# Ellipse by parameter, scale, rotation

I found it easier to work through the Arbelos problem by using an ellipse with a major half-axis of 1 (bound in the unit circle). This ellipse has only one parameter. Then the whole problem can be scaled and rotated. _____________________ Archimedes' Arbelos: [list] [*]1a. Inscribe a circle in the arc.[url]http://www.geogebratube.org/material/show/id/54105[/url] [*]1b. Tangent circles in the arc (Solution 1). [*]1c. Vector Reduction: [url]http://www.geogebratube.org/material/show/id/54557[/url] [*][b]→1d. Proposition: To give an ellipse by one parameter, scale and rotation.[/b] [*]1e. Final Construction: [url]http://www.geogebratube.org/material/show/id/54592[/url] [*]2a. Let one circle enclose another. Inscribe a third circle in the ring: [url]http://www.geogebratube.org/material/show/id/54595[/url] [*]2b. Tangent circles in the ring. [url]http://www.geogebratube.org/material/show/id/54596[/url] [/list] 3. Cyclic Solution: [list] [*]3a. An outer ring of tangent circles: [url]http://www.geogebratube.org/material/show/id/55009[/url] [*]3b. Determine the projection. [*]3c. Final Construction: [url]http://www.geogebratube.org/material/show/id/55883[/url] [/list]

Resource Type
Activity
Tags
archimedes  cyclic  exploration  pappus  projection  steiner
Target Group (Age)
19+
Language
English (United States)