rivers to be excluded from mapped savanna categories. Barrens has been used almost interchangeably with savanna in different parts of North America, sometimes midwestern savanna were described as grassland with trees. Different authors have defined the limits of savanna tree coverage as 5–10%. Two factors common to all environments are rainfall variations from year to year. In the Americas, e. g. in Belize, Central America, savanna vegetation is similar from Mexico to South America, savannas are subject to regular wildfires and the ecosystem appears to be the result of human use of fire. For example, Native Americans created the Pre-Columbian savannas of North America by periodically burning where fire-resistant plants were the dominant species, pine barrens in scattered locations from New Jersey to coastal New England are remnants of these savannas. Aboriginal burning appears to have responsible for the widespread occurrence of savanna in tropical Australia and New Guinea. The maquis shrub savannas of the Mediterranean region were created and maintained by anthropogenic fire. These fires are usually confined to the layer and do little long term damage to mature trees. However, these either kill or suppress tree seedlings, thus preventing the establishment of a continuous tree canopy which would prevent further grass growth
27.
Dinosaur
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Dinosaurs are a diverse group of reptiles of the clade Dinosauria that first appeared during the Triassic. Although the exact origin and timing of the evolution of dinosaurs is the subject of active research and they became the dominant terrestrial vertebrates after the Triassic–Jurassic extinction event 201 million years ago. Their dominance continued through the Jurassic and Cretaceous periods and ended when the Cretaceous–Paleogene extinction event led to the extinction of most dinosaur groups 66 million years ago, until the late 20th century, all groups of dinosaurs were believed to be extinct. As such, birds were the dinosaur lineage to survive the mass extinction event. This article deals primarily with non-avian dinosaurs, Dinosaurs are a varied group of animals from taxonomic, morphological and ecological standpoints. Birds, at over 10,000 living species, are the most diverse group of vertebrates besides perciform fish, using fossil evidence, paleontologists have identified over 500 distinct genera and more than 1,000 different species of non-avian dinosaurs. Dinosaurs are represented on every continent by both extant species and fossil remains, while dinosaurs were ancestrally bipedal, many extinct groups included quadrupedal species, and some were able to shift between these stances. Elaborate display structures such as horns or crests are common to all dinosaur groups, evidence suggests that egg laying and nest building are additional traits shared by all dinosaurs.7 meters and heights of 18 meters and were the largest land animals of all time. Still, the idea that dinosaurs were uniformly gigantic is a misconception based in part on preservation bias, as large. Many dinosaurs were small, Xixianykus, for example, was only about 50 cm long. Through the first half of the 20th century, before birds were recognized to be dinosaurs, most of the community believed dinosaurs to have been sluggish. Most research conducted since the 1970s, however, has indicated that all dinosaurs were active animals with elevated metabolisms and numerous adaptations for social interaction. The large sizes of some groups, as well as their seemingly monstrous and fantastic nature, have ensured dinosaurs regular appearance in best-selling books and films. Persistent public enthusiasm for the animals has resulted in significant funding for dinosaur science, the term is derived from the Greek words δεινός and σαῦρος. Though the taxonomic name has often interpreted as a reference to dinosaurs teeth, claws. Instead, dinosaurs, like many forms of reptile sub-groups, did not exhibit characteristics which were traditionally regarded as reptilian. Under phylogenetic nomenclature, dinosaurs are usually defined as the group consisting of Triceratops, Neornithes, their most recent common ancestor, Birds are now recognized as being the sole surviving lineage of theropod dinosaurs. In traditional taxonomy, birds were considered a class that had evolved from dinosaurs
28.
Cretaceous
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The Cretaceous is a geologic period and system that spans 79 million years from the end of the Jurassic Period 145 million years ago to the beginning of the Paleogene Period 66 Mya. It is the last period of the Mesozoic Era, the Cretaceous Period is usually abbreviated K, for its German translation Kreide. The Cretaceous was a period with a warm climate, resulting in high eustatic sea levels that created numerous shallow inland seas. These oceans and seas were populated with now-extinct marine reptiles, ammonites and rudists, during this time, new groups of mammals and birds, as well as flowering plants, appeared. The Cretaceous ended with a mass extinction, the Cretaceous–Paleogene extinction event, in which many groups, including non-avian dinosaurs, pterosaurs. The end of the Cretaceous is defined by the abrupt Cretaceous–Paleogene boundary, the name Cretaceous was derived from Latin creta, meaning chalk. The Cretaceous is divided into Early and Late Cretaceous epochs, or Lower and Upper Cretaceous series, in older literature the Cretaceous is sometimes divided into three series, Neocomian, Gallic and Senonian. A subdivision in eleven stages, all originating from European stratigraphy, is now used worldwide, in many parts of the world, alternative local subdivisions are still in use. As with other geologic periods, the rock beds of the Cretaceous are well identified. No great extinction or burst of diversity separates the Cretaceous from the Jurassic and this layer has been dated at 66.043 Ma. A140 Ma age for the Jurassic-Cretaceous boundary instead of the usually accepted 145 Ma was proposed in 2014 based on a study of Vaca Muerta Formation in Neuquén Basin. Víctor Ramos, one of the authors of the study proposing the 140 Ma boundary age sees the study as a first step toward formally changing the age in the International Union of Geological Sciences, due to the high sea level there was extensive space for such sedimentation. Because of the young age and great thickness of the system. Chalk is a type characteristic for the Cretaceous. It consists of coccoliths, microscopically small calcite skeletons of coccolithophores, the group is found in England, northern France, the low countries, northern Germany, Denmark and in the subsurface of the southern part of the North Sea. Chalk is not easily consolidated and the Chalk Group still consists of sediments in many places. The group also has other limestones and arenites, among the fossils it contains are sea urchins, belemnites, ammonites and sea reptiles such as Mosasaurus. In southern Europe, the Cretaceous is usually a marine system consisting of competent limestone beds or incompetent marls
29.
Gigaannus
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A year is the orbital period of the Earth moving in its orbit around the Sun. Due to the Earths axial tilt, the course of a year sees the passing of the seasons, marked by changes in weather, the hours of daylight, and, consequently, vegetation and soil fertility. In temperate and subpolar regions around the globe, four seasons are recognized, spring, summer, autumn. In tropical and subtropical regions several geographical sectors do not present defined seasons, but in the seasonal tropics, a calendar year is an approximation of the number of days of the Earths orbital period as counted in a given calendar. The Gregorian, or modern, calendar, presents its calendar year to be either a common year of 365 days or a year of 366 days, as do the Julian calendars. For the Gregorian calendar the average length of the year across the complete leap cycle of 400 years is 365.2425 days. The ISO standard ISO 80000-3, Annex C, supports the symbol a to represent a year of either 365 or 366 days, in English, the abbreviations y and yr are commonly used. In astronomy, the Julian year is a unit of time, it is defined as 365.25 days of exactly 86400 seconds, totalling exactly 31557600 seconds in the Julian astronomical year. The word year is used for periods loosely associated with, but not identical to, the calendar or astronomical year, such as the seasonal year, the fiscal year. Similarly, year can mean the period of any planet, for example. The term can also be used in reference to any long period or cycle, west Saxon ġēar, Anglian ġēr continues Proto-Germanic *jǣran. Cognates are German Jahr, Old High German jār, Old Norse ár and Gothic jer, all the descendants of the Proto-Indo-European noun *yeh₁rom year, season. Cognates also descended from the same Proto-Indo-European noun are Avestan yārǝ year, Greek ὥρα year, season, period of time, Old Church Slavonic jarŭ, Latin annus is from a PIE noun *h₂et-no-, which also yielded Gothic aþn year. Both *yeh₁-ro- and *h₂et-no- are based on verbal roots expressing movement, *h₁ey- and *h₂et- respectively, the Greek word for year, ἔτος, is cognate with Latin vetus old, from the PIE word *wetos- year, also preserved in this meaning in Sanskrit vat-sa- yearling and vat-sa-ras year. Derived from Latin annus are a number of English words, such as annual, annuity, anniversary, etc. per annum means each year, anno Domini means in the year of the Lord. No astronomical year has an number of days or lunar months. Financial and scientific calculations often use a 365-day calendar to simplify daily rates, in the Julian calendar, the average length of a year is 365.25 days. In a non-leap year, there are 365 days, in a year there are 366 days
30.
Multicellular organism
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Multicellular organisms are organisms that consist of more than one cell, in contrast to unicellular organisms. Multicellular organisms arise in different ways, for example by cell division or by aggregation of many single cells. Colonial organisms are the result of identical individuals joining together to form a colony. Multicellularity has evolved independently at least 46 times, including in some prokaryotes, like cyanobacteria, myxobacteria, actinomycetes, however, complex multicellular organisms evolved only in six eukaryotic groups, animals, fungi, brown algae, red algae, green algae, and land plants. It evolved repeatedly for Chloroplastida, once or twice for animals, once for brown algae, the first evidence of multicellularity is from cyanobacteria-like organisms that lived 3–3.5 billion years ago. To reproduce, true multicellular organisms must solve the problem of regenerating a whole organism from germ cells, animals have evolved a considerable diversity of cell types in a multicellular body, compared with 10–20 in plants and fungi. Loss of multicellularity occurred in some groups, fungi are predominantly multicellular, though early diverging lineages are largely unicellular and there have been numerous reversions to unicellularity across fungi. It may also have occurred in some red algae, but it is possible that they are primitively unicellular), loss of multicellularity is also considered probable in some green algae. In other groups, generally parasites, a reduction of multicellularity occurred, multicellular organisms, especially long-living animals, face the challenge of cancer, which occurs when cells fail to regulate their growth within the normal program of development. Changes in tissue morphology can be observed during this process, cancer in animals has often been described as a loss of multicellularity. There is a discussion about the possibility of existence of cancer in other organisms or even in protozoa. For example, plant galls have been characterized as tumors but some argue that plants do not develop cancer. In some multicellular groups, which are called Weismannists, a separation between a sterile somatic cell line and a cell line evolved. However, Weismannist development is relatively rare, as part of species have the capacity for somatic embryogenesis. One hypothesis for the origin of multicellularity is that a group of function-specific cells aggregated into a mass called a grex. This is essentially what slime molds do, another hypothesis is that a primitive cell underwent nucleus division, thereby becoming a coenocyte. A membrane would then form around each nucleus, thereby resulting in a group of connected cells in one organism and this is what plant and animal embryos do as well as colonial choanoflagellates. Because the first multicellular organisms were simple, soft organisms lacking bone, shell or other body parts
31.
Eukaryote
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A eukaryote is any organism whose cells contain a nucleus and other organelles enclosed within membranes. Eukaryotes belong to the taxon Eukarya or Eukaryota, the presence of a nucleus gives eukaryotes their name, which comes from the Greek εὖ and κάρυον. Eukaryotic cells also contain other membrane-bound organelles such as mitochondria and the Golgi apparatus, in addition, plants and algae contain chloroplasts. Eukaryotic organisms may be unicellular or multicellular, only eukaryotes form multicellular organisms consisting of many kinds of tissue made up of different cell types. Eukaryotes can reproduce asexually through mitosis and sexually through meiosis and gamete fusion. In mitosis, one cell divides to produce two identical cells. In meiosis, DNA replication is followed by two rounds of division to produce four daughter cells each with half the number of chromosomes as the original parent cell. These act as sex cells resulting from genetic recombination during meiosis, the domain Eukaryota appears to be monophyletic, and so makes up one of the three domains of life. The two other domains, Bacteria and Archaea, are prokaryotes and have none of the above features, eukaryotes represent a tiny minority of all living things. However, due to their larger size, eukaryotes collective worldwide biomass is estimated at about equal to that of prokaryotes. Eukaryotes first developed approximately 1. 6–2.1 billion years ago, in 1905 and 1910, the Russian biologist Konstantin Mereschkowsky argued three things about the origin of nucleated cells. Firstly, plastids were reduced cyanobacteria in a symbiosis with a non-photosynthetic host, secondly, the host had earlier in evolution formed by symbiosis between an amoeba-like host and a bacteria-like cell that formed the nucleus. Thirdly, plants inherited photosynthesis from cyanobacteria, the split between the prokaryotes and eukaryotes was introduced in the 1960s. The concept of the eukaryote has been attributed to the French biologist Edouard Chatton, the terms prokaryote and eukaryote were more definitively reintroduced by the Canadian microbiologist Roger Stanier and the Dutch-American microbiologist C. B. van Niel in 1962. In his 1938 work Titres et Travaux Scientifiques, Chatton had proposed the two terms, calling the bacteria prokaryotes and organisms with nuclei in their cells eukaryotes. However he mentioned this in one paragraph, and the idea was effectively ignored until Chattons statement was rediscovered by Stanier. In 1967, Lynn Margulis provided microbiological evidence for endosymbiosis as the origin of chloroplasts and mitochondria in cells in her paper. In the 1970s, Carl Woese explored microbial phylogenetics, studying variations in 16S ribosomal RNA and this helped to uncover the origin of the eukaryotes and the symbiogenesis of two important eukaryote organelles, mitochondria and chloroplasts
32.
Galaxy
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A galaxy is a gravitationally bound system of stars, stellar remnants, interstellar gas, dust, and dark matter. The word galaxy is derived from the Greek galaxias, literally milky, Galaxies range in size from dwarfs with just a few billion stars to giants with one hundred trillion stars, each orbiting its galaxys center of mass. Galaxies are categorized according to their morphology as elliptical, spiral. Many galaxies are thought to have holes at their active centers. The Milky Ways central black hole, known as Sagittarius A*, has a four million times greater than the Sun. Recent estimates of the number of galaxies in the observable universe range from 200 billion to 2 trillion or more, most of the galaxies are 1,000 to 100,000 parsecs in diameter and separated by distances on the order of millions of parsecs. The space between galaxies is filled with a gas having an average density of less than one atom per cubic meter. The majority of galaxies are organized into groups, clusters. At the largest scale, these associations are generally arranged into sheets and filaments surrounded by immense voids. In Greek mythology, Zeus places his son born by a mortal woman, the infant Heracles, on Heras breast while she is asleep so that the baby will drink her divine milk and will thus become immortal. Hera wakes up while breastfeeding and then realizes she is nursing a baby, she pushes the baby away, some of her milk spills and. In the astronomical literature, the capitalized word Galaxy is often used to refer to our galaxy, the Milky Way, to distinguish it from the other galaxies in our universe. The English term Milky Way can be traced back to a story by Chaucer c. 1380, See yonder, lo, the Galaxyë Which men clepeth the Milky Wey, For hit is whyt. However, the word Universe was later understood to mean the entirety of existence, so this expression fell into disuse and the objects instead became known as galaxies. Tens of thousands of galaxies have been catalogued, but only a few have well-established names, such as the Andromeda Galaxy, the Magellanic Clouds, the Whirlpool Galaxy, and the Sombrero Galaxy. Astronomers work with numbers from certain catalogues, such as the Messier catalogue, the NGC, the IC, the CGCG, all of the well-known galaxies appear in one or more of these catalogues but each time under a different number. For example, Messier 109 is a galaxy having the number 109 in the catalogue of Messier, but also codes NGC3992, UGC6937, CGCG 269-023, MCG +09-20-044. One of the arguments to do so is that these impressive objects deserve better than uninspired codes, for instance, Bodifee and Berger propose the informal, descriptive name Callimorphus Ursae Majoris for the well-formed barred galaxy Messier 109 in Ursa Major
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Universe
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The Universe is all of time and space and its contents. It includes planets, moons, minor planets, stars, galaxies, the contents of intergalactic space, the size of the entire Universe is unknown. The earliest scientific models of the Universe were developed by ancient Greek and Indian philosophers and were geocentric, over the centuries, more precise astronomical observations led Nicolaus Copernicus to develop the heliocentric model with the Sun at the center of the Solar System. In developing the law of gravitation, Sir Isaac Newton built upon Copernicuss work as well as observations by Tycho Brahe. Further observational improvements led to the realization that our Solar System is located in the Milky Way galaxy and it is assumed that galaxies are distributed uniformly and the same in all directions, meaning that the Universe has neither an edge nor a center. Discoveries in the early 20th century have suggested that the Universe had a beginning, the majority of mass in the Universe appears to exist in an unknown form called dark matter. The Big Bang theory is the prevailing cosmological description of the development of the Universe, under this theory, space and time emerged together 13. 799±0.021 billion years ago with a fixed amount of energy and matter that has become less dense as the Universe has expanded. After the initial expansion, the Universe cooled, allowing the first subatomic particles to form, giant clouds later merged through gravity to form galaxies, stars, and everything else seen today. Some physicists have suggested various multiverse hypotheses, in which the Universe might be one among many universes that likewise exist, the Universe can be defined as everything that exists, everything that has existed, and everything that will exist. According to our current understanding, the Universe consists of spacetime, forms of energy, the Universe encompasses all of life, all of history, and some philosophers and scientists suggest that it even encompasses ideas such as mathematics and logic. The word universe derives from the Old French word univers, which in turn derives from the Latin word universum, the Latin word was used by Cicero and later Latin authors in many of the same senses as the modern English word is used. Another synonym was ὁ κόσμος ho kósmos, synonyms are also found in Latin authors and survive in modern languages, e. g. the German words Das All, Weltall, and Natur for Universe. The same synonyms are found in English, such as everything, the cosmos, the world, the prevailing model for the evolution of the Universe is the Big Bang theory. The Big Bang model states that the earliest state of the Universe was extremely hot and dense, the model is based on general relativity and on simplifying assumptions such as homogeneity and isotropy of space. The Big Bang model accounts for such as the correlation of distance and redshift of galaxies, the ratio of the number of hydrogen to helium atoms. The initial hot, dense state is called the Planck epoch, after the Planck epoch and inflation came the quark, hadron, and lepton epochs. Together, these epochs encompassed less than 10 seconds of time following the Big Bang, the observed abundance of the elements can be explained by combining the overall expansion of space with nuclear and atomic physics. As the Universe expands, the density of electromagnetic radiation decreases more quickly than does that of matter because the energy of a photon decreases with its wavelength
34.
Metre
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The metre or meter, is the base unit of length in the International System of Units. The metre is defined as the length of the path travelled by light in a vacuum in 1/299792458 seconds, the metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole. In 1799, it was redefined in terms of a metre bar. In 1960, the metre was redefined in terms of a number of wavelengths of a certain emission line of krypton-86. In 1983, the current definition was adopted, the imperial inch is defined as 0.0254 metres. One metre is about 3 3⁄8 inches longer than a yard, Metre is the standard spelling of the metric unit for length in nearly all English-speaking nations except the United States and the Philippines, which use meter. Measuring devices are spelled -meter in all variants of English, the suffix -meter has the same Greek origin as the unit of length. This range of uses is found in Latin, French, English. Thus calls for measurement and moderation. In 1668 the English cleric and philosopher John Wilkins proposed in an essay a decimal-based unit of length, as a result of the French Revolution, the French Academy of Sciences charged a commission with determining a single scale for all measures. In 1668, Wilkins proposed using Christopher Wrens suggestion of defining the metre using a pendulum with a length which produced a half-period of one second, christiaan Huygens had observed that length to be 38 Rijnland inches or 39.26 English inches. This is the equivalent of what is now known to be 997 mm, no official action was taken regarding this suggestion. In the 18th century, there were two approaches to the definition of the unit of length. One favoured Wilkins approach, to define the metre in terms of the length of a pendulum which produced a half-period of one second. The other approach was to define the metre as one ten-millionth of the length of a quadrant along the Earths meridian, that is, the distance from the Equator to the North Pole. This means that the quadrant would have defined as exactly 10000000 metres at that time. To establish a universally accepted foundation for the definition of the metre, more measurements of this meridian were needed. This portion of the meridian, assumed to be the length as the Paris meridian, was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator
