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 ...
Contents
 
Links on this page
 
Site hosted by
Colin and
Rachel Wright:
 Maths, Design, Juggling, Computing,
 Embroidery, Proofreading,
 and other clever stuff.


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