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Comment by drgoodvibe | Hacker News Reader

I’m fortunate enough to have a an entire set from 1989 that my father bought for me and my older sister. I refuse to get rid of it. At the moment the set is in my old bedroom in my parents house but one day I intend to feature it prominently in my library.. it’s funny how one can get attached like that.

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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 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.

A 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.

For 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.

PI in itself is as exact as you desire it to be, the real world is unfortunately unable to handle infinite precision :)

Yes, 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.

See here for more on that: https://www.youtube.com/watch?v=5nW3nJhBHL0 the info on calculating the actual value starts at 14 minutes (it's an infinite series).

The Great Books are a treasure in and of themselves. The Syntopicon--now there's two volumes I'd like to see on Internet Archive.

Complete scans of Harvard Classics, a notable predecessor to Britannica’s Great Books collection, are available on the Archive: https://archive.org/details/harvardclassics?tab=about

Standard Ebooks also has a growing collection of formatted epubs of the Great Books—necessarily incomplete, as much of the full set is still copyrighted. https://standardebooks.org/collections/encyclopaedia-britann...

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