Trigonometry/A Brief History of Trigonometry
The Babylonians could measure angles, and are believed to have invented the division of the circle into 360º. 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.
First Tables of Sines or Cosines
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.
The Pythagorean Theorem
- 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, although it is often argued that knowledge of the theorem predates him. There is much evidence that Babylonian mathematicians understood the formula.
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 with the heron (a bird).
- Complete Dictionary of Scientific Biography. 2008.
- "Hipparchus of Rhodes". 1999. http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Hipparchus.html.
- George Johnston Allman (1889). Greek Geometry from Thales to Euclid (Reprinted by Kessinger Publishing LLC 2005 ed.). Hodges, Figgis, & Co. p. 26. ISBN 143260662X. http://books.google.com/?id=-gYCAAAAYAAJ&pg=PA26. "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 ..."
- (Heath 1921, Vol I, p. 144)
- Otto Neugebauer (1969). The exact sciences in antiquity (Republication of 1957 Brown University Press 2nd ed.). Courier Dover Publications. p. 36. ISBN 0486223329. http://books.google.com/?id=JVhTtVA2zr8C&pg=PA36. . For a different view, see Dick Teresi (2003). Lost Discoveries: The Ancient Roots of Modern Science. Simon and Schuster. p. 52. ISBN 074324379X. http://books.google.com/?id=pheL_ubbXD0C&pg=PA52. , 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 (2002). "Words and Pictures: New Light on Plimpton 322". The American Mathematical Monthly (Mathematical Association of America) 109 (2): 105–120. doi:10.2307/2695324. http://www.jstor.org/stable/2695324. See also pdf file. The accepted view today is that the Babylonians had no awareness of trigonometric functions. See Abdulrahman A. Abdulaziz (2010). "The Plimpton 322 Tablet and the Babylonian Method of Generating Pythagorean Triples". ArXiv preprint. http://arxiv.org/abs/1004.0025v1. §2, page 7.