Pappus's centroid theorem (Q6482800)
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theorem that, for a solid of revolution of a planar figure, the surface area equals the figure’s perimeter times the distance the perimeter’s centroid travels, and the volume equals the figure’s area times the distance the figure’s centroid travels
- Pappus–Guldinus theorem
- Guldinus theorem
- Pappus's theorem
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Pappus's centroid theorem |
theorem that, for a solid of revolution of a planar figure, the surface area equals the figure’s perimeter times the distance the perimeter’s centroid travels, and the volume equals the figure’s area times the distance the figure’s centroid travels |
|
Statements
Guldin demi cercle.svg
337 × 222; 23 KB
337 × 222; 23 KB
Pappus’ first theorem applied to a sphere: the surface area 𝐴 equals 𝑙 (length of the semicircle) times 𝑝 (distance travelled by the centroid of the semicircle) (English)
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Guldin demi disque.svg
337 × 222; 23 KB
337 × 222; 23 KB
Pappus’ second theorem applied to a ball: the volume 𝑉 equals 𝐴 (area of the half‐disc) times 𝑝 (distance travelled by the centroid of the half‐disc) (English)
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Identifiers
PappussCentroidTheorem
Pappus's Centroid Theorem
1 reference
pappus-centroid-theorems
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196931875
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