All Questions
Tagged with plane-geometry curves-and-surfaces
7 questions
6
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Rigid plane curves
A curve is a continuous one-to-one image of the real line $\mathbb R$.
A space $X$ is rigid if the only homeomorphism of $X$ onto itself is the identity.
Is there a rigid curve in the plane?
I am ...
- 3,317
25
votes
1
answer
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Why is it so hard to prove Toeplitz' conjecture?
I'm a layman in mathematics, so please excuse me in advance for anything in this question that may be inappropriate :D. Well: Four years ago, I was reading (and working to solve the puzzles on) ...
1
vote
2
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When is the inside of a Jordan curve open? [closed]
I'm working purely on intuition here. The Jordan curve theorem states that a Jordan curve separates the plane into a bounded component and an infinite component. For toy curves, it seems like this ...
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-2
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Is the conjecture true for n-sphere $(n>2)$? [closed]
This is higher dimension conjecture of Problem 3845 in Crux Mathematicorum and Theorem 2 in here:
PS: This figure is very nice, this is also generalization of Brianchon’s theorem, The Pascal theorem, ...
- 39.9k
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2
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Planar curves identical to their inverses
Is the right strophoid
the only planar curve $C$ whose inverse curve w.r.t. some circle (in this case: centered on the origin)
is identical to $C$?
&...
- 188
1
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Intersection points of closed curves inscribed in a convex polygon
Suppose that I have two distinct simple closed curves, $C_1$ & $C_2$, and each is inscribed in a convex polygon, D. By inscribed, I mean tangent to each side of D. In particular, I am most ...
- 6,210
13
votes
1
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699
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Including a Jordan arc into a Jordan loop (Can the Magi go home by another way?)
The title refers, of course, to Matthew (2:12) ''And being warned in a dream not to return to Herod, they departed to their own country by another way''. To be honest, it is not that specific ...
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