What is math made of

Pre-Greek mathematics

With the emergence of high cultures in Sumer and Egypt towards the end of the 4th millennium BC, mathematics also developed - probably as a religious and commercial instrument. Pre-Greek mathematics does not show itself to us as a teaching, but as a collection of tasks and procedures for solving computational and surveying problems.


Arithmetic - Algebra

From the Babylonian times there are extensive tables of numbers that were used as a calculation aid for addition and multiplication, but originally had the religious function of expressing the great cosmic order.
There were also methods of summing arithmetic series, forming Pythagorean numbers, and square root approximation.

Egypt
The Egyptians only knew number symbols for the powers of ten and as arithmetic methods only the addition, doubling and tenfold as well as the respective inversions. Fractions could also be written with the numerator 1.

Sumer - Babylon
The decimal system was created according to the number of human fingers; From the necessity of halving and thirding the quantities of goods, a unit based on the number six developed. A combination of both systems led to the base number 60.

Since it was assumed that the planet gods would influence the fate of the country and state according to their position within their heavenly houses (from which later the private, personal star German arose), it was necessary to determine their exact position.
For this purpose, simple circular divisions had to be carried out, for which the number six is ​​best suited, since the removal of the radius on the circular line results in a regular hexagon, which can easily be formed into a 12- or 24-corner by halving.


geometry

The Egyptians and Babylonians were familiar with the calculation of simple areas and volumes, as well as an approximation of the circular area. The "slope triangle" was also used to determine the slope of a slope.

Babylonians and Indians used a rule for making Pythagorean triangles; Thales circle and set of tendons were also known.


Greek mathematics

Babylonian knowledge was apparently also known in the Greek area. With the beginning of Greek philosophy, however, the actual mathematics also emerged: general theorems were expressed and proven.
The archaic-classical mathematics (600-300 BC) includes Thales, Anaximander, Pythagoras, Hippocrates, Anaxagoras, Democritus and Eudoxus, the Hellenistic mathematics (300 BC) Euclid, Archimedes and Apollonios.

There was no really Roman and later Byzantine mathematics: Hipparchus, Ptolemy, Heron and Diophantus were Greeks.


Thales (1st half of the 6th century BC) based his laws on the circle with the help of axis symmetry; The term angle appears here for the first time as an innovation.

The thaletic sentences are derived from the basic thaletic figure, which consists of a circle with an inscribed rectangle (as well as its diagonals and axes of symmetry):
1. The circle is bisected by each of its diameters.
2. The vertex angles are the same.
3. The base angles in the isosceles triangle are the same.
4. The edge angle in the semicircle is a right one.


Pythagoras (2nd half of the 6th century BC) was the founder of a philosophical doctrine which saw the essence of things in the relationships of whole numbers.
"The nature of number gives knowledge and guides and teaches everyone in everything that is doubtful and unknown to him."
He is reported to have made mathematics a free teaching, a science pursued for its own sake.


Euclid (around 300 BC) had arranged the entire mathematical knowledge of that time and summarized it in its elements (Stoicheia).
The book includes elementary geometry, numerology and spatial geometry.
The definitions and postulates (basic assumptions) are followed by theorems which are proven on the basis of the foregoing.
Today's geometry textbooks still follow Euclidean principles with major cuts.

Kurt Scheuerer 1998


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