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comment |
Which platonic solids can form a topological torus?
@Tracy-Hall, my eyes must be missing the reference to the 1972 paper on this page. What/where exactly is the paper you're referring to? Thanks for the Martin Garner reference. |
Jan
5 |
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Flux through a Mobius strip
@Scott-Carnahan, the Mobius resistor concept missing the fact that the only resistance being provided between two leads connected to it is the internal resistance of the conductor. In electrical circuit modeling, you take the resistance between two components connected to the same lead to be $0$ (zero). There's no need to worry about "self-inductance" with a mobius resistor because you're also connecting to the same side of a capacitor. It might act a little bit like an antenna perhaps, but not as a resistor in any useful sense of the word. A mobius resistor is a short circuit. |
Jan
5 |
answered | Flux through a Mobius strip |
Jan
5 |
comment |
Autocorrelation of a ±1-valued random process with certain statistics
Why do you make the statement or the claim that the switches are not independent here? Obviously, switches between $+1$ alternate with $-1$, so in one sense of sequence alone with disregard to the time between the sign changes there is a predictable component: $+1$ follows $-1$ follows $+1$... However, the time interval between the sign changes is still a random variable, isn't it? Also, the $\LaTeX$ command you want for $\pm$ is \pm, not \plusminus |
Dec
31 |
comment |
Floating polyhedra with fair equilibria
Prismatic die with a regular polygon bases would also exhibit the same behaviour with each prismatic face equally likely to float "up" with the $2$ flat polygon-base faces less likely to float "up" as long as the height of the prismatic die is larger than $ar$ where $r$ is the "radius" of the polygonal base. Extreme example 1: wooden nickel is going to float face up or face down, not very likely to float on its edge. Extreme example 2: hexagonal wooden pencil dowel (without metal/rubber eraser nub) is going to float with one of its prismatic faces "up" rather than one of the end faces. |
Dec
31 |
comment |
Floating polyhedra with fair equilibria
If the height is greater than $ax$, than the triangular sloped faces of the pyramid are all equally likely to be the "face up" stable face, with the "base face" unlikely to be the "face up" face. |
Dec
31 |
comment |
Floating polyhedra with fair equilibria
This square-based (or more-sided regular polygon base pyramid) would also have a second equilibrium point with the pointy pyramidal tip facing up, but that equilibrium would be an unstable equilibrium whereas the equilibrium with the pyramidal base facing upwards is a stable equilibrium. |
Dec
31 |
answered | Floating polyhedra with fair equilibria |
Dec
31 |
comment |
Floating polyhedra with fair equilibria
So you're asking if there are preferred orientations of floaty objects like ice-cubes and ice-bergs, particularly if they're shaped into polyhedra? |
Dec
31 |
comment |
Happy New Prime Year!
@Ricardo and @Wadim-Zudilin, yes the numerologists will see a way to make every year interesting, and the paradox of the first un-interesting year becoming interesting because of the fact that it is the first un-interesting year. ;>) Also, see Mayan, Hebrew, Chinese, Indian, and many other cultural artefacts for different origins and phase-shifts for yearly and weekly and monthly calendar objects. It's amazing how human beings have dissected the night sky and the numbers we pluck out of the sky and thin air. |