Thales’ theorem:

If two lines which intersect each other and are in the same plane are cut by parallel lines, segments determined in one line are proportional to the segments determined in the other line.
We use the Thales theorem to divide segments into equal or proportional parts.

Right triangle altitude theorem:

In Geometry, we say that two or more figures are “similar” when all of their angles are equal so their sides are proportional.
The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse. It states that in a right triangle, the altitude on the hypotenuse is the geometric mean to the two segments into which the hypotenuse is divided.

Golden ratio:

Here you can see a video created by KhanAcademy to learn more about Golden Ratio

In mathematics and the arts, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to their maximum. The golden ratio is also called the golden section (Latin: sectio aurea) or golden mean. The golden number is an irrational number and it is represented by the Greek letter \varphi in honor to Greek sculptor Phidias.

Expressed algebraically, for quantities a and b with a > b

Golden ratio

Where the Greek letter  phi (\varphi) represents the golden ratio. Its value is:

In this unit you will learn how to get this ratio graphically:

To learn more….

Thales of Miletus

There is considerable agreement that Thales was born in Miletus in Greek Ionia in the mid 620s BCE and died in about 546 BCE, but even those dates are indefinite. Greek philosopher who is considered the founder of Greek science, mathematics, and philosophy. He visited Egypt and probably Babylon, bringing back knowledge of astronomy and geometry. He invented deductive mathematics. To him is attributed Thales’ theorem. It is also attributed to Thales the prediction of a Solar Eclipse and more theorems.


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