Endangered Specie
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Thu Sep-16-04 08:07 PM
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Pi * d to the fourth power all over 32 ((pi*d^4)/32) |
unblock
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Thu Sep-16-04 08:11 PM
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1. you figured out how to square the circle? |
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Thu Sep-16-04 08:12 PM
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LynzM
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Thu Sep-16-04 08:12 PM
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2. Erm, dammit, I knew this! |
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At least, I think I knew this.... dammit, nope, I'm imagining things again.
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X_republican
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Thu Sep-16-04 08:13 PM
Response to Original message |
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Edited on Thu Sep-16-04 08:14 PM by X_republican
one.
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Thu Sep-16-04 08:17 PM
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5. volume of a 4-dimensional sphere? |
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Edited on Thu Sep-16-04 08:18 PM by unblock
pi*(d^4)/32 = pi^((2*r)^4)/32 = (16*pi*r^4)/32 = (pi*r^2^2)/2
pi*r^2 of course is the area of a circle. you've squared this so you've added 2 dimensions, so it's a 4-dimensional sphere.
i'm guessing volume.
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Thu Sep-16-04 08:25 PM
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7. The volume of a 4-d sphere would be infinity I believe... |
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(I got this from a Civil Engineering class, so I doubt it has to do with 4-d objects)
But assume you really meant a 4-d "volume".
Anyways
(pi*r^2)^2 = (pi*d^2/4)^2 = (pi^2*d^4)/64
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Thu Sep-16-04 08:41 PM
Response to Reply #7 |
10. might have to punt, i know zero about civil engineering. |
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does that mean this has something to do with building bridges?
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Thu Sep-16-04 08:49 PM
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11. It has to do with Torsion in a beam. (answer inside) |
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"Polar Moment of Inertia" (I-sub-p) used in this equation: Shear stress = Torque*radius / I-sub-p IF your are trying to find the shear stress in a (cylindrical) beam of given radius and some applied torque... Important to know if that shear stress is more than the beam can take without breaking.
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unblock
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Thu Sep-16-04 08:52 PM
Response to Reply #11 |
12. does this mean how high can i rev my engine before the axle snaps? |
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Thu Sep-16-04 09:02 PM
Response to Reply #12 |
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the person who designed it put an axle that could withstand the torques the engine was capable or producing, but, in a way that situation does apply.
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unblock
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Thu Sep-16-04 08:26 PM
Response to Reply #5 |
8. after a little googling, |
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the sources i'm finding from math geeks, not necessarily authoritative, but it looks like the volume of a 4-dimensional sphere is
(pi^2*r^4)/2
which is equal to what you've got except you have pi instead of pi^2.
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Thu Sep-16-04 08:32 PM
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9. Only trouble is I didnt get this from a math class |
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Although the coincidence is interesting.
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onebigbadwulf
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Thu Sep-16-04 09:12 PM
Response to Reply #8 |
14. Spheres are 3 dimensional |
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its the formula for a sphere.
4-d includes time which this formula does not.
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Thu Sep-16-04 09:24 PM
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a fourth dimension is a mathematical concept, having many theoretical and practical manifestations.
time as the fourth dimension, (with length, width, and depth being the first three) is merely one such manifestation (and application of a mathematical concept to physics.)
it's not true that a fourth dimension is not represented in the formulas we're discussing, nor is it the case that there can't be a meaning that applies one of those dimensions to time.
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jfalchion
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Thu Sep-16-04 08:17 PM
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