# A history of trigonometry in mathematics

History of Trigonometry Outline Trigonometry is, of course, a branch of geometry, but it differs from the synthetic geometry of Euclid and the ancient Greeks by being computational in nature. Such concepts would have been part of everyday life in hunter-gatherer societies. The idea of the "number" concept evolving gradually over time is supported by the existence of languages which preserve the distinction between "one", "two", and "many", but not of numbers larger than two.

For example, paleontologists have discovered in a cave in South Africaochre rocks about 70, years old, adorned with scratched geometric patterns.

Moreover, hunters and herders employed the concepts of one, two, and many, as well as the idea of none or zero, when considering herds of animals. One common interpretation is that the bone is the earliest known demonstration  of sequences of prime numbers and of Ancient Egyptian multiplication.

The Ishango bone consists of a series of tally marks carved in three columns running the length of the bone. Common interpretations are that the Ishango bone shows either the earliest known demonstration of sequences of prime numbers  or a six-month lunar calendar. The First 50, Years, Peter Rudman argues that the development of the concept of prime numbers could only have come about after the concept of division, which he dates to after 10, BC, with prime numbers probably not being understood until about BC.

He also writes that "no attempt has been made to explain why a tally of something should exhibit multiples of two, prime numbers between 10 and 20, and some numbers that are almost multiples of Iraqi mathematics Mesoptamian mathematics, or Babylonian mathematics, refers to any mathematics of the people of Mesopotamia modern Iraqfrom the days of the early Sumeriansthrough the Babylonian period, until the beginning of the Parthian period.

It is named Babylonian mathematics due to the central role of A history of trigonometry in mathematics as a place of study, which ceased to exist during the Hellenistic period.

From this point, Babylonian mathematics merged with Greek and Egyptian mathematics to give rise to Hellenistic mathematics. In contrast to the sparsity of sources in Egyptian mathematicsour knowledge of Babylonian mathematics is derived from more than clay tablets unearthed since the s.

Written in Cuneiform scripttablets were inscribed whilst the clay was moist, and baked hard in an oven or by the heat of the sun. Some of these appear to be graded homework. They developed a complex system of metrology from BC.

From around BC onwards, the Sumerians wrote multiplication tables on clay tablets and dealt with geometrical exercises and division problems. The earliest traces of the Babylonian numerals also date back to this period. Plimpton Babylonian clay tablet YBC with annotations.

The diagonal displays an approximation of the square root of 2 in four sexagesimal figures, which is about six decimal figures.

The Babylonian mathematical tablet Plimptondated to BC. The Old Babylonian period is the period to which most of the clay tablets on Babylonian mathematics belong, which is why the mathematics of Mesopotamia is commonly known as Babylonian mathematics.

Some clay tablets contain mathematical lists and tables, others contain problems and worked solutions. The majority of recovered clay tablets date from to BC, and cover topics which include fractions, algebra, quadratic and cubic equations, and the calculation of Pythagorean triples see Plimpton Babylonian mathematics were written using a sexagesimal base numeral system.

From this we derive the modern day usage of 60 seconds in a minute, 60 minutes in an hour, and 60 x 6 degrees in a circle. Babylonian advances in mathematics were facilitated by the fact that 60 has many divisors. Also, unlike the Egyptians, Greeks, and Romans, the Babylonians had a true place-value system, where digits written in the left column represented larger values, much as in the decimal system.

They lacked, however, an equivalent of the decimal point, and so the place value of a symbol often had to be inferred from the context. They are particularly known for pioneering mathematical astronomy. In the Hellenistic world, Babylonian astronomy and mathematics exerted a great influence on the mathematicians of Alexandriain Ptolemaic Egypt and Roman Egypt.

This is particularly apparent in the astronomical and mathematical works of HipparchusPtolemyHero of Alexandriaand Diophantus. Ancient Egyptian mathematics c. Egyptian mathematics Egyptian mathematics refers to mathematics written in the Egyptian language.

From the Hellenistic periodGreek replaced Egyptian as the written language of Egyptian scholars, and from this point Egyptian mathematics merged with Greek and Babylonian mathematics to give rise to Hellenistic mathematics.

Mathematical study in Egypt later continued under the Arab Empire as part of Islamic mathematicswhen Arabic became the written language of Egyptian scholars. Early Dynastic Period to Old Kingdom c. These labels appear to have been used as tags for grave goods and some are inscribed with numbers. The problem includes a diagram indicating the dimensions of the truncated pyramid. The earliest true Egyptian mathematical documents date to the Middle Kingdom period, specifically the 12th dynasty c.

The Rhind Mathematical Papyrus which dates to the Second Intermediate Period ca BC is said to be based on an older mathematical text from the 12th dynasty. Like many ancient mathematical texts, it consists of what are today called "word problems" or "story problems", which were apparently intended as entertainment.Van Brummelen, G.

() The Mathematics of the Heavens and the Earth: The Early History of Trigonometry. Princeton, Princeton University Press.

Princeton, Princeton University Press. This is the first major history in English of the early development of trigonometry. The development of modern trigonometry shifted during the western Age of Enlightenment, beginning with 17th-century mathematics (Isaac Newton and James Stirling) and reaching its modern form with Leonhard Euler ().

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles. Trigonometry is found all throughout geometry, as every straight-sided shape may be.

Van Brummelen, G. () The Mathematics of the Heavens and the Earth: The Early History of Trigonometry. Princeton, Princeton University Press.

Princeton, Princeton University Press. This is the first major history in English of the early development of trigonometry. The history of trigonometry Trigonometry and Pi We can not talk about Mathematics without mentioning Pi, the constant that has turned the .

History of Trigonometry Outline Trigonometry is, of course, a branch of geometry, but it differs from the synthetic geometry of Euclid and the ancient Greeks by being computational in nature. For instance, Proposition I.4 of the Elements is the angle-side-angle congruence theorem which states that a triangle is determined by any two angles and.

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