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.
Pi
–
The number π is a mathematical constant, the ratio of a circles circumference to its diameter, commonly approximated as 3.14159. It has been represented by the Greek letter π since the mid-18th century, being an irrational number, π cannot be expressed exactly as a fraction. Still, fractions such as 22/7 and other numbers are commonly used to approximate π. The digits appear to be randomly distributed, in particular, the digit sequence of π is conjectured to satisfy a specific kind of statistical randomness, but to date no proof of this has been discovered. Also, π is a number, i. e. a number that is not the root of any non-zero polynomial having rational coefficients. This transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass, ancient civilizations required fairly accurate computed values for π for practical reasons. It was calculated to seven digits, using techniques, in Chinese mathematics. The extensive calculations involved have also used to test supercomputers. Because its definition relates to the circle, π is found in many formulae in trigonometry and geometry, especially those concerning circles, ellipses, and spheres. Because of its role as an eigenvalue, π appears in areas of mathematics. It is also found in cosmology, thermodynamics, mechanics, attempts to memorize the value of π with increasing precision have led to records of over 70,000 digits. In English, π is pronounced as pie, in mathematical use, the lowercase letter π is distinguished from its capitalized and enlarged counterpart ∏, which denotes a product of a sequence, analogous to how ∑ denotes summation. The choice of the symbol π is discussed in the section Adoption of the symbol π, π is commonly defined as the ratio of a circles circumference C to its diameter d, π = C d The ratio C/d is constant, regardless of the circles size. For example, if a circle has twice the diameter of another circle it will also have twice the circumference, preserving the ratio C/d. This definition of π implicitly makes use of geometry, although the notion of a circle can be extended to any curved geometry. Here, the circumference of a circle is the arc length around the perimeter of the circle, a quantity which can be defined independently of geometry using limits. An integral such as this was adopted as the definition of π by Karl Weierstrass, definitions of π such as these that rely on a notion of circumference, and hence implicitly on concepts of the integral calculus, are no longer common in the literature. One such definition, due to Richard Baltzer, and popularized by Edmund Landau, is the following, the cosine can be defined independently of geometry as a power series, or as the solution of a differential equation
3.
Greater Toronto Area
–
The Greater Toronto Area is the most populous metropolitan area in Canada. As of the 2016 census, it has a population of 6,417,516, the Greater Toronto Area is defined as the central city of Toronto, and the four regional municipalities that surround it, Durham, Halton, Peel, and York. The regional span of the Greater Toronto Area is sometimes combined with the city of Hamilton, Ontario and its region, to form the Greater Toronto. The Greater Toronto Area anchors a much larger urban agglomeration known as the Golden Horseshoe. However, it did not come into everyday usage until the mid- to late 1990s, the latter includes communities like Barrie, Guelph and the Niagara Region. The GTA continues, however, to be in use elsewhere in the Government of Ontario. For example, Oshawa, which is the centre of its own CMA, other municipalities, such as New Tecumseth in southern Simcoe County and Mono Township in Dufferin County are included in the Toronto CMA but not in the GTA. Other nearby urban areas, such as Hamilton, Barrie or St. Catharines-Niagara and Kitchener-Waterloo, are not part of the GTA or the Toronto CMA, but form their own CMAs near the GTA. Ultimately, all the places are part of the Golden Horseshoe metropolitan region, an urban agglomeration. When the Hamilton, Oshawa and Toronto CMAs are agglomerated with Brock and Scugog and it is part of the Great Lakes Megalopolis, containing an estimated 59 million people in 2011. The term Greater Toronto and Hamilton Area refers to the usual GTA plus the former Regional Municipality of Hamilton–Wentworth, the Greater Toronto Area was home to a number of First Nations groups who lived on the shore of Lake Ontario long before the first Europeans arrived in the region. At various times the Neutral, Seneca, Mohawk and Huron nations were living in the vicinity, the Mississaugas arrived in the late seventeenth or early eighteenth century, driving out the occupying Iroquois. While it is unclear as to who was the first European to reach the Toronto area, the area would later become very crucial for its series of trails and water routes that led from northern and western Canada to the Gulf of Mexico. Known as the Toronto Passage, it followed the Humber River, for this reason area became a hot spot for French fur traders. In 1787, the British negotiated the purchase of more than a million acres of land in the area of Toronto with the Mississaugas of New Credit. The Town of York would later be attacked by American forces in the War of 1812 in what is now known as the Battle of York, in 1816, Wentworth County and Halton County were created from York County. In 1851, Ontario County and Peel County were separated from York, the idea for a single government municipality would not be seriously explored until the late 1940s when planners decided the city needed to incorporate its immediate suburbs. However, due to opposition from suburban politicians, a compromise was struck which resulted in the creation of Metropolitan Toronto
4.
Sterling silver
–
Sterling silver is an alloy of silver containing 92.5 by weight of silver and 7.5 by weight of other metals, usually copper. The sterling silver standard has a minimum millesimal fineness of 925 and these replacement metals include germanium, zinc and platinum, as well as a variety of other additives, including silicon and boron. Alloys such as argentium silver have red in recent decades, one of the earliest attestations of the term is in Old French form esterlin, in a charter of the abbey of Les Préaux, dating to either 1085 or 1104. The English chronicler Orderic Vitalis uses the Latin forms libræ sterilensium, the word in origin refers to the newly introduced Norman silver penny. According to the Oxford English Dictionary, the most plausible etymology is derivation from a late Old English steorling, there are a number of obsolete hypotheses. One suggests a connection with starling, because four birds were depicted on a penny of Edward I, in 1260, Henry III granted them a charter of protection. Because the Leagues money was not frequently debased like that of England, English traders stipulated to be paid in pounds of the Easterlings, and land for their Kontor, the Steelyard of London, which by the 1340s was also called Easterlings Hall, or Esterlingeshalle. The Hanseatic League was officially active in the London trade from 1266 to 1597 and this etymology may have been first suggested by Walter de Pinchebek with the explanation that the coin was originally made by moneyers from that region. The claim has also made in Henry Spelmans glossary as referenced in Commentaries on the Laws of England. Yet another claim on this hypothesis is from Camden, as quoted in Chambers Journal of Popular Literature, Science and Arts. By 1854, the tie between Easterling and Sterling was well-established, as Ronald Zupko quotes in his dictionary of weights, the British numismatist Philip Grierson disagrees with the star etymology, as the stars appeared on Norman pennies only for the single three-year issue from 1077–1080. In support of this he cites the fact one of the first acts of the Normans was to restore the coinage to the consistent weight and purity it had in the days of Offa. This would have perceived as a contrast to the progressive debasement of the intervening 200 years. The sterling alloy originated in continental Europe and was being used for commerce as early as the 12th century in the area that is now northern Germany. A piece of sterling silver dating from Henry IIs reign was used as a standard in the Trial of the Pyx until it was deposited at the Royal Mint in 1843 and it bears the royal stamp ENRI. REX but this was added later, in the reign of Henry III and this is equivalent to a millesimal fineness of 926. In Colonial America, sterling silver was used for currency and general goods as well, between 1634 and 1776, some 500 silversmiths created items in the “New World” ranging from simple buckles to ornate Rococo coffee pots. Although silversmiths of this era were typically familiar with all precious metals, stamping each of their pieces with their personal makers mark, colonial silversmiths relied upon their own status to guarantee the quality and composition of their products
5.
Sampi
–
Sampi is an archaic letter of the Greek alphabet. It later remained in use as a symbol for 900 in the alphabetic system of Greek numerals. Its modern shape, which resembles a π inclining to the right with a longish curved cross-stroke and its current name, sampi, originally probably meant san pi, i. e. like a pi, and is also of medieval origin. The letters original name in antiquity is not known and it has been proposed that sampi was a continuation of the archaic letter san, which was originally shaped like an M and denoted the sound in some other dialects. Besides san, names that have proposed for sampi include parakyisma and angma, while other historically attested terms for it are enacosis, sincope. It has been attested in the cities of Miletus, Ephesos, Halikarnassos, Erythrae, Teos, in the island of Samos, in the Ionian colony of Massilia, and in Kyzikos. In addition, in the city of Pontic Mesembria, on the Black Sea coast of Thrace, it was used on coins, Sampi occurs in positions where other dialects, including written Ionic, normally have double sigma, i. e. a long /ss/ sound. Some other dialects, particularly Attic Greek, have ττ in the same words, the sounds in question are all reflexes of the proto-Greek consonant clusters *, *, *, *, or *. Among the earliest known uses of sampi in this function is an abecedarium from Samos dated to the mid-7th century BC and this early attestation already bears witness to its alphabetic position behind omega, and it shows that its invention cannot have been much later than that of omega itself. The first known use of sampi in writing native Greek words is an inscription found on a silver plate in Ephesus. It can be dated between the late 7th century and mid 6th century BC, an inscription from Halicarnassus has the names Ἁλικαρναͳέν and the personal names Ὀαͳαͳιος and Πνυάͳιος. All of these appear to be of non-Greek, local origin. On a late 6th century bronze plate from Miletus dedicated to the sanctuary of Athena at Assesos and this is currently the first known instance of alphabetic sampi in Miletus itself, commonly assumed to be the birthplace of the numeral system and thus of the later numeric use of sampi. It has been suggested there may be an isolated example of the use of alphabetic sampi in Athens. In a famous painted black figure amphora from c.615 BC, known as the Nessos amphora, the expected regular form of the name would have been either Attic Νέττος – with a double τ – or Ionic Νέσσος. Traces of corrections that are still visible underneath the painted Τ have led to the conjecture that the painter originally wrote Νέͳος, a letter similar to Ionian sampi, but of unknown historical relation with it, existed in the highly deviant local dialect of Pamphylia in southern Asia Minor. According to Brixhe it probably stood for the sounds /s/, /ss/ and it is found in a few inscriptions in the cities of Aspendos and Perge as well as on local coins. For instance, an inscription from Perge dated to around 400 BC reads, anax, it is believed that the letter stood for some type of sibilant reflecting Proto-Greek */ktj/
6.
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
