Oh, yeah, to be clear I use math (well, I apply mathematical algorithms and formulas) many times a day. But the ROI for my time spent on formal math eduction peaks somewhere around 3rd grade and declines fast after that.

I (genuinely) wonder how much that is attributable to having no actual use for other math, vs

1. not having been taught math early enough for it to be second nature

2. not having been taught useful every day applications of the math so as to keep practicing it

I've also forgotten quite a bit of math, but I also frequently encounter scenarios where I acknowledge that having a better handle on it would be advantageous to myself or others. For example, a better understanding of statistics and probability would certainly help political discourse in our society.

>The most complex was when I used some trig to calculate the angle at which I had to wrap a square column with christmas lights to ensure I covered the column from top to bottom with a single string and no excess.

that doesn't seem trivial at all.. wonder how that's done.

The length l of the Christmas lights is the hypothenuse of a rectangular triangle of height h, the height of the column. So, if the slope angle is α, we have sin(α) = h/l, or α = arcsin(h/l).

Soundness check: that doesn’t have a solution if h > l. Looks good.

does this assume the xmas tree is shaped like a column or a cone?

edit: ah, i re-read the original problem and it does mention column. i thought it was a xmas tree that was being wrapped.

That would be harder, yes. Reading https://en.wikipedia.org/wiki/Conical_spiral#Slope, you want a logarithmic spiral (you need a constant angle to make the problem make sense)

Luckily, arc length isn’t too gnarly for those (same Wikipedia page), but you still have one equation with two variables.

I would have to think hard about whether those give you a unique solution.

I also doubt that spiral would give you uniform coverage of the cone (and that probably, is the real requirement, not constant angles), but again, I would have to do some thinking.

oh, interesting variation for uniform coverage! that is indeed what i'd want for the tree. in building a road around a cone, a constant angle would be more desirable.

Suppose you’ve got a 16 foot strand of lights and an 8 foot column. If you unwrap the column in your mind, you can see you’ve got a right triangle with a hypotenuse of 16 and vertical leg of 8. What’s the angle that the hypotenuse makes with the floor? It’s the angle whose sine is opposite/hypotenuse = 8/16 = 1/2. That’s 30 degrees. So wrap the lights around the column at a 30 degree angle and it’ll be close (with a bit of slop thanks to rounding corners on the column).

my xmas isn't shaped like a column, it's a cone.

edit: ahh, the original question was for a column. i misread it and thought it was for a xmas tree.

If you unwrap a cone you get a circular sector. Similar idea.

Years ago I had to correct a Bridge design I was tasked with writing a program to draw out the complex curved shape.

The engineer had used 2d instead of the 3d formulae :-)