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Some years ago I used the device of representing composite numbers by rectangular forms to demonstrate the structure of numbers to third grade students. Primes were represented by lines of various lengths. Number 10 would be a 2x5 rectangle and 20 a 2x2x5 rectangular solid. (I used various devices for dimensions > 3). Clearly this representation assigns trigonometric properties to composite numbers which might be deserving of study. I haven't run across any formal studies of these properties, but it seems they might give some insights into the structure of the natural numbers. Can anyone direct me to any studies of these properties assuming they might be worth studying.

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