Category Archives: pattern

Finding the repetend length of a decimal expansion

We’re still trying to find the prefix length and repetend length of the decimal expansion of a fraction , that is, the length of the part before it starts repeating, and the length of the repeating part. In my previous … Continue reading

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Finding the prefix length of a decimal expansion

Remember from my previous post that we’re trying to find the prefix length and repetend length of the decimal expansion of a fraction , that is, the length of the part before it starts repeating, and the length of the … Continue reading

Posted in number theory, pattern | Tagged , , , , | 3 Comments

Finding prefix and repetend length

We interrupt your regularly scheduled primality testing to bring you something else fun I’ve been thinking about. It’s well-known that any rational number has a decimal expansion that either terminates, or is eventually periodic—that is, the digits after the decimal … Continue reading

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Post without words #23

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Some words on PWW #22

There are lots of patterns to be found in the picture from my previous post! This is a really remarkable tiling. Here are a few special properties I know of: First of all, I hope you realized that the pattern … Continue reading

Posted in geometry, pattern | Tagged , , , | 9 Comments

Post without words #22

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From primitive roots to Euclid’s orchard

Commenter Snowball pointed out the similarity between Euclid’s Orchard… …and this picture of primitive roots I made a year ago: At first I didn’t see the connection, but Snowball was absolutely right. Once I understood it, I made this little … Continue reading

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