Formeln Kreis: Unterschied zwischen den Versionen

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== Kreis ==
== Kreis ==


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Version vom 25. März 2019, 13:48 Uhr

Kreis

kreis.gif

A = (π · d²) / 4
d = √ ((A · 4) / π)


A = π · r²
r = √ (A / π)


U = π · d
d = U / π


U = 2π · r
r = U / 2π


Näherungswert/Faustformel für den Kreisumfang

U ≈ (22 / 7) · d 
A  Fläche
d  Durchmesser
r  Radius
U  Umfang
π  Kreiszahl Pi (≈ 3,14159)

Kreisring

kreisring.gif

b = (D - d) / 2
D = d + b · 2
d = D - b · 2


dm = (D + d) / 2
D = dm · 2 - d
d = dm · 2 - D


A = (π / 4) · (D² - d²)
D = √ (d² + (A / π) · 4)
d = √ (D² - (A / π) · 4)


L = π · dm
dm = L / π 
A   Kreisringfläche
D   Außendurchmesser
d   Innendurchmesser
dm  mittlerer Durchmesser
R   Radius Kreisring außen
r   Radius Kreisring innen
b   breite des Kreisrings
L   gestreckte Länge
π   Kreiszahl Pi (≈ 3,14159)

Kreisausschnitt

kreisausschnitt.gif

A = (π · d² · α) / (4 · 360°)


A = (r · lB) / 2


lB = (π · d · α) / 360° 
A   Fläche des Kreisausschnitts
d   Durchmesser
r   Radius
lB  Bogenlänge
α   Innenwinkel
π   Kreiszahl Pi (≈ 3,14159)

Kreisabschnitt

kreisabschnitt.gif

A = (lB · r - l (r - b)) / 2


A = (π · d² ) / 4 · (α / 360) - (l(r - b)/2)


A = (l · r - r² · sin (l/r)) / 2


A ≈ 2 / 3 · l · b
b ≈ (A · 3) / (2 · l)


lB = (π · r · α ) / 180° 
A   Fläche
r   Radius
d   Durchmesser
lB  Bogenlänge
l   Sehnenlänge
b   Breite
α   Innenwinkel

Ellipse

ellipse.gif

A ≈ (π · D · d) / 4


A = π · R · r


U ≈ π · (D + d) / 2


U ≈ π · (R + r) 
A  Fläche
d  kleine Achse
D  große Achse
r  kleine Halbachse
R  große Halbachse
U  Umfang


Pfad: Home / Mathematik / Geometrie / Kreis

Abgerufen von „http://www.science-at-home.de/wiki/index.php?title=Formeln_Kreis&oldid=36702“