Definition of Hypotenuse and Leg

The word hypotenuse comes from the Greek word hypoteinousa and literally means "strongly tense". In its origin, it was used in connection with the corresponding ropes for measuring the terrain using stakes joined by a taut rope. It is worth remembering that strictly speaking the word geometry it means precisely measurement of the earth.

The word catheto also comes from the Greek, specifically from kathetos, which literally means "falling perpendicular".

From empirical observation to the Pythagorean Theorem

Both terms were part of the daily life of the Greeks, because with them the forms that certain measurements acquired were described. Of the simple observation empirical dimension abstract of math and the relationship between the hypotenuse and the legs was reflected in the famous Pythagorean theorem.

According to this theorem, if we have a triangle rectangle there are necessarily two sides of the triangle that form a 90 degree angle and both are the legs. The side that is in front of the angle formed by the two legs is precisely the hypotenuse.

The hypotenuse and the legs are directly related and this relationship is reflected in the formulation of the theorem:

In every right triangle the square of the hypotenuse is equal to the sum of the squares of the legs.

In this way, knowing the dimensions of the two legs, the dimension of the hypotenuse can be calculated or knowing the hypotenuse and one leg can obtain the value of the other leg.

As is logical, the Pythagorean theorem was a mathematical advance of the first order, since from it it was already possible to carry out all kinds of calculations for the edification of houses, to measure land without the need for ropes or to calculate any distance related to 90 degree angles. On synthesis, the Pythagorean theorem was a theoretical formulation that served to make any measurement in a precise and unambiguous way.

Pythagoras and mathematics

This Greek philosopher was born on the island of Samos in the Vl century BC. C and is considered the father of mathematics as we understand it today. His genius consisted in affirming that everything that exists in the universe can be expressed in language mathematical. After 2500 years this idea is accepted by the whole of the scientific community, because today we know that everything around us can be translated into a mathematical formula.

According to most researchers, it is believed that Pythagoras traveled through Egypt and it was there that he learned certain principles of mathematics that were finally embodied in the Pythagorean theorem.

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