©2020 Compass Learning Technologies → Live Mathematics on the Web → GXWeb Curve Construction Collection → GXWeb Limaçon of Pascal
GXWeb Limaçon of Pascal
Saltire Software, home of Geometry Expressions and GXWeb
GXWeb Curve Construction Collection (like this one!)
About the Limaçon (from Wolfram MathWorld)
\(a\) 0 0 10 \(b\) 0 0 10 \(\theta\) -1.57 0 1.57
The Limaçon of Pascal is defined as a roulette formed by the path of a point fixed to a circle when that circle rolls around the outside of a circle of equal radius. The cardioid is the special case in which the point generating the roulette lies on the rolling circle; the resulting curve has a cusp.
Worth noting that the Limaçon (from the French word for snail) is actually named, not after the famous Blaise Pascal, but after his father, Etienne!
The Limaçon constructed here is the locus of points A and D where
\(a = Length(OC) = Length(BC)\)
\(b = Length(AB) = Length(BD)\)
and \(angle(DOC) = \theta\).
Cartesian equation: \[X^4+Y^4-4\cdot X^3\cdot a-4\cdot X\cdot Y^2\cdot a\]\[=Y^2\cdot b^2-X^2\cdot (2\cdot Y^2+4\cdot a^2-b^2)\]
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 Limaçon of Pascal