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Results tagged with mg.metric-geometry
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user 3206
Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
0
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Can different bicycles leave the same tracks?
Perhaps circular tracks should also be excluded?
Gerhard "Ask Me About System Design" Paseman, 2010.01.15
- 3,209
1
vote
Regular polygon shadows of convex polyhedra
I've decided to expand my comments into a challenge. Hopefully those with the skills and interest will take it up and provide some definite answers for Joseph.
Take two polygons (with two distinct n …
- 3,209
1
vote
Regions on a sphere that avoid a fixed point set
This is the germ of an answer to suggest that a connected but not simply connected region R can be built that may have arbitrarily large area, and in any case an area larger than that occupied by the …
- 3,209
1
vote
what-if.xkcd.com: stabbing (simply connected) regions on the 2-sphere with few geodesics
Here is a suggestion following the idea of the original poster to show for the given instance that four is too low a bound. Assume that four geodesics suffice and aim for a contradiction as follows:
…
- 3,209
1
vote
get a point in polygon (maximize the distance from borders)
You seem willing to accept non-optimal solutions as long as they lead to optimal solutions. For convex polygons, I suggest using a midpoint method: pick pairs of vertices (ideally they are presented …
- 3,209
2
votes
Approximating a real by a ratio of primes
Here is an idea which might help show that the smallest prime is not much larger than the smallest integer needed.
One of the processes I like to use is the mediant $\frac{a+c}{b+d}$ of two positive …
- 3,209