Is it known that 1 and 2 are the only impossible sides of (integer) Heron triangles? It appears that all such triangles with side 3 are of the form 3 n n 1 [- ((sqrt(8) + 3) + (3 - sqrt(8)) ) + -, 4 2 3 n n 1 - ((sqrt(8) + 3) + (3 - sqrt(8)) ) - -, 3], 4 2 and all with side 6 are either twice that, or 3 fib(6 n) 3 fib(6 n) [3 fib(6 n - 1) + ---------- + 2, 3 fib(6 n - 1) + ---------- - 2, 6], 2 2 or the lone isosceles case [5,5,6] (= twinned [3,4,5]s). Similarly for a side of any small integer. --rwg radiolytic cordiality
participants (1)
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Bill Gosper