GXWeb Trifolium

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About the Trifolium (from Wolfram MathWorld)

$r$
	0	5	10
$\theta$
	-3.14	1.58	3.14

App generated by GXWeb

A Trifolium (from the Greek for "three leafed") is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle.

The Trifolia constructed here are the locii of points E (inner trifolium) and F (outer trifolium) where

$r = Length(OA)$

radius of circle with centre C = $\frac{r}{3}$

and $angle(AOB) = \theta$ .

Line DE(F) makes an angle of $\pi-3 \cdot \theta$ with the y-axis.

Cartesian Equation 1 (inner): $3·X^4+6·X^2·Y^2+3·Y^4+X^3·r-3·X·Y^2·r$

Cartesian Equation 2 (outer): $12·X^4+24·X^2·Y^2+12·Y^4+4·X^3·r$ $-12·X·Y^2·r-9·X^2·r^2-9·Y^2·r^2+r^4$

GXWeb Trifolium

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WolframAlpha: CAS+

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