The theorem that structured our knowledge of Earth’s position and geography.

The Pythagorean theory appears simple. The equation a2+b2=c2 explains the connection between the sides of right-angle triangle, where a, b and c are the three sides forming the triangles, where the longest side is c.

Even though the theory is simple, it was a major step in enhancing the techniques of geometry that are needed to make accurate maps the method known as triangulation. As we know, triangles can be cut out of all polygons and right angles triangles from all triangles, thus equation permits the evaluation of the angles and sides of a given polygon. In the case of mapmaking, the field which is being plotted is initially covered with the system of triangles. This facilitates the calculation of the angles and distances between landmasses.

With the advancements in the measuring tools, there is not much requirement for explicit triangulation. Nevertheless, it is to date in use to deduce the locations from satellite data. The generalization of this theory also aids us to evaluate the universe’s shape. Our planet is spherical but have we wondered about our universe? It does not seem possible, right?

But with the generalization of this theorem, we can do something else. The Pythagorean theorem applies to the triangles on a flat level. However, with the generalizations, it can be applied to the triangles that are curved, in space. In addition to these, the generalizations also help us in knowing how curved the space is. Thus, by measuring the triangles that are within the space, we can compute the curvature.