Trigonometry/A Brief History of Trigonometry

thumb|right|A painting of the famous greek geometrist, and "father of measurement", Euclid. In the times of the greeks, trigonometry and geometry were important mathematical principles used in building, agriculture and education. The Babylonians could measure angles, and are believed to have invented the division of the circle into 360º.http://www.lscc.edu/faculty/steven_a_boast/Shared%20Documents/MAC%201114%20Trigonometry/Activities%20and%20Labs/MAC%201114%20Measuring%20Angles%20Lab.pdf However, it was the Greeks who are seen as the original pioneers of trigonometry. A Greek mathematician, Euclid, who lived around 300 BC was an important figure in geometry and trigonometry. He is most renowned for Euclid's Elements, a very careful study in proving more complex geometric properties from simpler principles. Although there is some doubt about the originality of the concepts contained within Elements, they're influential in how we think about proofs and geometry today; indeed, it has been said that the Elements have "exercised an influence upon the human mind greater than that of any other work except the Bible.Complete Dictionary of Scientific Biography 2008 First Tables of Sines or Cosines thumb|150px|Hiparchus In the second century BC a Greek mathematician, Hipparchus, is thought to have been the first person to produce a table for solving a triangle's lengths and angles.http://www-groups.dcs.st-and.ac.uk/Biographies/Hipparchus.html Hipparchus of Rhodes 1999 The Pythagorean Theorem thumb|left|200px|Pythagoras, depicted on a 3rd-century coin In a right triangle: The square of the hypotenuse is equal to the sum of the squares of the other two sides. The Pythagorean theorem is named after the Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof,Greek Geometry from Thales to Euclid George Johnston Allman 26 http://books.google.com/?id=-gYCAAAAYAAJ&pg=PA26 Hodges, Figgis, & Co 1889 The discovery of the law of three squares, commonly called the "theorem of Pythagoras" is attributed to him by – amongst others – Vitruvius, Diogenes Laertius, Proclus, and Plutarch ... Reprinted by Kessinger Publishing LLC 2005 143260662XHeath 1921 Vol I, p. 144 although it is often argued that knowledge of the theorem predates him. There is much evidence that Babylonian mathematicians understood the formula.The exact sciences in antiquity 36 http://books.google.com/?id=JVhTtVA2zr8C&pg=PA36 Otto Neugebauer 0486223329 1969 Republication of 1957 Brown University Press 2nd Courier Dover Publications. For a different view, see Dick Teresi 52 Lost Discoveries: The Ancient Roots of Modern Science http://books.google.com/?id=pheL_ubbXD0C&pg=PA52 074324379X 2003 Simon and Schuster, where the speculation is made that the first column of a tablet 322 in the Plimpton collection supports a Babylonian knowledge of some elements of trigonometry. That notion is pretty much laid to rest by Eleanor Robson Words and Pictures: New Light on Plimpton 322 2002 10.2307/2695324 http://www.jstor.org/stable/2695324 The American Mathematical Monthly 109 2 105–120 Mathematical Association of America harv See also pdf file. The accepted view today is that the Babylonians had no awareness of trigonometric functions. See The Plimpton 322 Tablet and the Babylonian Method of Generating Pythagorean Triples Abdulrahman A. Abdulaziz 2010 http://arxiv.org/abs/1004.0025v1 ArXiv preprint harv §2, page 7. Heron's Formula thumb|left|150px|Heron of Alexandria The area of a triangle whose sides have lengths is where is the semiperimeter of the triangle: And, for a cyclic quadrilateral (one whose all 4 sides lie inside a circle), this formula can be used:- The formula is believed to be due to Heron of Alexandria (10 – 70 AD), a Greek mathematician. The formula has nothing to do with the Heron (a type of bird). References