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
r U d U

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


A r A d

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