A Helical Hassle!

A Helical Hassle!

Posers and Puzzles

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R
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8528
07 May 21
1 edit

A string is wound symmetrically around a circular rod ( common helix ). The string goes exactly š‘› times around the rod and the rod has a circumference of š‘› and a length of 3š‘›

Find the value of š‘› for which the length of the string is 20.

Assumptions: neglect any dimension of the string itself.

Standard memberBigDogg
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10 May 21

@joe-shmo

Basically, we are solving a right triangle of hypotenuse 20 and other sides n and 3n. 9n^2 + n^2 = 400; n^2 = 40; n = 2 sqrt 10

R
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10 May 21

@BigDoggProblem

On the right track. š‘› is an integer

Still open.

Standard memberBigDogg
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@joe-shmo

I think I have it now. Starting equation is nā“ + 9n^2 = 400. Solving for n, I get n=4.

R
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10 May 21

@BigDoggProblem

Now you got it!