Formeln Kreis: Unterschied zwischen den Versionen
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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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|'''A''' = (π · d² · α) / (4 · 360°) | |'''A''' = (π · d² · α) / (4 · 360°) | ||
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{| border="1" cellpadding="4" cellspacing="0" style="BORDER-COLLAPSE: collapse" borderColor="#336699" align="center" | {| border="1" cellpadding="4" cellspacing="0" style="BORDER-COLLAPSE: collapse" borderColor="#336699" align="center" | ||
|- bgcolor="#e1e8f2" align="center" valign="middle" | |- bgcolor="#e1e8f2" align="center" valign="middle" | ||
|'''A''' = (r · l<sub>B</sub>) / 2 | |'''A''' = (r · l<sub>B</sub>) / 2 | ||
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{| border="1" cellpadding="4" cellspacing="0" style="BORDER-COLLAPSE: collapse" borderColor="#336699" align="center" | {| border="1" cellpadding="4" cellspacing="0" style="BORDER-COLLAPSE: collapse" borderColor="#336699" align="center" | ||
|- bgcolor="#e1e8f2" align="center" valign="middle" | |- bgcolor="#e1e8f2" align="center" valign="middle" | ||
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|'''A''' = (l<sub>B</sub> · r - l (r - b)) / 2 | |'''A''' = (l<sub>B</sub> · r - l (r - b)) / 2 | ||
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{| border="1" cellpadding="4" cellspacing="0" style="BORDER-COLLAPSE: collapse" borderColor="#336699" align="center" | {| border="1" cellpadding="4" cellspacing="0" style="BORDER-COLLAPSE: collapse" borderColor="#336699" align="center" | ||
|- bgcolor="#e1e8f2" align="center" valign="middle" | |- bgcolor="#e1e8f2" align="center" valign="middle" | ||
|'''A''' = (π · d² ) / 4 · (α / 360) - (l(r - b)/2) | |'''A''' = (π · d² ) / 4 · (α / 360) - (l(r - b)/2) | ||
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{| border="1" cellpadding="4" cellspacing="0" style="BORDER-COLLAPSE: collapse" borderColor="#336699" align="center" | {| border="1" cellpadding="4" cellspacing="0" style="BORDER-COLLAPSE: collapse" borderColor="#336699" align="center" | ||
|- bgcolor="#e1e8f2" align="center" valign="middle" | |- bgcolor="#e1e8f2" align="center" valign="middle" | ||
|'''A''' = (l · r - r² · sin (l/r)) / 2 | |'''A''' = (l · r - r² · sin (l/r)) / 2 | ||
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|- bgcolor="#e1e8f2" align="center" valign="middle" | |- bgcolor="#e1e8f2" align="center" valign="middle" | ||
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|'''A''' ≈ (π · D · d) / 4 | |'''A''' ≈ (π · D · d) / 4 | ||
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|- bgcolor="#e1e8f2" align="center" valign="middle" | |- bgcolor="#e1e8f2" align="center" valign="middle" | ||
|'''A''' = π · R · r | |'''A''' = π · R · r | ||
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{| border="1" cellpadding="4" cellspacing="0" style="BORDER-COLLAPSE: collapse" borderColor="#336699" align="center" | {| border="1" cellpadding="4" cellspacing="0" style="BORDER-COLLAPSE: collapse" borderColor="#336699" align="center" | ||
|- bgcolor="#e1e8f2" align="center" valign="middle" | |- bgcolor="#e1e8f2" align="center" valign="middle" | ||
|'''U''' ≈ π · (D + d) / 2 | |'''U''' ≈ π · (D + d) / 2 | ||
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{| border="1" cellpadding="4" cellspacing="0" style="BORDER-COLLAPSE: collapse" borderColor="#336699" align="center" | {| border="1" cellpadding="4" cellspacing="0" style="BORDER-COLLAPSE: collapse" borderColor="#336699" align="center" | ||
|- bgcolor="#e1e8f2" align="center" valign="middle" | |- bgcolor="#e1e8f2" align="center" valign="middle" |
Version vom 28. Oktober 2010, 14:08 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
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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