File:Circle-tangent-angle-over-arc-length.svg
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Original file (SVG file, nominally 528 × 528 pixels, file size: 21 KB)
Summary
| Description |
English: A diagram supporting a geometric explanation of why the curvature of a circle of radius R is 1/R.
The diagram shows a circle of radius R and a red arc of length L from points A to B along with the arc's central angle ACB and tangent lines at the arc's endpoints, AD and DB. The measure of the central angle is L/R radians, which is the same as the measure of angle BDE, which is the angle between the arc endpoint tangents, where E is on the tangent line AD with D between A and E. Those two angles are the same size because they are each supplementary angles to angle ADB. The ratio of the angle between the arc endpoint tangents, measured in radians, divided by the arc length L is (L/R)/L = 1/R. Since that the ratio is 1/R for any arc of the circle that is less than a quarter circle, for arcs containing any point P on the circle, the limit of the ratio as arc length approaches zero is also 1/R. Hence the curvature of the circle at any point P is 1/R. |
| Date | |
| Source | Own work |
| Author | DCary |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 15:33, 26 November 2025 | | 528 × 528 (21 KB) | wikimediacommons>DCary | Uploaded own work with UploadWizard |
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