π corresponds to 180 degrees, 2π to 360 degrees, and π/2 to 90 degrees. Euler's equation, considered the most beautiful in the world, is e^(iπ) + 1 = 0, and it encapsulates the following five mathematical constants:
0, 1, e, π, i
in a single formula.

However, according to Albert Eagle's book 'The Elliptic Functions As They Should Be', by defining τ not as 2π but as π/2 (approximately 1.571, or 90 degrees), one can arrive at the formula e^(2iτ) + 1 = 0. This incorporates the following six mathematical constants:
0, 1, τ, 2, e, i
into a single equation. This definition is considered to have mathematical symmetry. Applying this definition to various other mathematical and physical formulas could potentially result in more intuitive and beautiful expressions.

For example, the relation sin(x + τ) = cos(x) holds true. This demonstrates a perpendicular relationship between the two.