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Does Mamikon's theorem have any good generalizations, say to higher dimensions?
by Sniffnoy 3y ago
Does Mamikon's theorem have any good generalizations, say to higher dimensions?
- mindcrime 3y agoI have no idea, but your comment does remind me of a joke I heard once: "If you want to look smart at a maths conference, just wait for the presenter to say something that everyone reacts to, then raise your hand ask 'Yes, but does it generalize?'" And no, there is no intent on my part to suggest that you are doing the equivalent of that here!
- eru 3y agoThat might be especially fun at a conference on 'generalised abstract nonsense', ie category theory.
- Sharlin 3y agoShame that nobody can come up with a meta-category theory because category theory is already its own metatheory.
- bordercases 3y agoDoes it scale though?
- mindcrime 3y agoMongoCalculus™ is Web Scale!
- Someone 3y agoThere’s “Volumes of Solids Swept Tangentially Around General Surfaces” (https://forumgeom.fau.edu/FG2015volume15/FG201504.pdf https://forumgeom.fau.edu/FG2015volume15/FG201504.pdf) by Tom M. Apostol and Mamikon A. Mnatsakanian (the “Mamikon” of this theorem)
- jameshart 3y agoThis Mathologer video talks about applying a similar approach to some 3D calculus problems - although the tangent swept shapes are arcs not triangles. https://www.youtube.com/watch?v=5q_sfXY-va8&t=0s https://www.youtube.com/watch?v=5q_sfXY-va8&t=0s The model of taking the same swept shapes and rearranging them into another shape whose area or volume is easy to calculate is the same approach though.
- lupire 3y agoI came to post this. Great channel. More in depth than 3B1B but less fancy animations. But he makes his videos in PowerPoint! Not a bullet point in sight, so Edward Tufte would allow it