And that's why you need maths.

When I was starting to study archaeology, I was happy to leave some of my less favourite school subjects behind me. Those included chemistry and maths.

One of my companion subjects with archaeology was heritage conservation, though, and that included "Bauforschung" - documentation and analysis of historical buildings. For that, one of the things you do is draw an accurate plan of floors, walls, and so on. Which means you will need to measure. Everything.

And then... there was this complex process of taking the distances and the angles you had measured, along your main lines or around the outside of the building, and calculate whether your measurements were accurate enough or not. It included things like sinus and cosinus and tangens, and when the prof explained it, you could hear half the room go "aaaaooouuugh". There I was, thinking I'd happily escaped those numbers and calculations... until said day.

Guess what I needed these days? More of those old and slightly dusty maths skills, especially that stuff about angles. So much of maths skills, unfortunately, that I also needed the assistance of the Most Patient Husband of Them All, who graciously agreed to help me tackle a complex formula to calculate the typical spinning angles of industrially-spun warp yarns from wool. (To my great delight, my calculations were not completely wrong. In fact, all I had not done was an additional, and not-really-obvious step to transform kilometres into metres. That step was so non-obvious that it also took my husband a while to track down the cause of the impossible result and figure out why it had happened.)

Oh, and the result of that formula-cracking? Warp yarn angles run between about 14.7° and 17.1° - while medieval yarns usually are above 30°, and very frequently at about 40°. No wonder modern spinners tend to spin soft stuff, it's the only thing we are used to!