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Keplerian trigonometry
Abstract Taking the hint from usual parametrization of circle and hyperbola, and inspired by the pathwork initiated by Cayley and Dixon for the parametrization of the “Fermat” elliptic curve $$x^3+y^3=1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>x</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:mo>+</mml:mo> <mml:msup> <mml:mi>y</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , we develop an …