Ellipse by parameter, scale, rotation
- Author:
- Ryan Hirst
For more complicated problems I find it easier to give figures in position, bound in the unit circle, solve the desired relationships, and then scale and rotate the whole thing.
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Archimedes' Arbelos:
- 1a. Inscribe a circle in the arc.http://www.geogebratube.org/material/show/id/54105
- 1b. Tangent circles in the arc (Solution 1).
- 1c. Vector Reduction: http://www.geogebratube.org/material/show/id/54557
- →1d. Proposition: To give an ellipse by one parameter, scale and rotation.
- 1e. Final Construction: http://www.geogebratube.org/material/show/id/54592
- 2a. Let one circle enclose another. Inscribe a third circle in the ring: http://www.geogebratube.org/material/show/id/54595
- 2b. Tangent circles in the ring. http://www.geogebratube.org/material/show/id/54596
- 3a. An outer ring of tangent circles: http://www.geogebratube.org/material/show/id/55009
- 3b. Determine the projection.
- 3c. Final Construction: http://www.geogebratube.org/material/show/id/55883