Harvard Extension Math for Teaching Capstone Project

History Of Distance Formula

Three mathematicians are most responsible for the development of this formula

Euclid, Pythagoras and DesCartes.


Euclid was known as the father of Geometry. We call high school geometry Euclidean Geometry (for the most part) because most of it is based upon concepts handed down from Euclid and his students.

Euclids third Axiom States: It is possible to construct a circle with any point as its center and with a radius of any length.

You may wonder why a circle matters here? Well, the distance formula is really just the equation of the circle formula re-arranged.


The man who invented the distance formula must have been amazed by distances. And why not? He was a traveler. He was a scientist and a philosopher always seeking the meaning in life. Aside from being educated in Greece, the distance formula inventor traveled other parts of the world to learn from other civilizations.


Many acknowledge that Pythagoras was the person who invented the distance formula. He was from Samos and born around 570 B.C. He traveled not just to Egypt and Babylon, but also to Arabia, Phoenicia, Judea, and India. He did this in search of knowledge. According to records, he was much amazed by what knowledge was available in Egypt. He was also fond of experimenting with numbers and later on ended up being the distance formula inventor.

Pythagorean Theorem

Vertical, horizontal, or diagonal distance can be solved using Pythagoras distance formula, or what is called “Pythagorean theorem.” The man who invented the distance formula based this on the dimensions of a right triangle or a 90 degree triangle. This triangle has three sides—the base, the height, and the hypotenuse, which is the diagonal side. If 2 sides have known dimensions the third unknown can be solved.

Thus, to solve the distance from one point to a standing structure, and the dimensions for the structure height and the hypotenuse are given, the distance can be calculated. The formula for this is C squared is equal to A squared plus B squared. According to the distance formula inventor, C is the value for the base, A is the value for the height, and B is the value for the hypotenuse side. The man who invented the distance formula figured any unknown value of this equation can be solved by merely manipulating or transposing the formula.

The Pythagorean Theorem is a vital formula in Geometry and Trigonometry. Architects, engineers, pilots, and seamen use it in their works. Pythagoras was said to have learned basic Geometry from the Egyptians—the famed Pyramid builders, Arithmetic from the Phoenicians, and Astronomy from the Babylonians. But his contribution to Geometry and Trigonometry was exemplary. In fact, Plato was so influenced by Pythagoras’ ideas. Scores of other philosophers and scientists were likewise influenced by the distance formula inventor.


Pythagoras’ fondness for numbers was mixed with his delight for magic. Later, he established the religion Pythagoreanism. He believed that Mathematics and numbers governed life and afterlife. Together with magic, they also enabled him to predict future events.

Renee Descartes

Renee DesCartes played probably an even greater role in developing this formula.. because he was the developer of the coordinate system that connected algebra and geometry.

So he took the concepts of Euclid and Pythagoras and used algebra to relate the radius to the center point of the circle.

So he essentially came up with the equations used today for circles and for the distance from one point to another