# Arbelos 1c: Vector Reduction

[b]Proposition:[/b] To inscribe a chain of tangent circles in the figure known as the Arbelos (shoemaker's knife). Solution; vector reduction. Giving the kth circle in terms of the ellipse parameters, and k. _____________________ 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). [*][b]→1c. Vector reduction[/b] [*]1d. Ellipse from one 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] [*]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  circle  exploration  pappus  vectors
Target Group (Age)
19+
Language
English (United States)

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