Linked Questions
11 questions linked to/from Conway's lesser-known results
406
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85
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Proofs without words
Can you give examples of proofs without words? In particular, can you give examples of proofs without words for non-trivial results?
(One could ask if this is of interest to mathematicians, and I ...
19
votes
4
answers
1k
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Representation theorem for modular lattices?
Birkhoff's representation theorem implies that every distributive lattice embeds into the lattice of subsets of a set. Is there also some representation theorem for modular lattices?
For example, I ...
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27
votes
1
answer
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An anecdote by R. Schmidt
Did anybody here ever read those lines by R. Schmidt (?) where he talked about the terseness of articles in group theory in the days prior to the conclusion of the classification of the finite simple ...
20
votes
3
answers
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The Angel and Devil problem with a random angel
In the classic version of Conway's Angel and the Devil problem, an angel starts off at the origin of a 2-D lattice and is able to move up to distance $r$ to another lattice point. The devil is able ...
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8
votes
2
answers
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What's the name of this geometric mathematical modeling problem?
There is a right angle corner with width 1 in both directions. One wants to find the largest area shape which can pass through this corner.
I know that this is a famous problem, but what is it called?
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37
votes
1
answer
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Sofa in a snaky 3D corridor
What is the largest volume object that can pass though a
$1 \times 1 \times L$ "snaky" corridor, where $L$ is large
enough to be irrelvant, say $L > 6$.
...
- 151k
20
votes
0
answers
814
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Series for envelope of triangle area bisectors
The lines which bisect the area of a triangle form an envelope as shown in this picture
It is not difficult to show that the ratio of the area of the red deltoid to the area of the triangle is $$\...
- 842
6
votes
2
answers
515
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On 'fair bisectors' of planar convex regions
Definitions (https://www.ias.ac.in/article/fulltext/pmsc/122/03/0459-0467):
Given a planar convex region $C$ (could be smooth or polygonal), an area bisector of $C$ is any line that partitions $C$ ...
- 5,979
2
votes
1
answer
224
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Self-intersecting path of stacked regular tetrahedra
(This question occurred to me after reading
@IanAgol's reminisces
of Conway's spiral tetrahedron billiard path.)
Let $T_i$ be a regular tetrahedron,
and $P$ a collection of regular tetrahedra
glued ...
- 151k
3
votes
1
answer
418
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Generalization of Tucker circle, Conway circle and van Lamoen circle
Theorem 9.1 in this paper as follows is a generalization of Turker circle. Turker circles is a generalization of many circles as: Cosine Circle, circum circle, First Lemoine Circle, Gallatly Circle, ...
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25
votes
1
answer
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Is there an inventory of closed billiard paths in a regular tetrahedron?
Conway found a closed billiard-ball trajectory in a regular tetrahedron:
Image: Izidor Hafner
Since then Bedaride and Rao
Bedaride, Nicolas, and Michael Rao. "Regular simplices and periodic ...
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