[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 343
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P.S. I doubt very much that even the "pure" problem of finding a package of circles of equal diameter such that the large circle encompassing it has the minimum area (or minimum diameter) has been solved in general form.
In fact, a 'clean' solution could be useful. I have not encountered any calculation software either, there are only calculation tables. The task is not to determine the cable diameter by cross-section, but to determine the diameter of the thermowell by the outer diameter of the cables (assume that the cross-section is the same and the cross-section is a circle).
Here is a real example: We need n CONTROL cables (low-capacity) with diameter d to be pulled between the floors - you need to select a thermowell D and make a hole accordingly. And this diameter should not exceed dimension X (you need to create a separate task for constructors, which is too much trouble). It's also not correct to multiply holes in the floor for safety reasons. That's why I wanted to know if there is a mathematical best solution in pure approximation?
qwerty, I don't even know from which angle to approach this problem. Show me the optimal packing for 8 circles :)
well this is only rough, only for a large number of cores
There is one classic unsolved problem in mathematics, the Lebesgue problem. The formulation is simple:
Find a figure of minimal area covering any figure of diameter 1.
The diameter of an arbitrary figure is the maximum distance between its points.
Mischek, ты забыл возвести D в квадрат.
Damn, that was a rush, it's not D, it's S (internal area of the cartridge case) and D is clear.qwerty1235813, as an approximation, the inner diameter of the sleeve is calculated as follows:
D=1.7*d*sqrt(n);
Of course, this is for control cables or any other round low-current cables, not for power cables.
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Example: Let's assume there are 9 RG-6u cables. The diameter of the cable is 6.5 mm. The diameter of the bundle is 33.2 mm.
So take PVC pipe with an outside diameter of 40 mm. No allowance has been made here.
Thank you all!
For the numbers 1, ..., 1999 arranged on a circle, calculate the sum of the products of all the sets of 10 numbers in a row. Find the arrangement of the numbers that gives the greatest sum.
ihor, you can't get any prettier with squares. OK, fine!
For the numbers 1, ..., 1999 arranged on a circle, calculate the sum of the products of all the sets of 10 numbers in a row. Find the arrangement of the numbers that gives the greatest sum.
You can't even know which way to look at it. There are a lot of permutations. Intuition says that it's not a 1, 2, 3, 4, 5, 6, 7 .........1998, 1999. And since it is a circle - a closed straight line, it is more likely that the arrangement must be symmetrical.