Abstract
Pythagorean triples have intrigued generations of mathematics explorers, including students, since ancient times. One of their most charming features is their connection with various other areas of mathematics. In the Mathematics Teacher, for example, authors have shown that Pythagorean triples can be generated from the Fibonacci numbers (Bertucci 1991), from geometric sequences (Carbeau 1993), and from both the addition and multiplication tables of whole numbers (DiDomenico 1993, 1995). These findings are indeed fascinating; when shared with students, they spark interest and curiosity and lead to a truly enriching mathematical experience. Students, in fact, independently found that Pythagorean triples could be generated from Fibonacci numbers and geometric sequences. This article reveals another surprising connection that shows how all primitive Pythagorean triples can be generated from harmonic sequences.
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