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Would you be kind enough to check if that version contains anything on calculating the length of the perimeter of an ellipse. Backstory, I was living in London
by I_complete_me 4y ago
Would you be kind enough to check if that version contains anything on calculating the length of the perimeter of an ellipse. Backstory, I was living in London in 1990 and this guy was trying to sell me & girlfriend a set of the E.B. I asked him to show me the article on the length of the perimeter of an ellipse and he ... well, he didn't. Later I discovered that it is a very tricky matter. But I wonder if there is anything in that version that mentions the difficulty.
- dehrmann 4y agoA lot of these problems in math with no exact solution could have an exact solution if we defined some new function. Another way, we wouldn't have exact solutions to the angles of a triangle from the length of the sides without the sine function. I wonder if any of these hypothetical functions have utility outside their specific problems.
- ars 4y agoFor anyone confused: There is no exact equation for the perimiter of a circle either. It looks like there is because we use Pi - but Pi is not exact, you need an infinite series to calculate it, just like you need an infinite series for the perimeter of a ellipse.
- perryizgr8 4y agoPI in itself is as exact as you desire it to be, the real world is unfortunately unable to handle infinite precision :)
- oplaadpunt 4y agoYes, but the point is the Pi is hiding an infinite series, just like the what you'd see for an ellipse length. The more interesting point for me is to phrase it as: why can't we write the lenght of an ellipse as some function of pi, since you're able to do that for most trig functions.
- ars 4y agoSee here for more on that: https://www.youtube.com/watch?v=5nW3nJhBHL0 https://www.youtube.com/watch?v=5nW3nJhBHL0 the info on calculating the actual value starts at 14 minutes (it's an infinite series).