Definition:Folium of Descartes/Cartesian Form
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Definition
The folium of Descartes is the locus of the equation:
- $x^3 + y^3 - 3 a x y = 0$
Also presented as
The equation defining the folium of Descartes can also be presented as:
- $x^3 + y^3 = 3 a x y$
Also see
- Results about Folium of Descartes can be found here.
Source of Name
This entry was named for René Descartes.
Historical Note
Marin Mersenne had communicated to René Descartes the method devised by Pierre de Fermat for calculating the tangent to a curve.
René Descartes seems to have thought little of this method, believing that it was not sufficiently general to be useful.
The curve now known as the folium of Descartes was used by him as a challenge to Fermat, believing that he would be unable to use this method on it.
Reportedly he was seriously annoyed at Fermat when the latter solved it without any trouble.
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 11$: Special Plane Curves: Folium of Descartes: $11.24$
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.13$: Fermat ($\text {1601}$ – $\text {1665}$)
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $6$: Curves and Coordinates: Cartesian coordinates
- Weisstein, Eric W. "Folium of Descartes." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FoliumofDescartes.html