**Thales of Miletus**

#### Thales (Miletus, present-day Turkey, 624 B.C. – 548 B.C.) Greek philosopher and mathematician. Initiator of the school of Miletus, the first of the philosophical schools of ancient Greece, he is considered to be the first of the seven sages of ancient Greece.

Such was an illustrious Greek geometrician who lived approximately between the years 624 to 548 B.C. who is known as the «Father of Greek Mathematics».

He is also considered one of the «Seven Wise Men of Greece»; he stood out in two well marked fields: Philosophy and Mathematics. Thales is credited with many unfamiliar mathematical works that elevate to general truths what for the Egyptians were results of simple measurements.

As a young man he was a prosperous merchant of Miletus, whose business allowed him to travel to various places. While in Egypt he was fascinated by the Arithmetic and Geometry practiced by the priests and it was there where a method was devised to find the height of the pyramids through the shadow they projected.

Then it is said that he retired from commerce to dedicate himself to the study of mathematics and philosophy.

**Contributions of Thales in Geometry**

This is how the first demonstrations of geometric theorems are known through logical reasoning, among them we can cite:

- All diameter biseca to the Circumference.
- The angles at the base of an isosceles triangle are equal.
- The angles opposed by the vertex are equal.
- Two triangles that have two angles and one side respectively equal are equal.
- Every semi-inscribed angle in a circle is right.
- The famous «Theorem of Thales»; perhaps his greatest work, remembered for thousands of years.

**Theorem of Thales**

The **Theorem of Thales** is, together with **Pythagoras theorem**, the most famous theorems in history; so much so, that to this day they are still studied in schools because of their importance in the calculation of lengths and because they are a practical and simple tool to use.

**The Theorem of Thales indicates that:**

#### «The segments determined by a series of parallels cut by two transversals are proportional»,

Graphically:

This relationship of segments that is fulfilled in the theorem of Thales has served humanity, it is even said that it was Thales who first found the height of the pyramid of Egypt (Cheops) with his famous theorem.

**Height of the Pyramid of Egypt**

**Thales of Miletus** is remembered for its famous theorem and perhaps one of the most remembered applications was to find in its time the height of the pyramid of Egypt, in a very ingenious way.

**How’d he do that?**

I take advantage of a sunny day where the shadow of the pyramid was projected towards the floor. Besides to have a stick of fixed measure with its respective length of known shade, everything in a same instant.

Take a look at the following figure:

From this figure the height of the pyramid is «H». Here we can apply the theorem of Thales in similar right triangles as well:

Where the lengths «a», «b» and «h» are all known. So Tales was able to calculate the height of the Pyramid in approximate form.

The reasoning Thales made seems very simple; however, we must give all credit to this Sage, since this calculation was made more than 2500 years ago.

**Anecdotes**

Many anecdotes are told about such. According to Plutarch, he was the typical distracted sage focused on his astronomical research.

**He is said to have predicted the solar eclipse of 585 B.C.** and the exact calculation of the number of days of the year (365 years). Such for his interesting and multiple works acquired great popular fame.

He was the famous sage who fell into a well for looking at the stars when an old woman said to him: **«You pretend to observe the stars and you don’t even see what you have at your feet»**.

Thales is also credited with the story of the mule that carried salt and got into the river to dissolve it and lighten its weight; Thales removed that bad habit by carrying it with sponges.

When Thales was asked what reward he wanted for his discoveries, he replied, **«I would consider myself well rewarded if others did not attribute my findings to themselves and acknowledge that they are mine».**

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