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Cubical Parabola

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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.

See also

Cubical Ellipse, Cubical Hyperbola, Cubical Parabolic Hyperbola, Parabola, Semicubical Parabola

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References

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 215 and 223, 1987.Loomis, E. S. "The Cubic Parabola." §2.6 in The Pythagorean Proposition: Its Demonstrations Analyzed and Classified and Bibliography of Sources for Data of the Four Kinds of "Proofs," 2nd ed. Reston, VA: National Council of Teachers of Mathematics, pp. 28-29, 1968.

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Cubical Parabola

Cite this as:

Weisstein, Eric W. "Cubical Parabola." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CubicalParabola.html

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