Patterns And Predictions

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Some patterns fail quickly:

Take a circle and put n points on its circumference. Join them all with straight lines. How many pieces can you get? The points don't need to be equally spaced - what's the largest number of pieces?

Points 1 2 3 4 5 6 7 8 9 10 ...
Pieces 1 2 4 8 16 . . . . 256 ...

  • What is the formula?
  • How can you tell?
A mathematics talk given by Colin Wright, this starts with some seductively obvious patterns that seem successfully to predict the future, but then goes on to show that not all patterns are trustworthy.

We start with simple arithmetic sequences, and talk briefly about why we claim a sequence "should" continue in a particular way. Then we look at a specific problem and look at the sequence it generates, only to discover that it's not the sequence we expect.

In an apparent shift of topic we then look at Morse Code, and look for patterns in how it's designed, and some implications. Oddly enough, both the doubling sequence (1, 2, 4, 8, 16, ...) and the Fibonacci sequence (1, 1, 2, 3, 5, 8, ...) arise naturally.

We finish by going meta, and using a pattern of patterns to predict the existence of Juggling Patterns.

This talk covers a lot of ground, and can be mined for a long time to come ...



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Site hosted by Colin and Rachel Wright:
  • Maths, Design, Juggling, Computing,
  • Embroidery, Proof-reading,
  • and other clever stuff.

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