©2020 Compass Learning Technologies → Live Mathematics on the Web → GXWeb Curve Construction Collection → GXWeb Trifolium
GXWeb Trifolium
Saltire Software, home of Geometry Expressions and GXWeb
GXWeb Curve Construction Collection (like this one!)
About the Trifolium (from Wolfram MathWorld)
\(r\) 0 0 10 \(\theta\) -3.14 0 3.14
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): \[ 12·X^4+24·X^2·Y^2+12·Y^4+4·X^3·r\]\[-12·X·Y^2·r-9·X^2·r^2-9·Y^2·r^2+r^4 \]
Try this yourself with the tools below...
Construct your own Model with GXWeb
WolframAlpha: CAS+
The powerful Wolfram Alpha online CAS engine will answer almost anything you care to ask - within reason! From the continued fraction of pi to Solve x^2=x+1 to the population of Australia!
Behind the Scenes
©2020 Compass Learning Technologies ← Live Mathematics on the Web ← GXWeb Curve Construction Collection ← GXWeb Trifolium