I've discovered Wolfram Alpha's widget builder. It's very easy to make little searches that help focus your readers (or students) on certian topics in Wolfram's massive database. Use the above to investigate the follium ... as I mentioned in an earlier post.
Look at the graph in the previous post. I was right! They don't intersect at a common point, rather the limit of the consecutive intersections is .
This is just numeric, from Mathematica ... I'll try to prove it later...
By the way an answer to the question of fining a curve orthogonal to the follium of Descartes is the reflection in the line . Do you know of any other trivial answers?
Goodnight! Tomorrow: Back to the generating functions, Owen has been bugging me!
, , ...
You get the idea. Naturally I want to know what those intersections are! I need to go for a run before it gets dark, but It seems that if we fix x=1 then as
Maybe the spots that look like common points aren't after all. Maybe it's just a very tight sequence of intersections.