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The Cosmic Identity

Is this a mathematical identity or just a very interesting equation? Lets find out.

What is most interesting is that we can link this identity to Pythagoras’s theorem, as shown below .

This means that for each number (x) we have a corresponding right angled triangle and each triangle has height (A) = 2, base (B) = x-1/x and hypotenuse (C) = x+1/x.

For example, if we make our number (x) equal Phi (Φ), this makes its reciprocol (1/x) equal (1/Φ).

Because of the ‘cosmic’ nature of these numbers, we can write them down like this:

Using simple arithemitic and the number (x) we can calculate the lengths of the triangle. When x=Φ then 1/x = 1/Φ, A = 2, B = 1 and C = √5 (Square root of 5):

Use this cosmic triangle interactive diagram to explore this triangle in more detail or to try a different number (x).

The folowing table shows the numbers (x) equal to 1-9, and some cosmic numbers.

It is assumed that (x) is always ≥ 1 and the (1/x) is always ≤ 1.

I have been told that this is a mathematical identity, I have also been told that it is NOT an identity because it does not work for zero (0)., but it does, see below:


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