Category Archives: arithmetic

Fibonacci’s Problem of the Birds

I have been enjoying reading Keith Devlin’s new book, Finding Fibonacci. I’ll write more about the book later. For now, I just wanted to share a nice problem I learned about which Leonardo Pisano, aka Fibonacci, included in his book … Continue reading

Posted in algebra, arithmetic, challenges, people | Tagged , , | 6 Comments

Sigma notation ninja tricks 2: splitting sums

[Previous posts in this series: jumping constants] Trick 2: splitting sums I’ve written about this before, but it’s worth spelling it out for completeness’ sake. If you have a sum of something which is itself a sum, like this: you … Continue reading

Posted in algebra, arithmetic | Tagged , , , , , | 3 Comments

Sigma notation ninja tricks 1: jumping constants

Almost exactly ten years ago, I wrote a page on this blog explaining big-sigma notation. Since then it’s consistently been one of the highest-traffic posts on my blog, and still gets occasional comments and questions. A few days ago, a … Continue reading

Posted in algebra, arithmetic | Tagged , , , , | 1 Comment

Games with factorization diagram cards

Since I published a deck of factorization diagram cards last September, a few teachers have picked up copies of the cards and started using them with their students. I’ve started collecting ideas for games you can play using the cards, … Continue reading

Posted in arithmetic, counting, games, pattern, pictures, primes, teaching | Tagged , , , , , | 4 Comments

The Möbius function proof, part 2 (the subset parity lemma)

Continuing from my previous post, we are in the middle of proving that satisfies the same equation as , that is, and that therefore for all , that is, is the sum of all the th primitive roots of unity. … Continue reading

Posted in arithmetic, combinatorics, complex numbers, primes, proof | Tagged , , , , , , , , , | 3 Comments

Factorization diagram cards are here!

It’s been a long process, but factorization diagram cards are finally available for purchase! If you just want to purchase a set right this minute, then click the above link! If you want to learn more, keep reading. History As … Continue reading

Posted in arithmetic, counting, pattern, pictures, primes, teaching | Tagged , , | 2 Comments

Factorization diagram card redesign: feedback welcome!

After getting a printed set of factorization diagram cards, I decided there were a few design tweaks I wanted to make. I’ve gone through a few iterations and I think they are definitely better now. Here are some representative samples … Continue reading

Posted in arithmetic, counting, pattern, pictures, primes, teaching | Tagged , , | 6 Comments