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I can't work all the time... I need to goof off a bit to stay happy. I'm afraid this, together with working hard on some papers, has slowed down the production of lectures here.
This week I've been doing some recreational mathematics with some Greg Egan, Dan Piponi, John D. Cook and other people on Twitter. We've shown things like this:
$$ \displaystyle{\frac{32}{9 \pi}} \approx 1.13176848421 \dots $$
$$ \displaystyle{ \frac{2^{14}3^2}{5^3 7^3 \pi} \approx 1.0947335878 \dots } $$
You can see the whole story here:
Comments
What happens if you put the \(n\)-sphere under a deformation?
What happens if you put the \\(n\\)-sphere under a deformation?
I'm not sure what you mean, but it probably destroys all the delicate beautiful stuff we're talking about in these posts! It's like asking what happens to trig functions if you take the unit circle and squash it. There's probably some answer, but it ain't as pretty as trig functions!
I'm not sure what you mean, but it probably destroys all the delicate beautiful stuff we're talking about in these posts! It's like asking what happens to trig functions if you take the unit circle and squash it. There's probably some answer, but it ain't as pretty as trig functions!
Though that raises an interesting question, can we construct a canonical probability distribution on the "unit hyperbola" by using sinh and cosh?
Though that raises an interesting question, can we construct a canonical probability distribution on the "unit hyperbola" by using sinh and cosh?
Is it possible to devise some important link of this results , on the n-sphere, to antipodals and the Borsuk Ulam theorem? best
Is it possible to devise some important link of this results , on the n-sphere, to antipodals and the Borsuk Ulam theorem? best