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Things of interest in Maths & Science

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When you add times of the day together, the sums you do are somehow unusual. For example 11pm plus 6 is not 17pm, but 5am the next day! In some sense 11+6=5. This is called clock or modulo arithmetic, what counts is the remainder when you divide by 12. This picture shows some of the structure in arithmetic modulo 37. Each section is what happens to the numbers when you raise them to different powers. For example in the top left the power is 1, every number gets sent to itself. The structure in the right hand side is closely related to Fermat’s Little Theorem. [my code for those interested]

When you add times of the day together, the sums you do are somehow unusual. For example 11pm plus 6 is not 17pm, but 5am the next day! In some sense 11+6=5. This is called clock or modulo arithmetic, what counts is the remainder when you divide by 12. This picture shows some of the structure in arithmetic modulo 37. Each section is what happens to the numbers when you raise them to different powers. For example in the top left the power is 1, every number gets sent to itself. The structure in the right hand side is closely related to Fermat’s Little Theorem. [my code for those interested]

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Matt Henderson

I post original stuff about maths, space, computational linguistics and other things that I like. This blog is meant to be accessible and interesting to people of all backgrounds. My undergrad was maths in Cambridge, and I'm now starting research in Speech and Language technology. Email me at If you're new, check out this overview of my posts. All code posted is in Mathematica.

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