Talk:Pi: Difference between revisions
→Pi vs tau
(→Pi vs tau: conciseness, task description complications, Pi/Pi and Tau really wouldn't bother me.) |
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::: That http://esr.ibiblio.org/?p=3481 argument (and the pi manifesto it referenses) suggests that this whole thing is just about conciseness, and not about some of the other issues (like constant 1/2 in simple r^2 equations and 1/6 in simple r^3 equations). I can understand that conciseness has advantages, and I also agree that pi's familiarity/popularity can be a major advantage in a cookbook equation context. Anyways, the "pi is wrong" slogan, while catchy and motivating is itself wrong. "Pi is useful, but pi can also occasionally be misleading or confusing" would be a more accurate (though boring) phrasing. There's room in the world for both constants, and I dislike reasoning (even from its advocates) that suggest that there can be only one. And "tau is 2*pi" is simple, but too trivial? We have "Goodbye, world" here. And, 99 bottles of beer -- how can "tau is 2*pi" be too trivial? (Though, ok, I can understand not wanting to like to a "pi is wrong" page.) --[[User:Rdm|Rdm]] 11:48, 2 August 2011 (UTC)
:::: First, "constant 1/2 in simple r^2 equations" and "1/6 in simple r^3 equations" are ''exactly'' questions of conciseness; which is more concise? <math>\frac{1}{2}\pi r^2</math> or <math>\tau\pi</math>? For these equations, <math>\tau</math> is easily more concise. (And this is the area of debate I really wanted to avoid)--[[User:Short Circuit|Michael Mol]] 13:37, 2 August 2011 (UTC)
::::: Ok, yes, that can be a question of conciseness. But it's also a simplicity issue and, thus, a mnemonic issue. It's the same reasoning behind the coefficients in a taylor series. For the n-space analog of area of an n-space analog of a sphere, the equation would be <math>\scriptstyle 2\pi x^n \div n! \equiv \tau x^n \div n! </math>. By optimizing for second degree equations you obscure the simplicity of the issue for every other degree. And optimizing for second degree equations can be the right thing to do, in some contexts, but not for all contexts. Meanwhile, I am uncomfortable talking with someone on a subject that they say they do not want to talk about, but I am also uncomfortable leaving alone the issues that you bring up. --[[User:Rdm|Rdm]] 14:38, 2 August 2011 (UTC)
:::: Second, I was far more concerned about scenarios involving geometric tasks which chose to use {{tau}} rather than {{pi}}, as each of those tasks would need to note how to derive {{tau}} from {{pi}}, which would complicate them. (A trivial complication yes, but still a reduction in their simplicity)--[[User:Short Circuit|Michael Mol]] 13:37, 2 August 2011 (UTC)
:::: Third, I really wouldn't mind a [[Pi/Pi and Tau]] which showed how convert from pi to tau and back. That kind of triviality isn't something that bothers me, though it may tend to bother contributors who are completeness-driven. --[[User:Short Circuit|Michael Mol]] 13:37, 2 August 2011 (UTC)
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