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The trisectrix and Langley's problem

Published online by Cambridge University Press:  24 February 2022

John R. Silvester*
Affiliation:
Department of Mathematics, King’s College Strand, London WC2R 2LS e-mail: john.silvester@cantab.net
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If a circle rolls without slipping around an equal fixed circle, then a point carried by the rolling circle traces out a limaçon of Pascal. (This is Etienne Pascal, father of Blaise. The word limaçon is derived from the Latin limax, a snail.) If the fixed and rolling circles have radius 1, and the point P carried by the rolling wheel is distant a from its centre, then for a > 1 the limaçon has an inner and an outer loop, joining up at a node. For a = 1 it has a cusp, and is then a cardioid, so-called because it is heart-shaped. See Figure 1, where we have plotted the cases a = $${3 \over 4}$$, a = 1 and a = $${3 \over 2}$$.

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Articles
Copyright
© The Authors, 2022. Published by Cambridge University Press on behalf of The Mathematical Association

References

Langley, E. M., Problem, A, Math. Gaz. 11 (October 1922) p. 173.Google Scholar
Quadling, D. A., Last word on adventitious angles, Math. Gaz. 62 (October 1978) pp. 174183.Google Scholar
https://www.scribd.com/doc/86809487/Angles-in-Mahatmas-s-triangle Google Scholar
Clarke, Robert J., The return of the cotangent rule, Math. Gaz. 88 (March 2004) pp. 116118.10.1017/S0025557200174418CrossRefGoogle Scholar