# Formeln:Mathematik - Geometrie - Kreis ○

## Kreis ○

A circle is a basic shape consisting of the points at a given distance from a given point on a plane.

### Definitionen:

• r: Radius
• d: Durchmesser
• U: Umfang
• A: Fläche

#### Umfang eines Kreises

The circumference U is the distance around a closed curve.

$${\color{blue} {U}} = 2 \times \pi \times {\color{red} {r} }$$
U = Umfang
r = Radius

$${\color{red} {r}} = \frac{ {\color{blue} {U} } }{ 2 \times \pi }$$
r = Radius
U = Umfang

$${\color{blue} {U}} = \pi \times {\color{red} {d} }$$
U = Umfang
d = Durchmesser

$${\color{red} {d}} = \frac{ {\color{blue} {U} } }{ \pi }$$
d = Durchmesser
U = Umfang

#### Fläche eines Kreises

The region inside a circle.

$${\color{OliveGreen} {A}} = \pi \times {\color{red} {r} }^{2}$$
A = Fläche
r = Radius

$${\color{red} {r}} = \sqrt{ \frac{\color{OliveGreen} {A}}{\pi} }$$
r = Radius
A = Fläche

$${\color{OliveGreen} {A}} = \frac{\pi}{4} \times {\color{red} {d} }^{2}$$
A = Fläche
d = Durchmesser

$${\color{red} {d}} = \sqrt{ \frac{4 \times {\color{OliveGreen} {A} } }{\pi}}$$
d = Durchmesser
A = Fläche