>> The Phew Theorem >> 1/8 C = (Sin45) + (1-Cos45)² or

1/8 C = (Sin45)² + (1-Cos45)

might initially not convice people easily. But its formulas will give clear descriptions about the true calculations for curve shaped objects. It can be tested in real experiments. I dare you (and anyone) to do such experiments.

What thread is the derivation of that formula given?

Also, is that conventional sin/cos? They can be defined with reference to Euler's formula using pi, is pi accepted in that context or should it be replaced with phew?

I wrote that theorem once in a while in various threads. No special thread posted to explain Phew Theorem.

The idea is: 45° is the summary of the entire circumference. Basic calculation comes from 45° realities.

Sin and Cos are unchanged. It's universally proven that Sin45 equals 0.7071 and 1-Cos45 equals 0.2929.

It's a pure equation, not series. Phew/4 AKA 1/8 C is resulted from figures in a circle line with its connections with various projection of 'height' and 'wide' at both coordinate lines.

There are 'hidden code' in 45° angle e.g. 0.7071, 0.2929, 0.4142 etc.

Phew value comes from such figures, with certain processing methods.

For example: Sin45 is considered as distance obtained by velocity. While (1-cos45)² is the additional distance due to acceleration.

If 1/8 C (45°) = 0.7071 + 0.2929², 1/4 C (90°) will be 1 + 2×0.2929 or 1 + 1-0.4142.

Everything is "hint" by definite figures while a circle line put within a square.