58132764
72645831
76125483
81274365

I first saw these numbers in the book “Fun with Mathematics” by Jerome S. Meyer, published in 1961. I have had them on my computer terminal at work for years. The first two numbers are my favorites, I have been waiting for inspiration or insight, I want these numbers to talk to me - but nothing. They both have four sets of two numbers that should be telling me something 58, 13/31, 27/72, 64, some simple idea of shape, form or pattern. Mathematics, after all, has been described as the study of all possible patterns, therefor I should be able to ask and logically expect an answer to why these patterns occur and what they signify. This isn’t just my flight-of-fancy, W. W. Sawyer wrote in “Prelude to Mathematics,” (1982) “Where there is pattern there is significance. If in mathematical work of any kind we find a certain striking pattern recurs, it is always suggested that we should investigate why it occurs.”

Now for some mathematical mysticism.

You may have noticed that each of the four numbers has eight digits, 1 through 8 that do not repeat. If you multiply any of these numbers by 9 your answer will be nine digits, 1 through 9 that do not repeat. Take it up a step, if you multiply any of the original four numbers by 18 you will get a ten digit answer with numbers 1 through 0 that do not repeat. Now press your luck, try to go three for three - a pattern is emerging, will it continue? Unfortunately no, no other multiples of nine appear to give any results other than chaos, but I didn’t try everything. Back to the original problem, the four sets of numbers that appear in the first two numbers. My gut feeling is, this is more than random chance, but I do not have a clue as to why. If you have any ideas – reply. p.s. note, this is a “Recreational Number Theory” post, emphasis on “recreational,” not a hard core mathematics post.