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On Some General Ovals of Cassinian Type
Published online by Cambridge University Press: 15 September 2017
Extract
The following discussion of the curves r1r2 = crn, where r1, r2, r are the distances of a point from the “foci” ±α, 0 and the origin, c a positive constant and n rational (integral or fractional, positive or negative), provides a good example of extensive knowledge of general curves obtained by elementary-considerations. The attention of the author was first drawn to these curves by the remark of a colleague, Mr. N Davy, M.Sc., that the curves r1r2=cr⅓ appeared in the design of the pole-pieces of certain electromagnets.
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- Copyright © Mathematical Association 1943
References
Page 4 of note * For numerical calculation a convenient form is
Page 6 of note * No ambiguity arises from the root, as we must take the real value satisfying the value (X, 0). The subsequent work is valid for all values of p/q, including negative ones.
Page 10 of note * At this stage the dy/dx locus changes from the form shown in Fig. 8 to “bean-shaped”, to break up into circles when q = − 4p as in Fig. 9.