1.
Roman numerals
–
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
2.
Gottfried Wilhelm Leibniz
–
Leibnizs notation has been widely used ever since it was published. It was only in the 20th century that his Law of Continuity and he became one of the most prolific inventors in the field of mechanical calculators. He also refined the number system, which is the foundation of virtually all digital computers. Leibniz, along with René Descartes and Baruch Spinoza, was one of the three great 17th-century advocates of rationalism and he wrote works on philosophy, politics, law, ethics, theology, history, and philology. Leibnizs contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters and he wrote in several languages, but primarily in Latin, French, and German. There is no complete gathering of the writings of Leibniz in English, Gottfried Leibniz was born on July 1,1646, toward the end of the Thirty Years War, in Leipzig, Saxony, to Friedrich Leibniz and Catharina Schmuck. Friedrich noted in his journal,21. Juny am Sontag 1646 Ist mein Sohn Gottfried Wilhelm, post sextam vespertinam 1/4 uff 7 uhr abents zur welt gebohren, in English, On Sunday 21 June 1646, my son Gottfried Wilhelm is born into the world a quarter after six in the evening, in Aquarius. Leibniz was baptized on July 3 of that year at St. Nicholas Church, Leipzig and his father died when he was six and a half years old, and from that point on he was raised by his mother. Her teachings influenced Leibnizs philosophical thoughts in his later life, Leibnizs father had been a Professor of Moral Philosophy at the University of Leipzig, and the boy later inherited his fathers personal library. He was given access to it from the age of seven. Access to his fathers library, largely written in Latin, also led to his proficiency in the Latin language and he also composed 300 hexameters of Latin verse, in a single morning, for a special event at school at the age of 13. In April 1661 he enrolled in his fathers former university at age 15 and he defended his Disputatio Metaphysica de Principio Individui, which addressed the principle of individuation, on June 9,1663. Leibniz earned his masters degree in Philosophy on February 7,1664, after one year of legal studies, he was awarded his bachelors degree in Law on September 28,1665. His dissertation was titled De conditionibus, in early 1666, at age 19, Leibniz wrote his first book, De Arte Combinatoria, the first part of which was also his habilitation thesis in Philosophy, which he defended in March 1666. His next goal was to earn his license and Doctorate in Law, in 1666, the University of Leipzig turned down Leibnizs doctoral application and refused to grant him a Doctorate in Law, most likely due to his relative youth. Leibniz then enrolled in the University of Altdorf and quickly submitted a thesis, the title of his thesis was Disputatio Inauguralis de Casibus Perplexis in Jure. Leibniz earned his license to practice law and his Doctorate in Law in November 1666 and he next declined the offer of an academic appointment at Altdorf, saying that my thoughts were turned in an entirely different direction
3.
Computer science
–
Computer science is the study of the theory, experimentation, and engineering that form the basis for the design and use of computers. An alternate, more succinct definition of science is the study of automating algorithmic processes that scale. A computer scientist specializes in the theory of computation and the design of computational systems and its fields can be divided into a variety of theoretical and practical disciplines. Some fields, such as computational complexity theory, are highly abstract, other fields still focus on challenges in implementing computation. Human–computer interaction considers the challenges in making computers and computations useful, usable, the earliest foundations of what would become computer science predate the invention of the modern digital computer. Machines for calculating fixed numerical tasks such as the abacus have existed since antiquity, further, algorithms for performing computations have existed since antiquity, even before the development of sophisticated computing equipment. Wilhelm Schickard designed and constructed the first working mechanical calculator in 1623, in 1673, Gottfried Leibniz demonstrated a digital mechanical calculator, called the Stepped Reckoner. He may be considered the first computer scientist and information theorist, for, among other reasons and he started developing this machine in 1834, and in less than two years, he had sketched out many of the salient features of the modern computer. A crucial step was the adoption of a card system derived from the Jacquard loom making it infinitely programmable. Around 1885, Herman Hollerith invented the tabulator, which used punched cards to process statistical information, when the machine was finished, some hailed it as Babbages dream come true. During the 1940s, as new and more powerful computing machines were developed, as it became clear that computers could be used for more than just mathematical calculations, the field of computer science broadened to study computation in general. Computer science began to be established as an academic discipline in the 1950s. The worlds first computer science program, the Cambridge Diploma in Computer Science. The first computer science program in the United States was formed at Purdue University in 1962. Since practical computers became available, many applications of computing have become distinct areas of study in their own rights and it is the now well-known IBM brand that formed part of the computer science revolution during this time. IBM released the IBM704 and later the IBM709 computers, still, working with the IBM was frustrating if you had misplaced as much as one letter in one instruction, the program would crash, and you would have to start the whole process over again. During the late 1950s, the science discipline was very much in its developmental stages. Time has seen significant improvements in the usability and effectiveness of computing technology, modern society has seen a significant shift in the users of computer technology, from usage only by experts and professionals, to a near-ubiquitous user base
4.
Display resolution
–
The display resolution or display modes of a digital television, computer monitor or display device is the number of distinct pixels in each dimension that can be displayed. It is usually quoted as width × height, with the units in pixels, for example,1024 ×768 means the width is 1024 pixels and this example would normally be spoken as ten twenty-four by seven sixty-eight or ten twenty-four by seven six eight. A consequence of having a display is that, for multi-format video inputs. Note that for broadcast television standards the use of the word here is a misnomer. In digital measurement, the resolution would be given in pixels per inch. In analog measurement, if the screen is 10 inches high, in the case of television inputs, many manufacturers will take the input and zoom it out to overscan the display by as much as 5% so input resolution is not necessarily display resolution. The eyes perception of display resolution can be affected by a number of factors – see image resolution, one factor is the display screens rectangular shape, which is expressed as the ratio of the physical picture width to the physical picture height. This is known as the aspect ratio, a screens physical aspect ratio and the individual pixels aspect ratio may not necessarily be the same. An array of 1280 ×720 on a 16,9 display has square pixels, an example of pixel shape affecting resolution or perceived sharpness, displaying more information in a smaller area using a higher resolution makes the image much clearer or sharper. Most television display manufacturers overscan the pictures on their displays, so that the effective on-screen picture may be reduced from 720 ×576 to 680 ×550, the size of the invisible area somewhat depends on the display device. HD televisions do this as well, to a similar extent, Computer displays including projectors generally do not overscan although many models allow it. CRT displays tend to be underscanned in stock configurations, to compensate for the distortions at the corners. As of July 2002,1024 ×768 eXtended Graphics Array was the most common display resolution, many web sites and multimedia products were re-designed from the previous 800 ×600 format to the layouts optimized for 1024 ×768. The availability of inexpensive LCD monitors has made the 5,4 aspect ratio resolution of 1280 ×1024 more popular for desktop usage during the first decade of the 21st century. Many computer users including CAD users, graphic artists and video game players ran their computers at 1600 ×1200 resolution or higher such as 2048 ×1536 QXGA if they had the necessary equipment. A new more-than-HD resolution of 2560 ×1600 WQXGA was released in 30-inch LCD monitors in 2007, as of March 2012,1366 ×768 was the most common display resolution. In 2010, 27-inch LCD monitors with the 2560 × 1440-pixel resolution were released by manufacturers including Apple. Panels for professional environments, such as use and air traffic control
5.
Binary number
–
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
6.
Senary
–
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
