File:Gudermannian function.png
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Original file (1,652 × 1,274 pixels, file size: 246 KB, MIME type: image/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 12φ = tanh 12ψ. 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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File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 16:00, 29 June 2022 | | 1,652 × 1,274 (246 KB) | Jacobolus | use phi instead of varphi |
| 21:41, 28 June 2022 |  | 1,672 × 1,304 (261 KB) | Jacobolus | minor stylistic changes | |
| 21:36, 28 June 2022 |  | 1,632 × 1,282 (255 KB) | Jacobolus | Clarify that the shaded areas are half the magnitude of the named variables (if we define area 1 to mean the area of a unit square) | |
| 20:53, 28 June 2022 |  | 1,600 × 1,224 (249 KB) | Jacobolus | Use an area representation of s for consistency. | |
| 19:02, 28 June 2022 |  | 1,624 × 1,278 (254 KB) | Jacobolus | Uploaded own work with UploadWizard |
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