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Cake day: June 5th, 2025

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  • You’re right that using geometry and ratios is only good for a few digits of π. Some ancient mathematicians used to draw polygons on the inside and the outside of a circle, and then use the circumferences of those polygons as an upper or lower limit on what π was. Archimedes approximated π as being between 223/71 and 22/7, using 96-sided regular polygons.

    The real breakthroughs happened when people realized certain infinite series converge onto π, where you add and/or subtract a series of smaller and smaller terms so that the only digits of the sum that changes with each additional term are already way to the right of the decimal point.

    The Leibniz formula, proven to converge to π/4, is 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 . . .

    So if you have a pen and paper, you can add and subtract each one in sequence, and eventually they get really small to where you’re adding and subtracting numbers so small that it leaves the first few digits untouched. At that point you can be confident that the digits that can’t change anymore are the right digits.

    Later breakthroughs in new formulas made much faster convergences, so that you didn’t have to make as many calculations to get a few digits. And computers make these calculations much, much faster. So today the computer methods generally use the Chudnovsky algorithm that spits out digits of 1/π, which can easily be converted to digits of π itself.




  • A lot of young people don’t realize just how difficult post-school dating was before online dating. Once we exhausted the pool of 5-10 single people who were friends of friends, that was basically it. We’d have to go find strangers at the bar.

    That conditioned everyone to be slightly more willing to settle for less perfect matches, knowing that there wasn’t necessarily a replacement available. That could be a good thing (people more likely to have the patience to let a spark develop) or a bad thing (a higher percentage of couples who just resented each other).

    I can see an argument that things were better before online dating for some subset of people. But having lived that period, I can say from experience that it wasn’t easy then, either. And for someone like me, who is a better writer than I am a speaker, especially over the phone, the rise of text-based communication was helpful for navigating the early stages of relationships when that became the norm.