12/28/05
Chit Chat # 32 RTFROLIBob Chen |
(2) It is delightful to read Arthur Ma's work. They are
deep and profound. It comes to no surprise to me since he was the only one wrote in old
fashioned Chinese for the 20th year book. It is not easy to write that way as compared to
"Pu-Tung-Hua". Similarly, Peter Sun's article is no easy task to type by Chinese
word processing. I tried (3) Humphrey Hung Chu has surfaced, and talked to me, Desmond Wang, and Dennis Su. Dennis will try to get him to come to Toronto in August. He lives in Vancouver now. May be Dennis can get both Arthur Ma, and Humphrey to join us. Humphrey was a Lighter from '54 to '58, that qualifies him as a friend for sure. (4) I don't know how Desmond Wang solved James T. Koo's
puzzle by calculating the areas of two triangles to show the diagonal is slightly
concave-up. I found a long write-up on this family of puzzles in one of Martin Gardner's
Dover books. He showed that if one picks the sides from a Fibonacci series (i.e.,
1,2,3,5,8,13,21,...) one can always get a hole in integer number of squares. In James
Koo's case, they are 5 by 13. Also the middle number (8) when squared, differs to the
product of the first and last number (5, and 13; or 5x13=65) by 1. Gardner claimed that he
got all these from an ophthalmologist in New York City in the '40s. James, and Pat, may be
you two want to check this out. One more clue (5x8)-(3x13)=1. The 1 can be generalized to
2,3,4,... by simply multiplying all the terms in the Fibonacci series by 2^1/2,
3^1/2,...;or, starting any other Fibonacci series other than 1,2,3,5,8,13,...rembmbering
the only rule to form a Fibonacci series is: the third number is the sum of the two
numbers before, with no restrictions on the two starting numbers! |
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