Quote Originally Posted by sblanck View Post
Her question is why three buttons,
It's all based on mathematics.

You see three is the first odd prime number, and the second smallest prime. It is both the first Fermat prime (2²º + 1) and the first Mersenne prime (2² - 1), as well as the first lucky prime. However, it's the second Sophie Germain prime, the second Mersenne prime exponent, the second factorial prime (2! + 1), the second Lucas prime, the second Stern prime. Three is the first unique prime due to the properties of its reciprocal. Three is the third Heegner number. Three is the second triangular number and it is the only prime triangular number. Three is the only prime which is one less than a perfect square. Any other number which is n² - 1 for some integer n is not prime, since it is (n - 1)(n + 1). This is true for 3 as well, but in its case one of the factors is 1. Three non-collinear points determine a plane and a circle. Three is the fourth Fibonacci number and the third that is unique. In the Perrin sequence, however, 3 is both the zeroth and third Perrin numbers. Three is the fourth open meandric number. therefore we use buttons in groups of three.

I hope that helps clear it up for you.