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Real Numbers

Real numbers

The real numbers  form the universe of reckoning. They are needed in daily life. They consist of the natural numbers , integers , rational  and irrational numbers . This number set is represented by the number line.

Number line (Picture: Romanm)

Some famous irrational numbers

Length of a diagonal of a square with sides = 1

The square root of 2 is the length of the diagonal of a square with a side length 1.

Bust of Pythagoras of Samos in the Capitoline Museums, Rome (Picture: Galilea)

The theorem of Pythagoras says: . In any right-angled triangle, the area of the square whose side is the hypotenuse c is equal to the sum of the areas of the squares ot the two cathetus’ a and b.

In the special case both cathetus have the length 1, the equation is . The square root of the equation is .

Result: The length of the diagonal (hypothenuse) is .

Leonhard Euler (Picture: Soerfm)

Euler’s number is defined:

It is a permanent multiplication of the same factors which consist of a fraction greater than 1. It is comparable with the paying of interests for a capital which permanently grows by adding the interests and multiplying the new capital with the same interest rate.

Definition of pi (Picture: Oleg Alexandrov)

 is commonly defined as the ratio of a circle's circumference C to its diameter d.

The constant  in this mosaic outside the mathematics building at the Technische Universität Berlin (Picture: Holger Motzkau)