Category Archives: geometry

Complex multiplication and roots of unity

If played around with the question from my previous post, you probably found something like the following: That is, as the powers of we get , , and with all possible sign combinations. Of course, since , if we continue … Continue reading

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Complexifying our dots

It’s time to up our game a bit. Previously we have considered some cool pictures with dots and bespoked circles, looking for patterns, without really considering what sort of mathematical objects these circles might represent. In fact, they turn out … Continue reading

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Totient sums

I took a bit of a break to travel to Japan for a conference, but I’m back now to continue the series I started with Post Without Words #10, a follow-up post, and Post Without Words #11. Recall that we … Continue reading

Posted in geometry, pattern, pictures, posts without words, proof | Tagged , , , , , | 3 Comments

Post without words #11

Posted in geometry, pattern, pictures, posts without words, proof | Tagged , , , , , | 7 Comments

A few words about PWW #10

If you still want to think more about the picture in my previous post, stop reading now! Here’s a simple way to think about how the picture is made, as noted by Fergal Daly. The th circle (starting with ) … Continue reading

Posted in geometry, pattern, pictures, posts without words | Tagged , , , | 5 Comments

Post without words #10

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Post without words #9

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