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Cubical Parabola

DOWNLOAD Mathematica Notebook CubicalParabola

An equation of the form

y=ax^3+bx^2+cx+d,
(1)

where the three roots of the equation coincide (and are therefore real), i.e.,

y=a(x-r)^3=a(x^3-3rx^2-3r^2x-r^3).
(2)

Loomis (1968, p. 28) considers a cubical parabola of the form

x^3-3x-2a=0,
(3)

which can be used for angle trisection.

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