Trigonometry/A Brief History of Trigonometry

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. 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

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.

The Pythagorean Theorem

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, although it is often argued that knowledge of the theorem predates him. There is much evidence that Babylonian mathematicians understood the formula.

Heron's Formula

Heron of Alexandria

The area $A$ of a triangle whose sides have lengths $a,b,c$ is

$A=\sqrt{s(s-a)(s-b)(s-c)}$

where $s$ is the semiperimeter of the triangle:

$s=\frac{a+b+c}{2}$

And, for a cyclic quadrilateral (one whose all 4 sides lie inside a circle), this formula can be used:-

$A=\sqrt{(s-a)(s-b)(s-c)(s-c)(s-d)}$

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).