Maths and music

Answers to Task 3c: Group theory and dancing

Most of the answers to this section are in the text of the task.

Question 5

To work out bc in the dance:

b is   A  B  C  D  A  C  B  D, c is   A  B  C  D  B  A  D  C
So bc is   A  B  C  D  A  C  B  D C  A  D  B

Then to work out bcbcbcbc:

bc = bba = ea = a (from Task 3b)
So bcbcbcbc = aaaa = e (from Task 3b)

Alternatively, remembering that each b is an 'inner twiddle' and each c is an 'outer twiddle':

		inner twiddle		outer twiddle
	A  B  C  D		A  C  B  D		C  A  D  B
			C  D  A  B		D  C  B  A
			D  B  C  A		B  D  A  C
			B  A  D  C		A  B  C  D

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