# The famous task of Thales

Here, after the big problems, the resolution of which has been going on for centuries, we note a few more small, but very exciting in their simplicity questions that were once worthy of really great mathematicians, but now reduced to the level of almost childish problems.

One of the most ancient tasks was the calculation of the height of the Egyptian pyramid by the length of its shadow made by Thales (VII – VI centuries BC). Most likely, this was done at a time of day when the length of the shadow is equal to the height of the object casting it. But it is also possible that the brilliant student of the Egyptian priests already knew how to use the sign of the likeness of triangles.

If the height of the pyramid is denoted by the inevitable x (Fig. 1), the length of its shadow by means of a, the height of the column by 1, and the length of the shadow cast by it by b, then, of course,

x : a = 1 : b.

From here:

x = a : b.

This is all just now so amazingly simple, but what a wonderful discovery it was for its time!

Thales, upon returning to Greece, solved the well-known problem of determining the distance of the ship from the coast.

Let the ship be at point K (Fig. 1), and at point A a marina. It is necessary to determine the spacecraft distance.

Having built a right angle at point A, Thales laid down two equal segments along the coast: AB = BC. At point C, he again built a right angle and walked along the perpendicular CD until he reached the point from which K (ship) and B were visible lying on the same straight line KBD.

The triangle BCD is equal to the triangle AKB, therefore, CD = AK.

The CD segment could, of course, be directly and accurately measured.

In the memory of centuries there remained the moment when a person took possession of a space inaccessible to his legs, to his hands and to his measuring hole.