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Re: The Reason Why Tau Is Fundamental And Why Pi Is Not
Posted:
Feb 9, 2013 9:20 PM
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On Wed, 2 Jan 2013 03:04:18 -0800 (PST),
tdadamemd-spamblock-@excite.com wrote:
>The reason why Tau is a fundamental number is because it is the Identity Operator for Rotation. Pi is lacking in such fundamental utility.
>
>Tau is as fundamental to Rotation as Zero is to Addition and One is to Multiplication. Tonight I watched several YouTube videos about Tau and I didn't see anyone make mention of this fact. Bob Palais wrote an excellent article back in 2001. But the arguments that I've seen favoring Tau over Pi were basically a matter of style and taste.
>
>The reason why Tau is worthy of primacy over Pi is not because of any such artistic reasons, but because of this fundamental mathematical reason.
>
>~ CT
What would the adoption of tau do to:
1. The Taylor series for trig functions, such as:
http://en.wikipedia.org/wiki/Sine#Series_definition
2. The relationships between trig and hyperbolic functions, such as:
http://en.wikipedia.org/wiki/Hyperbolic_function#Hyperbolic_functions_for_complex_numbers
cosh(ix) = cos(x)
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