# Was mathematics invented or discovered 1

## The history of mathematics

**3.3 Doctrines and formulas**

I) Thales

1. The base angles in the isosceles triangle are the same.

2. The vertex angles between two intersecting straight lines are the same.

3. A triangle is defined by one side and the two adjacent angles.

4. The diameter bisects the circle.

5. The diagonals of a rectangle are the same and bisect each other.

6. The peripheral angle in the semicircle is a right one.

II) The Pythagorean Theorem

In the right triangle, the sum of the squares over the cathetus is equal to the square over the hypotenuse:

a^{2} + b^{2} = c^{2}

3² + 4² = 5²

9 + 16 = 25

Another number triple would be:

9² + 12² = 15²Û81 + 144 = 225

Ancient evidence:

Consider the square (a + b)^{2}.

On the one hand it has the content a^{2} + b^{2} + 2ab. On the other hand, it consists of the small square with side length c and four times the right triangle in the corners of the large square. This gives the area

c^{2} + 4 * (ab / 2) = c^{2} + 2ab.

III) Euclid

You can draw a line from any point to any point.

A limited straight line can be extended continuously.

You can draw the circle with any center point and distance.

All right angles are equal to each other.

What is equal to the same is also equal to one another.

When like is added to like, whole is equal.

If like is taken away from the same, the remains are the same.

What covers one another is equal to one another.

The whole is bigger than the part.

IV) Plato

The Platonic solids also come from Plato:

## cube | ## octahedron | ## Dodecahedron |

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