For those of us enamored with the subtle obscurities of the fundamentals, much to my delight a recent posting on π (Twitter) by Dr. James Tanton was brought to my attention. Here he describes a unique Pythagorean Triple curiosity. In subsequent correspondence, Dr. Tanton recalled to me his thoughts of Pythagorean Triples with side lengths as powers of two. He stated: βThere is exactly one integer right triangle with a side length of 4, two with a side length of 8, three with a side length of 16, and so on, N-1 with a side length of 2N.β His thinking evolved into...
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