File:Archimedean-involute-circle-spirals-comparison.svg
Summary
Comparison of the Archimedean spiral generated by the equations x=θcosθ and y=θsinθ with the Involute of a circle, generated by the equations x=cosθ+θsinθ and y=sinθ-θcosθ (where "θ" is an angle expressed in radians). The Archimedean spiral is shown in red, and corresponds to the values 0 ≤ θ ≤ 8π of the angle parameter, while the Involute of the circle is shown in black, and corresponds to the values 0 ≤ θ ≤ 17π/2 of the angle parameter. The x-axis extends from -25 to +28 and the y-axis from -26.4 to +23.4, and there are tick marks at -20, -10, +10, +20 along the axes.
The curves are 1 unit apart at their start points, while they are slightly more than 1.5 (and slightly less than π/2) units apart where they intersect the x-axis for the final time in this plot.
Licensing
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 01:58, 5 January 2017 | | 639 × 600 (101 KB) | 127.0.0.1 (talk) | <p>Comparison of the Archimedean spiral generated by the equations <tt>x=θcosθ</tt> and <tt>y=θsinθ</tt> with the Involute of a circle, generated by the equations <tt>x=cosθ+θsinθ</tt> and <tt>y=sinθ-θcosθ</tt> (where "θ" is an angle expressed in radians). The Archimedean spiral is shown in red, and corresponds to the values <tt>0 ≤ θ ≤ 8π</tt> of the angle parameter, while the Involute of the circle is shown in black, and corresponds to the values <tt>0 ≤ θ ≤ 17π/2</tt> of the angle parameter. The x-axis extends from -25 to +28 and the y-axis from -26.4 to +23.4, and there are tick marks at -20, -10, +10, +20 along the axes. </p> <p>The curves are 1 unit apart at their start points, while they are slightly more than 1.5 (and slightly less than π/2) units apart where they intersect the x-axis for the final time in this plot. </p> |
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