Here's one about electric current flow:

sonhouse
Posers and Puzzles 13 Aug '06 06:17
1. sonhouse
Fast and Curious
13 Aug '06 06:17
I was thinking of some of the problems I got in electronics 101 and came up with this one, I suppose its been done before but here goes:
you have a triangular pyramid, triangular base, 6 lines describes it.
So each of those 6 lines outlining the pyramid happens to be a one ohm resistor. So measuring from any apex to another apex will show the same resistance but what is that resistance? Each line is a 1 ohm resistor.
2. 13 Aug '06 07:26
0.5 ohm
3. XanthosNZ
Cancerous Bus Crash
13 Aug '06 09:01
You can solve this through repeated use of delta-wye conversions. You could also make a giant mess with mesh analysis.
4. XanthosNZ
Cancerous Bus Crash
13 Aug '06 09:411 edit
If anyone can solve this and wants a challenge then find the resistance of the three cases in a similar cube.

The cases being:

1. Between two points that share a side.
2. Between two points that share a face but not a side.
3. Between two points that don't share a face or a side.

Now solve for any regular polyhedron.
5. sonhouse
Fast and Curious
13 Aug '06 13:24
Originally posted by XanthosNZ
If anyone can solve this and wants a challenge then find the resistance of the three cases in a similar cube.

The cases being:

1. Between two points that share a side.
2. Between two points that share a face but not a side.
3. Between two points that don't share a face or a side.

Now solve for any regular polyhedron.
Don't forget the cases where the polygon is a solid resistance or the case where its only conductive on the surface but the whole surface is conductive and you measure any two points.
6. 13 Aug '06 15:07
Originally posted by sonhouse
you have a triangular pyramid, triangular base, 6 lines describes it.
So each of those 6 lines outlining the pyramid happens to be a one ohm resistor. So measuring from any apex to another apex will show the same resistance but what is that resistance? Each line is a 1 ohm resistor.
A tetraeder has 4 points, we name them A, the incoming point, and D, the outgoing point, and B and C the others.

Then from A to D the current can tacke this paths:
From A to D directly,
From A to B to D, and
From A to C to D.

No, those have the same potential so no current is flowing that way, right?.
Just cut that wire and there will be no difference.

Connect resistors in serial is R = R1+R2
Connect resistors in parallel is 1/R = 1/R1+1/R2
Each resistor R is here 1 ohm so you get:
1/Rtot = 1/R + 1/R+R + 1/R+R = 1/1 + 1/2 + 1/2 = 2
Rtot = 1/2 = 0.5 ohms.

Mephisto2 is right and this is the explanation.
7. sonhouse
Fast and Curious
13 Aug '06 16:17
Originally posted by FabianFnas
A tetraeder has 4 points, we name them A, the incoming point, and D, the outgoing point, and B and C the others.

Then from A to D the current can tacke this paths:
From A to D directly,
From A to B to D, and
From A to C to D.