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I would like to spiral wrap the columns in front of my home with Christmas lights. The answer I'm looking for is: If know the height of the column, the circumference and the length of the light string, how far apart do I space the spiral? column height: 90" column circumference: 54" length of lights: 56' (or 672")

I plan on installing wire hooks at these intervals on the back of the column. Let me know if I'm missing some information. THANKS!

davidf59
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  • You need to know how to compute the length of a helix (https://math.stackexchange.com/q/2160851) or (https://math.stackexchange.com/q/2307561) – Jean Marie Dec 04 '17 at 21:29

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If you imagine your ideal spiral, and "unroll" your column like a paper towel, then your lights will be the hypotenuse of a right triangle.

Imagine a right triangle with a hypotenuse of length $672$ and one leg of length $90$. The other leg will have length $\sqrt{672^2 - 90^2} \approx 666$. This is how much length you have to wrap around the circumference: you can wrap around $\approx \frac{666}{54}\approx 12.3$ "laps".

Thus, during each "lap" the lights go upward $\approx \frac{90}{12.3} \approx 7.3$ inches.

angryavian
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  • Makes perfect sense and that explanation took me back to my highschool classes before computers, heck, before the abacus. :) Thanks for the quick response!! – davidf59 Dec 04 '17 at 22:54