My sister had to do some artwork for school, and she decided to make some curved shapes out of lines. It looks pretty cool (although it would have been even better with pencil I think, but she wouldn’t listen, and I’m too lazy to do it myself right now), and making curves out of just lines, well, I find that pretty fancy. But I wondered what the curves actually were… Circles? Parabolas? Ellipses? Something different?
If you studied physics, one of the first things you probably did was graph the “motion” of objects. That is the displacement, velocity, and acceleration at an instant t. Didn’t it remind you of a mathematical concept?
After misunderstanding a question in physics, I thought I had to calculate the length of a curved trajectory (ie. the distance) instead of just the straight line (ie. the displacement). Turns out it was the easy option, but I now wanted to know how to get the length of a curve. I mean, it’d just be summing up an infinite number of straight lines, which is almost exactly what integration is…