Arbelos, 2a

[b]Proposition:[/b] Given two circles, one enclosing the other, inscribe a third circle in the ring between the first two. _____________________ 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] [*]1d. Ellipse from parameter, scale and rotation:[url]http://www.geogebratube.org/material/show/id/55256[/url] [*]1e. Final Construction: [url]http://www.geogebratube.org/material/show/id/54592[/url] [*][b]→2a. Let one circle enclose another. Inscribe a third circle in the ring. [/b] [*]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]

 

Ryan Hirst

 
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archimedes  ellipse  knife  pappus  shoemaker 
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