##### Arbelos and parbelos help!

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What is a similar shape to the arbelos but drawn using a curbe or shape other than circle? If it is parbelos, then what it is, what are the difference between both and how to draw it.

Jul 30th, 2015

Thank you for the opportunity to help you with your question!

A cone, in particular, is not shaped like an "ice cream cone" but rather like two ... arbelos - a plane region bounded by three mutually tangent semicircles

The area of the arbelos is equal to the area of a circle with diameter HA .

For a cone, only its surface area and volume becomes calculate-able

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 30th, 2015

I want to know more about parbelos. I have googled it but all the information is hard to understand and not recent

Jul 30th, 2015

Ok, am giving you all the needed information in a short while.

Jul 30th, 2015

The arbelos is a classical geometric shape bounded by three mutually tangent semicircles with collinear diameters.

The parbelos is defined as the region bounded by the three latus rectum arcs.

Latus rectum is defined as the chord perpendicular to the principal axis and passing through a focus of an ellipse, parabola, or hyperbola.

You can study all these from this book; Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, pp. 116-118, 1969.

Jul 30th, 2015

Thanks

Jul 31st, 2015

Welcome.

Jul 31st, 2015

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Jul 30th, 2015
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Jul 30th, 2015
Sep 25th, 2017
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