File:Gudermannian function.png
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Summary
| Description |
English: The w:Gudermannian function relates the area of a w:circular sector to the area of a w:hyperbolic sector, via a common w:stereographic projection. If twice the area of the blue hyperbolic sector is ψ, then twice the area of the red circular sector is φ = gd ψ. Twice the area of the purple triangle is the stereographic projection s = tan 1/2φ = tanh 1/2ψ. The blue point has coordinates (cosh ψ, sinh ψ). The red point has coordinates (cos φ, sin φ). The purple point has coordinates (0, s).
The Gudermannian function is used in the construction of the w:Mercator projection. Image created using Desmos, https://www.desmos.com/calculator/yvendpvrig |
| Date | |
| Source | Own work |
| Author | Jacob Rus |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 21:30, 29 June 2022 | | 1,652 × 1,274 (246 KB) | wikimediacommons>Jacobolus | use phi instead of varphi |
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