MF79: Calculus on a cubic: the Folium of Descartes

[alexzarhin]

Hello.

We all know how important tangent lines are.

Could you explain please where tangent conics can be used?

What is the motivation to study them, except of their beautiful properties?

[recursion11]

Hello norman.

If the set of natural numbers cannot be a completed whole, then how do you know that all natural numbers have a successor? Or that all even numbers are of the form 2n where n is some natural number? In fact, none of the theorems in mathematics seem provable for all of anything, because there objects are infinite.

Thanks

[DanPartelly]

For anyone wanting to play more and have fun with beautiful curves , Google search "Fifty Famous Curves, Lots of Calculus Questions, And a Few Answers".

[njwildberger]

@DanPartelly Thanks for that reference, it is an informative article. One should perhaps also mention two classic texts: A Catalog of Special Plane Curves by Lawrence (1972) and A Book of Curves by Lockwood (1961). It seems a nice project to compute some tangent lines/conics/cubics to the quartic curves that appear in these references, and see what interesting things happen with them.