Chapter 1: Trigonometry

1.3 Pythagorean theorem

In addition to the three trig functions, which relate two sides and an angle, we also have a relationship between the three sides. This is known as the Pythagorean theorem. For a right triangle with sides a and b, and hypotenuse c, the three lengths have the relationship

\[
a^2 + b^2 = c^2 \tag{1.4}
\]

While in the Western science tradition we name this relationship after the Greek mathematician Pythagoras, it had been discovered earlier by the Mesopotamians, Indians and Chinese. It is unclear if one particular culture made the discovery first and others learned from them, or if it was discovered independently by each. It is likely that the Greeks learned about it from the Mesopotamians, by way of Egyptians.1 It is also unclear that Pythagoras himself recorded a proof of this theorem. Pythagoras founded a community of philosophers and mathematicians, all of whom wrote under the name of Pythagoras.2

Lacking a commonly-recognized alternative, I’ll continue to refer to this relationship by the name “the Pythagorean theorem.” It provides us another tool to use when working with right triangles.

Example

Example

Practice

Practice

Practice


1The Pythagorean Theorem: The story of its power and beauty, by Alfred S. Posamentier

2Hypatia’s Heritage: A history of women in science from antiquity through the nineteenth century, by Margaret Alic.