Definition:Semicubical Parabola

Definition

The semicubical parabola is the plane curve whose locus can be described with the equation:

$y^2 = a^2 x^3$

Also known as

The semicubical parabola is also known as:

Neile's parabola, after William Neile

the cuspidal cubic.

Also see

• Results about the semicubical parabola can be found here.

Historical Note

The semicubical parabola was discovered and rectified by William Neile, who published his findings in $1657$.

In $1659$, John Wallis published the method he had used, giving William Neile full credit.

It was the first curve to be rectified, apart from conic sections and some of the spirals.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): semicubical parabola
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): semicubical parabola

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