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Pascal (Mod p)

Published online by Cambridge University Press:  03 November 2016

W. Antony Broomhead
W. Antony Broomhead*
Affiliation:
2 Clifton Walk, Newcastle-Upon-Tyne
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Extract

This story is an object lesson in the art of picking other people’s brains.

After one of my fifth form had pointed out for me the result in Classroom Note 248 (ii) (June 1971), it occurred to me that some attractive patterns might result from re-writing Pascal's triangle with the numbers reduced modulo n. I tried it at first with n = 2, using a red dot for odd numbers and a green dot for even. The pattern was, as I had hoped, pleasing. Since we had an Open Day in the near future, I persuaded another fifth-former, P. W. Swinyard, to try the same thing for other small n. Attractive patterns resulted for n = 3, 4, and 5, a rather less attractive pattern for n = 6, but nice ones again for n = 7, 8, and 9. (I recommend readers to try this for themselves.)

Type
Research Article
Information
The Mathematical Gazette , Volume 56 , Issue 398 , December 1972 , pp. 267 - 271
Copyright
Copyright © Mathematical Association 1972

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References

page 267 note * Some of these patterns are attractively displayed in a film-loop Pascal’s Triangle, originally made for the B.B.C. Maths Today programmes, and available from Gateway Educational Films, Ltd. D.A.Q.