Tschirnhausen cubic
Plane Curves
Description
Tschirnhaus's cubic is the negative pedal of a parabola with respect to the focus of the parabola. The caustic of Tschirnhaus's cubic where the radiant point is the pole is Neile's parabola.
Object definitions
Mapping
- TeX
- MathML
- Mathematica input
- Maple input
\left\{x\to a \left(1-3 t^2\right),y\to a t \left(3-t^2\right)\right\}
<math>
<mrow>
<mo>{</mo>
<mrow>
<mrow>
<mi>x</mi>
<semantics>
<mo>→</mo>
<annotation encoding='Mathematica'>"\[Rule]"</annotation>
</semantics>
<mrow>
<mi>a</mi>
<mo>⁢</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mrow>
<mn>3</mn>
<mo>⁢</mo>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
<mo>,</mo>
<mrow>
<mi>y</mi>
<semantics>
<mo>→</mo>
<annotation encoding='Mathematica'>"\[Rule]"</annotation>
</semantics>
<mrow>
<mi>a</mi>
<mo>⁢</mo>
<mi>t</mi>
<mo>⁢</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>3</mn>
<mo>-</mo>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
</mrow>
<mo>}</mo>
</mrow>
</math>
{x -> a*(1 - 3*t^2), y -> a*t*(3 - t^2)}
[x = a*(1-3*t^2), y = a*t*(3-t^2)]
Constants
- TeX
- MathML
- Mathematica input
- Maple input
\{a\}
<math>
<mrow>
<mo>{</mo>
<mi>a</mi>
<mo>}</mo>
</mrow>
</math>
{a}
[a]
Cite this as:
Plane Curves: Tschirnhausen cubic from Differential Geometry Library. http://digi-area.com/DifferentialGeometryLibrary/PlaneCurves/Tschirnhaus-Cubic.php
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