September 24, 2011

intothecontinuum: “ This picture illustrates that there are 512 different ways to color a 3x3 grid using only two colors. In general, to do this for a MxM grid with M2=N blocks, there are 2N different ways. This is also equivalent to the following: •...

intothecontinuum:

This picture illustrates that there are 512 different ways to color a 3x3 grid using only two colors.

In general, to do this for a MxM grid with M2=N blocks, there are 2N different ways.

This is also equivalent to the following:

  • 2N is the sum of all the numbers in the Nth row of Pascal’s triangle.
  • For a set S with N elements, 2N is the size of the power set of S, which is how many unique subsets there are of S.
  • 2N is the number of ways of choosing 0 things from N things, plus the number of ways of choosing 1 thing from N things, plus the number of ways from choosing 2 things from N things, etc… , plus the number of ways of choosing N things from N.
  •  2N is the number of different sequences of outcomes from flipping a coin N times.
  •  2N is the number of basis states needed to completely express the state of a quantum computer with N qubits (cf. here).

Can you think of anymore?


(via wowgreat)

(via ultrazapping)

305 notes
tags #2^N #Math #combinatorics #counting #quantum computing #geometry #graphic design

repeat from vellum

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