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CTK Exchange
Deep G
Member since Nov-6-05
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Dec-03-05, 03:17 AM (EST) |
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"Physics-based solution to Fermat pt. finding problem."
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Hi, tie one end of three identical pieces of thread together. That shud loo like - \******/
*\****/
**\**/
***\/
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( Spare me for my 'not so well' drawing ! The '*' are for proper indentation) on a horizontal table attach 3 pulleys at the three vertices of the triangle whose fermat's pt. is to be located. pass the free ends of the 3 threads over the pulleys and attach equal weights at those ends. When freely suspended, the system comes into equilibrium when the tied end of the 3 threads coincides with the fermat point. I hope I am correct...What say? d:-)
Deep G
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mpdlc
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Dec-04-05, 05:25 PM (EST) |
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1. "RE: Physics-based solution to Fermat pt. finding problem."
In response to message #0
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A few years ago, I saw this problem solved in small russian book author Y.A.Uspenki. The solution is based in the minimum potential energy for the three masses. I am more than sure Alex will know about it and he can explain it in better words than me. The problem in the book is referred where to locate a facility building, so the total distance from three villages were minimal, considering different number of inhabitants for each village and it is solved using weights proportional to each population.
The Fermat point is obviously a particular case of it, since all the population are the same.
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mpdlc
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Dec-15-05, 07:21 PM (EST) |
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3. "RE: Physics-based solution to Fermat pt. finding problem."
In response to message #2
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Thank you Alex for the links it does cover even more cases, some of its content was absolutely new for me. I knew for sure you were well informed. |
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