%0 Generic %1 sondow2012parbelos %A Sondow, Jonathan %D 2012 %K analog arbelos parabolic parbelos %T The parbelos, a parabolic analog of the arbelos %U http://arxiv.org/abs/1210.2279 %X The arbelos is a classical geometric shape bounded by three mutually tangent semicircles with collinear diameters. We introduce a parabolic analog, the parbelos. After a review of the parabola, we use theorems of Archimedes and Lambert to demonstrate seven properties of the parbelos, drawing analogies to similar properties of the arbelos, some of which may be new. The seventh constructs a parbelos directly from an arbelos via a locus. Along the way we mention the Universal Parabolic Constant (an analog of pi) and an origami fold.

@misc{sondow2012parbelos, abstract = {The arbelos is a classical geometric shape bounded by three mutually tangent semicircles with collinear diameters. We introduce a parabolic analog, the parbelos. After a review of the parabola, we use theorems of Archimedes and Lambert to demonstrate seven properties of the parbelos, drawing analogies to similar properties of the arbelos, some of which may be new. The seventh constructs a parbelos directly from an arbelos via a locus. Along the way we mention the Universal Parabolic Constant (an analog of pi) and an origami fold.}, added-at = {2013-12-23T07:09:03.000+0100}, author = {Sondow, Jonathan}, biburl = {https://www.bibsonomy.org/bibtex/229f3db77e5105be1391d4c794746f2dd/aeu_research}, description = {The parbelos, a parabolic analog of the arbelos}, interhash = {c2d9b0df8844ae9384c4b504d7aeb48f}, intrahash = {29f3db77e5105be1391d4c794746f2dd}, keywords = {analog arbelos parabolic parbelos}, note = {cite arxiv:1210.2279Comment: Cited Tsukerman's solution of the Problem and Tahir's discovery of a locus; 8 pages, 11 figures, to appear in the Monthly}, timestamp = {2013-12-23T08:22:34.000+0100}, title = {The parbelos, a parabolic analog of the arbelos}, url = {http://arxiv.org/abs/1210.2279}, year = 2012 }