All Questions
Tagged with plane-geometry euclidean-geometry
104 questions
6
votes
1
answer
676
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Does an origin-centered ellipse in the plane intersect each $L^p$-circle at most 8 times?
The question is in the title: Let $E$ be an origin-centered ellipse in ${\mathbb R}^2$ and let $S$ be an "$L^p$-circle": $S = \{(x,y) : |x|^p + |y|^p = \text{const}\}$, where $1 \leq p \leq \infty$. ...
CommunityBot
- 1
5
votes
3
answers
1k
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Finding an invisible circle by drawing another line
A friend of mine taught me the following question. He said he found it on a book a few years ago. Though I've tried to solve it, I'm facing difficulty.
Question: You know on a plane there is an ...
CommunityBot
- 1
10
votes
1
answer
231
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2-layer tilings with a center-of-gravity constraint
I've encountered a tiling problem with a physical constraint that
might place it outside the literature on tiling.
"Tiling" is a bit of a misnomer; it is a special type of cover.
All the tiles are ...
- 151k
6
votes
1
answer
373
views
Symmetric black-hole curves
Is there a curve $C$ that connects $(0,1)$ to $(a,0)$ for some $a>0$, and, when reflected
to $C'$ in the $x$-axis, the shape $S=C \cup C'$ has the property that each horizontal
light ray entering $...
- 45k