Geometry: In April 2012 I put up a puzzle asking to dissect a regular
hexagon into 8 congruent quadralaterals. I showed a solution but now I
another solution. What is it?
Answer available March 25,
Answer to math puzzle of March 11
Algebra: The harmonic mean of two integers a and b is defined as
2ab/(a+b). If the larger integer is twice the smaller and the harmonic
mean is 1 less than the arithmetic mean ((a+b)/2) what are the numbers?
Solution: If b is twice a then the harmonic mean is 4a2
/ 3a or 4a/3. The arithmetic mean is 3a/2 so 3a/2 = 4a/3 + 1. So, a = 6 and b = 12.
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updated 18 March 2013