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Sunday, November 9, 2003

Sunday November 9, 2003

Filed under: General,Geometry — Tags: — m759 @ 5:00 PM

For Hermann Weyl's Birthday:

A Structure-Endowed Entity

"A guiding principle in modern mathematics is this lesson: Whenever you have to do with a structure-endowed entity S, try to determine its group of automorphisms, the group of those element-wise transformations which leave all structural relations undisturbed. You can expect to gain a deep insight into the constitution of S in this way."

— Hermann Weyl in Symmetry

Exercise:  Apply Weyl's lesson to the following "structure-endowed entity."

4x4 array of dots

What is the order of the resulting group of automorphisms? (The answer will, of course, depend on which aspects of the array's structure you choose to examine.  It could be in the hundreds, or in the hundreds of thousands.)

1 Comment

  1. You can expect to gain a deep insight into the constitution of S in this way … by going to her website and reading and it may be advisable, before looking for such configurations, to study the subgroups themselves, e.g. the subgroups of those automorphism which leave one element fixed, or leave two distinct elements fixed, and investigate, or in other words, read her links.

    Comment by oOMisfitOo — Sunday, November 9, 2003 @ 5:10 PM

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