Almost Convergence.

The title of my last post "Almost Cauchy Sequence" made me wonder if "Almost Cauchy" was already defined in some formal sense. I could not find much on "Almost Cauchy" ... but I did find out about "Almost Convergence." (I think I have ran in to this before... but it is very neat... observe:) A […]

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Looks can be deceiving!

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 […]

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Quickie.

A curve A is orthogonal to B is the tangent lines at their intersections are perpendicular. Thinking of the follium of Descartes again, give the equation for a function orthogonal to the follium. I have found one trivial answer that requires no complex calculations. (Do, you see it?) On the other hand, it's quite hard […]

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Rational points on the folium.

My students are studying implicit differentiation, we look at the folium of Descartes: They found the equation of the tangent at For their homework I want to have them look at another point, but I wanted it to be rational, I almost gave them the origin... But that's good. The expression given by implicit differentiation […]

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