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Roots of Unity

What’s so Great about Continued Fractions?

The continued fraction expansion for the number pi.

The more I learn about continued fractions, the more enamored I am with them. Last week, when I wrote about how much better continued fractions are than the arbitrary decimal digits we usually use to describe numbers, I mentioned that continued fractions tell us the “best approximations” of irrational numbers. Continued fractions are just fractions [...]

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Roots of Unity

Don’t Recite Digits to Celebrate Pi. Recite Its Continued Fraction Instead.


The digits of pi reciting contest is an all-too-common Pi Day event. And as this year is a once-in-a-century confluence of month/day/year with the first few decimal digits of pi, we might be in for more of those than usual. Our 10 fingers make decimal digits a natural choice, but if we were capybaras or [...]

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Roots of Unity

Romance, Continued Fractions, and You

About a month ago, I awoke from a dream totally psyched about the brilliant blog post I would write for Valentine’s Day. In my dream, I had seen the mathematical concept of continued fractions as a metaphor for romance, and I was shocked that no one else had ever written about the beautiful, natural correspondence [...]

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