As seen it forms a loop in the first qudrant of the cartesian plane [which I also designed] with a double point at the origin and an asymptote.
This algebraic curve is represented by the equation:
x^3+y^3-3axy=0
I discovered this form of calculus when challenging Fermat to find the tangent line of a curve at an arbitrary point since Fermat has just discovered a method for finding tangent lines.
Although Fermat was able to solve the problem easily, i was able to determine that the slope of the tangent line can be found easily using implicit differentiation.
"I think therefore I am"
- Rene Descartes
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