1.
Decimal
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This article aims to be an accessible introduction. For the mathematical definition, see Decimal representation, the decimal numeral system has ten as its base, which, in decimal, is written 10, as is the base in every positional numeral system. It is the base most widely used by modern civilizations. Decimal fractions have terminating decimal representations and other fractions have repeating decimal representations, Decimal notation is the writing of numbers in a base-ten numeral system. Examples are Brahmi numerals, Greek numerals, Hebrew numerals, Roman numerals, Roman numerals have symbols for the decimal powers and secondary symbols for half these values. Brahmi numerals have symbols for the nine numbers 1–9, the nine decades 10–90, plus a symbol for 100, Chinese numerals have symbols for 1–9, and additional symbols for powers of ten, which in modern usage reach 1072. Positional decimal systems include a zero and use symbols for the ten values to represent any number, positional notation uses positions for each power of ten, units, tens, hundreds, thousands, etc. The position of each digit within a number denotes the multiplier multiplied with that position has a value ten times that of the position to its right. There were at least two independent sources of positional decimal systems in ancient civilization, the Chinese counting rod system. Ten is the number which is the count of fingers and thumbs on both hands, the English word digit as well as its translation in many languages is also the anatomical term for fingers and toes. In English, decimal means tenth, decimate means reduce by a tenth, however, the symbols used in different areas are not identical, for instance, Western Arabic numerals differ from the forms used by other Arab cultures. A decimal fraction is a fraction the denominator of which is a power of ten. g, Decimal fractions 8/10, 1489/100, 24/100000, and 58900/10000 are expressed in decimal notation as 0.8,14.89,0.00024,5.8900 respectively. In English-speaking, some Latin American and many Asian countries, a period or raised period is used as the separator, in many other countries, particularly in Europe. The integer part, or integral part of a number is the part to the left of the decimal separator. The part from the separator to the right is the fractional part. It is usual for a number that consists only of a fractional part to have a leading zero in its notation. Any rational number with a denominator whose only prime factors are 2 and/or 5 may be expressed as a decimal fraction and has a finite decimal expansion. 1/2 =0.5 1/20 =0.05 1/5 =0.2 1/50 =0.02 1/4 =0.25 1/40 =0.025 1/25 =0.04 1/8 =0.125 1/125 =0.008 1/10 =0
2.
Letter case
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Letter case is the distinction between the letters that are in larger upper case and smaller lower case in the written representation of certain languages. The writing systems that distinguish between the upper and lower case have two sets of letters, with each letter in one set usually having an equivalent in the other set. Basically, the two variants are alternative representations of the same letter, they have the same name and pronunciation. Letter case is generally applied in a fashion, with both upper- and lower-case letters appearing in a given piece of text. The choice of case is often prescribed by the grammar of a language or by the conventions of a particular discipline, in mathematics, letter case may indicate the relationship between objects, with upper-case letters often representing superior objects. In some contexts, it is conventional to use only one case, the terms upper case and lower case can be written as two consecutive words, connected with a hyphen, or as a single word. These terms originated from the layouts of the shallow drawers called type cases used to hold the movable type for letterpress printing. Traditionally, the letters were stored in a separate case that was located above the case that held the small letters. Majuscule, for palaeographers, is technically any script in which the letters have very few or very short ascenders and descenders, or none at all. By virtue of their impact, this made the term majuscule an apt descriptor for what much later came to be more commonly referred to as uppercase letters. The word is often spelled miniscule, by association with the word miniature. This has traditionally been regarded as a mistake, but is now so common that some dictionaries tend to accept it as a nonstandard or variant spelling. Miniscule is still less likely, however, to be used in reference to lower-case letters, the glyphs of lower-case letters can resemble smaller forms of the upper-case glyphs restricted to the base band or can look hardly related. There is more variation in the height of the minuscules, as some of them have higher or lower than the typical size. In Times New Roman, for instance, b, d, f, h, k, l, t are the letters with ascenders, and g, j, p, q, y are the ones with descenders. In addition, with old-style numerals still used by traditional or classical fonts,6 and 8 make up the ascender set. Writing systems using two separate cases are bicameral scripts, languages that use the Latin, Cyrillic, Greek, Coptic, Armenian, Adlam, Varang Kshiti, Cherokee, and Osage scripts use letter cases in their written form as an aid to clarity. Other bicameral scripts, which are not used for any modern languages, are Old Hungarian, Glagolitic, the Georgian alphabet has several variants, and there were attempts to use them as different cases, but the modern written Georgian language does not distinguish case
3.
Gottfried Wilhelm Leibniz
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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
4.
Hexagram
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A hexagram or sexagram is a six-pointed geometric star figure with the Schläfli symbol,2, or. It is the compound of two equilateral triangles, the intersection is a regular hexagon. It is used in historical, religious and cultural contexts, for example in Hanafism, Jewish identity, in mathematics, the root system for the simple Lie group G2 is in the form of a hexagram, with six long roots and six short roots. A six-pointed star, like a hexagon, can be created using a compass. Without changing the radius of the compass, set its pivot on the circles circumference, with the pivot on the last point found, similarly find a third point on the circumference, and repeat until six such points have been marked. With a straight edge, join alternate points on the circumference to form two overlapping equilateral triangles. It is possible that as a geometric shape, like for example the triangle, circle, or square. The hexagram is a symbol called satkona yantra or sadkona yantra found on ancient South Indian Hindu temples. It symbolizes the nara-narayana, or perfect meditative state of balance achieved between Man and God, and if maintained, results in moksha, or nirvana, some researchers have theorized that the hexagram represents the astrological chart at the time of Davids birth or anointment as king. The hexagram is also known as the Kings Star in astrological circles, in antique papyri, pentagrams, together with stars and other signs, are frequently found on amulets bearing the Jewish names of God, and used to guard against fever and other diseases. Curiously the hexagram is not found among these signs, in the Greek Magical Papyri at Paris and London there are 22 signs side by side, and a circle with twelve signs, but neither a pentagram nor a hexagram. Six-pointed stars have also found in cosmological diagrams in Hinduism, Buddhism. The reasons behind this symbols common appearance in Indic religions and the West are unknown, one possibility is that they have a common origin. The other possibility is that artists and religious people from several cultures independently created the hexagram shape, within Indic lore, the shape is generally understood to consist of two triangles—one pointed up and the other down—locked in harmonious embrace. The two components are called Om and the Hrim in Sanskrit, and symbolize mans position between earth and sky, the downward triangle symbolizes Shakti, the sacred embodiment of femininity, and the upward triangle symbolizes Shiva, or Agni Tattva, representing the focused aspects of masculinity. The mystical union of the two triangles represents Creation, occurring through the union of male and female. The two locked triangles are known as Shanmukha—the six-faced, representing the six faces of Shiva & Shaktis progeny Kartikeya. This symbol is also a part of several yantras and has significance in Hindu ritual worship
5.
Mathematics
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Mathematics is the study of topics such as quantity, structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof, when mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry, rigorous arguments first appeared in Greek mathematics, most notably in Euclids Elements. Galileo Galilei said, The universe cannot be read until we have learned the language and it is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth, carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. Benjamin Peirce called mathematics the science that draws necessary conclusions, David Hilbert said of mathematics, We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein stated that as far as the laws of mathematics refer to reality, they are not certain, Mathematics is essential in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, the history of mathematics can be seen as an ever-increasing series of abstractions. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns, in Babylonian mathematics elementary arithmetic first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have many and diverse. Between 600 and 300 BC the Ancient Greeks began a study of mathematics in its own right with Greek mathematics. Mathematics has since been extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. The word máthēma is derived from μανθάνω, while the modern Greek equivalent is μαθαίνω, in Greece, the word for mathematics came to have the narrower and more technical meaning mathematical study even in Classical times
6.
Slit drum
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A slit drum is a hollow percussion instrument. In spite of the name, it is not a drum but an idiophone. Most slit drums have one slit, though two and three slits occur, if the resultant tongues are different width or thicknesses, the drum will produce two different pitches. It is used throughout Africa, Southeast Asia, and Oceania, in Africa such drums, strategically situated for optimal acoustic transmission, have been used for long-distance communication. The ends of a drum are closed so that the shell becomes the resonating chamber for the sound vibrations created when the tongues are struck. The resonating chamber increases the volume of the produced by the tongue. The people of Vanuatu cut a log with totem type carvings on the outer surface. This hollowed out log gives the deep resonance of drums when hit on the outside with sticks, planet Drum, A Celebration of Percussion and Rhythm. ISBN9780062504142, ISBN9780062503978, ISBN9780062504623
7.
George Boole
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George Boole was an English mathematician, educator, philosopher and logician. He worked in the fields of differential equations and algebraic logic, Boolean logic is credited with laying the foundations for the information age. Boole was born in Lincoln, Lincolnshire, England, the son of John Boole Sr and he had a primary school education, and received lessons from his father, but had little further formal and academic teaching. William Brooke, a bookseller in Lincoln, may have helped him with Latin and he was self-taught in modern languages. At age 16 Boole became the breadwinner for his parents and three siblings, taking up a junior teaching position in Doncaster at Heighams School. Boole participated in the Mechanics Institute, in the Greyfriars, Lincoln, without a teacher, it took him many years to master calculus. At age 19, Boole successfully established his own school in Lincoln, four years later he took over Halls Academy in Waddington, outside Lincoln, following the death of Robert Hall. In 1840 he moved back to Lincoln, where he ran a boarding school, Boole became a prominent local figure, an admirer of John Kaye, the bishop. He took part in the campaign for early closing. With E. R. Larken and others he set up a society in 1847. He associated also with the Chartist Thomas Cooper, whose wife was a relation, from 1838 onwards Boole was making contacts with sympathetic British academic mathematicians and reading more widely. He studied algebra in the form of symbolic methods, as far as these were understood at the time, Booles status as mathematician was recognised by his appointment in 1849 as the first professor of mathematics at Queens College, Cork in Ireland. He met his wife, Mary Everest, there in 1850 while she was visiting her uncle John Ryall who was Professor of Greek. They married some years later in 1855 and he maintained his ties with Lincoln, working there with E. R. Larken in a campaign to reduce prostitution. Boole was awarded the Keith Medal by the Royal Society of Edinburgh in 1855 and was elected a Fellow of the Royal Society in 1857 and he received honorary degrees of LL. D. from the University of Dublin and the University of Oxford. In late November 1864, Boole walked, in rain, from his home at Lichfield Cottage in Ballintemple to the university. He soon became ill, developing a cold and high fever. As his wife believed that remedies should resemble their cause, she put her husband to bed and poured buckets of water over him – the wet having brought on his illness, Booles condition worsened and on 8 December 1864, he died of fever-induced pleural effusion
8.
Mangareva
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Mangareva is the central and largest island of the Gambier Islands in French Polynesia. It is surrounded by islands, Taravai in the southwest, Aukena and Akamaru in the southeast. Mangareva has a permanent population of 1,239 and the largest village on the island, the island is approximately 8 km long and, at 15.4 km², it comprises about 56% of the land area of the whole Gambier group. Mangareva has a central ridge which runs the length of the island. The highest point in the Gambiers is Mt. Duff, on Mangareva, the island has a large lagoon 24 km in diameter containing reefs whose fish and shellfish helped ancient islanders survive much more successfully than on nearby islands with no reefs. Mangareva was once forested and supported a large population that traded with other islands via canoes. However, excessive logging by the islanders during the 10th to the 15th centuries resulted in deforestation of the island, with results for its environment. The first European to arrive at Mangareva was British Captain James Wilson in 1797 on the ship Duff, Wilson named the island group in honour of Admiral James Gambier, who had helped him to equip his vessel. Mangareva along with its dependencies in the Gambier Islands were ruled by a line of kings, a French protectorate was requested on 16 February 1844 by King Maputeoa but was never ratified by the French government. On 4 February 1870, Prince Regent Arone Teikatoara and the Mangarevan government formally withdrew the protectorate request, the Gambier Islands were finally annexed on 21 February 1881 under Prince Regent Bernardo Putairi and approved by the President of France on 30 January 1882. Mangarevas history and its ancient links with the Pitcairn and Henderson islands is well-covered in Jared Diamonds book, Collapse, Mangareva is reached by boat from the nearby airport across the lagoon. Mangareva is an important travel link to Pitcairn Island, practically the only way a traveler can reach Pitcairn Island is to fly to Tahiti, then to Mangareva. From there, a 32-hour boat ride will take the traveler to the island, some reach Pitcairn by commercial shipping traffic, but that is less and less common as shipping lanes do not typically pass close to Pitcairn. Painter and author Robert Lee Eskridges book Manga Reva, The Forgotten Islands offers first-hand observations of the environment, peoples and it includes original illustrations and photographs by the author. In 1962, adventure-fiction writer Garland Roark acknowledged Eskridges work in a foreword to his novel The Witch of Manga Reva, eskridge also wrote and illustrated a childrens book about his visit to Mangareva, South Sea Playmates. The Mangarevan people had developed a number system 300 years ahead of Europeans. The discovery of the system being used as far back as 1450 CE is particularly surprising. This old way of common numbering has been all but lost, because the islands were controlled by the French for such a long period, the Arabic number system with which the West is most familiar has taken its place
9.
French Polynesia
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It is composed of 118 geographically dispersed islands and atolls stretching over an expanse of more than 2,000 kilometres in the South Pacific Ocean. Its total land area is 4,167 square kilometres, among its 118 islands and atolls,67 are inhabited. Tahiti, which is located within the Society Islands, is the most populous island and it has more than 68% of the population of the islands in 2012. Although not a part of its territory, Clipperton Island was administered from French Polynesia until 2007. Following the Great Polynesian Migration, European explorers visited the islands of French Polynesia on several occasions, traders and whaling ships also visited. In 1842, the French took over the islands and established a French protectorate they called Etablissements des français en Océanie, in 1946, the EFOs became an overseas territory under the constitution of the French Fourth Republic, and Polynesians were granted the right to vote through citizenship. In 1957, the EFOs were renamed French Polynesia, French Polynesia as we know it today was one of the last places on Earth to be settled by humans. Scientists believe the Great Polynesian Migration happened around 1500 BC as Austronesian people went on a journey using celestial navigation to find islands in the South Pacific Ocean, the first islands of French Polynesia to be settled were the Marquesas Islands in about 200 BC. The Polynesians later ventured southwest and discovered the Society Islands around AD300, European encounters began in 1521 when Portuguese explorer Ferdinand Magellan, sailing at the service of the Spanish Crown, sighted Puka-Puka in the Tuāmotu-Gambier Archipelago. Over a century later, British explorer Samuel Wallis visited Tahiti in 1767, French explorer Louis Antoine de Bougainville also visited Tahiti in 1768, while British explorer James Cook arrived in 1769. A short-lived Spanish settlement was created in 1774, and for a time some maps bore the name Isla de Amat after Viceroy Amat, in 1772, Dutchman Jakob Roggeveen came across Bora Bora in the Society Islands. Christian missions began with Spanish priests who stayed in Tahiti for a year, protestants from the London Missionary Society settled permanently in Polynesia in 1797. King Pōmare II of Tahiti was forced to flee to Moorea in 1803, he, French Catholic missionaries arrived on Tahiti in 1834, their expulsion in 1836 caused France to send a gunboat in 1838. In 1842, Tahiti and Tahuata were declared a French protectorate, the capital of Papeetē was founded in 1843. In 1880, France annexed Tahiti, changing the status from that of a protectorate to that of a colony, the island groups were not officially united until the establishment of the French protectorate in 1889. In the 1880s, France claimed the Tuamotu Archipelago, which belonged to the Pōmare Dynasty. Having declared a protectorate over Tahuata in 1842, the French regarded the entire Marquesas Islands as French, in 1885, France appointed a governor and established a general council, thus giving it the proper administration for a colony. The islands of Rimatara and Rūrutu unsuccessfully lobbied for British protection in 1888, postage stamps were first issued in the colony in 1892
10.
Francis Bacon
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Francis Bacon, 1st Viscount St Alban, PC KC was an English philosopher, statesman, scientist, jurist, orator, and author. He served both as Attorney General and as Lord Chancellor of England, after his death, he remained extremely influential through his works, especially as philosophical advocate and practitioner of the scientific method during the scientific revolution. Bacon has been called the father of empiricism and his works argued for the possibility of scientific knowledge based only upon inductive reasoning and careful observation of events in nature. Most importantly, he argued this could be achieved by use of a sceptical and methodical approach whereby scientists aim to avoid misleading themselves. This marked a new turn in the rhetorical and theoretical framework for science, Bacon was generally neglected at court by Queen Elizabeth, but after the accession of King James I in 1603, Bacon was knighted. He was later created Baron Verulam in 1618 and Viscount St. Alban in 1621, because he had no heirs, both titles became extinct upon his death in 1626, at 65 years of age. Bacon died of pneumonia, with one account by John Aubrey stating that he had contracted the condition while studying the effects of freezing on the preservation of meat. Francis Bacon was born on 22 January 1561 at York House near the Strand in London, the son of Sir Nicholas Bacon by his wife, Anne Bacon. His mothers sister was married to William Cecil, 1st Baron Burghley, biographers believe that Bacon was educated at home in his early years owing to poor health, which would plague him throughout his life. He received tuition from John Walsall, a graduate of Oxford with a leaning toward Puritanism. Bacons education was conducted largely in Latin and followed the medieval curriculum and he was also educated at the University of Poitiers. It was at Cambridge that he first met Queen Elizabeth, who was impressed by his precocious intellect and his studies brought him to the belief that the methods and results of science as then practised were erroneous. His reverence for Aristotle conflicted with his rejection of Aristotelian philosophy, on 27 June 1576, he and Anthony entered de societate magistrorum at Grays Inn. A few months later, Francis went abroad with Sir Amias Paulet, the state of government and society in France under Henry III afforded him valuable political instruction. For the next three years he visited Blois, Poitiers, Tours, Italy, and Spain, during his travels, Bacon studied language, statecraft, and civil law while performing routine diplomatic tasks. On at least one occasion he delivered diplomatic letters to England for Walsingham, Burghley, the sudden death of his father in February 1579 prompted Bacon to return to England. Sir Nicholas had laid up a sum of money to purchase an estate for his youngest son, but he died before doing so. Having borrowed money, Bacon got into debt, Bacon stated that he had three goals, to uncover truth, to serve his country, and to serve his church
