Christmas is here - How much Garland do I need?

Question

Christmas is here and so are a lot of questions.

I'm trying to wrap around a column with Christmas lights and garland.

What would be the equation I should use to figure out the length of garland needed?

Thanks

Answer 1

Let R be the diameter of the Column. We assume R is a constant, otherwise we will need more info about the dimensions of the column.

Let t the spacing between the windings.

Let N represent the number of windings.

Let L represent the total length of the garland needed.

Recall Pythagorean's relation for a right triangle: a² + b² = c²

Using the equation for the circumference of a circle, we get C=2πR for the approximate length of the first winding. Taking into account that the spacing between windings is t, we can use Pythagorean's formula to improve the length of the first winding: C^{2 = (}2πR)² + t². Hence, we have the answer:

L = N ⋅ C = N ⋅ √C^{2 =} N ⋅ sqrt⁽⁽2πR)² + t²⁾