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== Kreis == | == Kreis == | ||
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=== Näherungswert/Faustformel für den Kreisumfang === | |||
{{Formel|='''U''' ≈ (22 / 7) · d}} | |||
A Fläche | A Fläche | ||
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r Radius | r Radius | ||
U Umfang | U Umfang | ||
π Kreiszahl Pi (≈ 3,14159) | π [[Kreiszahl Pi]] (≈ 3,14159) | ||
== Kreisring == | == Kreisring == | ||
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== Kreisausschnitt == | == Kreisausschnitt == | ||
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|<html><a href="http://www.amazon.de/gp/product/3895172537/ref=as_li_tf_il?ie=UTF8&camp=1638&creative=6742&creativeASIN=3895172537&linkCode=as2&tag=sciencehomede-21"><img border="0" src="http://ws-eu.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=3895172537&Format=_SL160_&ID=AsinImage&MarketPlace=DE&ServiceVersion=20070822&WS=1&tag=sciencehomede-21" ></a><img src="http://ir-de.amazon-adsystem.com/e/ir?t=sciencehomede-21&l=as2&o=3&a=3895172537" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" /></html> || <html><a href="http://www.amazon.de/gp/product/3127185103/ref=as_li_tf_il?ie=UTF8&camp=1638&creative=6742&creativeASIN=3127185103&linkCode=as2&tag=sciencehomede-21"><img border="0" src="http://ws-eu.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=3127185103&Format=_SL160_&ID=AsinImage&MarketPlace=DE&ServiceVersion=20070822&WS=1&tag=sciencehomede-21" ></a><img src="http://ir-de.amazon-adsystem.com/e/ir?t=sciencehomede-21&l=as2&o=3&a=3127185103" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" /></html> | |||
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|'''A''' = (π · d² · α) / (4 · 360°) | |'''A''' = (π · d² · α) / (4 · 360°) | ||
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|'''A''' = (r · l<sub>B</sub>) / 2 | |||
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|'''l<sub>B</sub>''' = (π · d · α) / 360° | |||
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== Kreisabschnitt == | == Kreisabschnitt == | ||
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|<html><a href="http://www.amazon.de/gp/product/3860726552/ref=as_li_tf_il?ie=UTF8&camp=1638&creative=6742&creativeASIN=3860726552&linkCode=as2&tag=sciencehomede-21"><img border="0" src="http://ws-eu.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=3860726552&Format=_SL160_&ID=AsinImage&MarketPlace=DE&ServiceVersion=20070822&WS=1&tag=sciencehomede-21" ></a><img src="http://ir-de.amazon-adsystem.com/e/ir?t=sciencehomede-21&l=as2&o=3&a=3860726552" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" /></html> || | |||
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|'''A''' = (l<sub>B</sub> · r - l (r - b)) / 2 | |||
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|'''A''' = (π · d² ) / 4 · (α / 360) - (l(r - b)/2) | |||
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|'''A''' = (l · r - r² · sin (l/r)) / 2 | |||
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|'''A''' ≈ 2 / 3 · l · b | |||
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|'''b''' ≈ (A · 3) / (2 · l) | |||
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|'''l<sub>B</sub>''' = (π · r · α ) / 180° | |||
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A Fläche | |||
r Radius | |||
d Durchmesser | |||
l<sub>B</sub> Bogenlänge | |||
l Sehnenlänge | |||
b Breite | |||
α Innenwinkel | |||
== Ellipse == | == Ellipse == | ||
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|'''A''' ≈ (π · D · d) / 4 | |||
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|'''A''' = π · R · r | |||
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|'''U''' ≈ π · (D + d) / 2 | |||
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|'''U''' ≈ π · (R + r) | |||
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A Fläche | |||
d kleine Achse | |||
D große Achse | |||
r kleine Halbachse | |||
R große Halbachse | |||
U Umfang | |||
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Version vom 25. März 2019, 12:48 Uhr
Kreis
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Näherungswert/Faustformel für den Kreisumfang
U ≈ (22 / 7) · d |
A Fläche d Durchmesser r Radius U Umfang π Kreiszahl Pi (≈ 3,14159)
Kreisring
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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
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
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 |
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lB = (π · r · α ) / 180° |
A Fläche r Radius d Durchmesser lB Bogenlänge l Sehnenlänge b Breite α Innenwinkel
Ellipse
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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
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