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On this date, we need to join in the celebration of the number Phi = 1.618033989....

So, I will offer two well-known oddities using the form ...that tend to not be well-known!

First, start with Phi. Square it. Add 1. What do you get?

Second, start with Phi. Subtract 1. what do you get?

In the first case, you should get Phi again. In the second, you should get the reciprocal of Phi, or 1/φ.

In both instances, Phi is the only number that fits these patterns:

  • Phi2 = Phi + 1
  • Phi - 1 = Phi