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Jun
18
comment insphere/circumsphere ratio of a polyhedron the same as its dual polyhedron?
You may want to look at David Moews answer, which already covers all those shapes. Do you have anything to add that isn't already covered by that answer?
Jun
18
comment insphere/circumsphere ratio of a polyhedron the same as its dual polyhedron?
The original question already pointed out that the ratios seemed to be equal for the duals of the 5 Platonic solids. This answer shows that the ratios actually are exactly equal, which is nice to know. What about other dual solids, such as the triangular prism and its dual the triangular bipyramid, the cuboctahedron and its dual the rhombic dodecahedron, the Archimedean solids and their duals the Catalan solids, etc.?
May
19
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Apr
25
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Apr
18
answered If $f(t)$ is periodic, is there any $t$ that would equal to DC components?
Apr
5
awarded  Popular Question
Feb
18
answered In a finite field, is there ever a homomorphism from the additive group to the multiplicative group?
Dec
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Aug
19
answered Simulate repeated rolls of a 7-sided die with a 6-sided die
Aug
18
comment Simulate repeated rolls of a 7-sided die with a 6-sided die
@Daenyth: Huh? I see 35 non-X possibilities, 5 of them result in a 7, which gives the correct desired probability of 5/35 = 1/7 chance of resulting in a 7.
Aug
18
revised Simulate repeated rolls of a 7-sided die with a 6-sided die
clarified (I hope)
Aug
18
suggested approved edit on Simulate repeated rolls of a 7-sided die with a 6-sided die
Aug
18
comment Simulate repeated rolls of a 7-sided die with a 6-sided die
@cHao: Yes, sometimes we want exactly one fair 1d7 value, and you're right that it's impossible to do that with only 1 roll of a 1d6 dice -- we need at least 2, sometimes more, and andre shows an excellent algorithm for that case. However, if we want several hundred independent and fair 1d7 values, it is (theoretically) possible to derive those values from (on average) log(7)/log(6) =~ 1.09 rolls of a fair 1d6 die per desired 1d7 value. However, the algorithm to do that is complex and more difficult to prove that it gives fair, independent 1d7 values.
Jul
11
answered Why square units?
Jul
2
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May
19
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May
19
answered Why square units?
May
2
comment Platonic solids and charged particles
@LeeMosher: Min-Energy Configurations of Electrons On A Sphere says that N = 16 electrons has 2 local minima, but only one of them is the unique global minimum.