Re: [86attendees] Pie?

I looked over the tau-manifesto, and am even more convinced now that
the most natural constant is neither pi nor 2 pi, but pi/2.
Let's call that L (note the right angle of pi/2 radians).

L is much more fundamental than either pi or tau.
When you first learn trigonometry you understand angles as fractions of a right angle,
and the trigonometric functions as ratios of sides of right triangles.
In this usage the natural measure is L = pi/2.

And of course, sin^-1(x) + cos^-1(x) = L, and tan^-1(x) + cot^-1(x) = L.

And think of how this simplifies so many other formulas.
For example, Integral_0^infinity  (1 / 1 + x^2) dx = L 
             Integral_0^a  (1 / sqrt(a^2 - x^2) dx = L 
             Integral_0^infinity tan(x) / x  dx = L
             Integral_0^1 sin^-1(x) / x  dx = L * ln(2)
             Integral_0^infinity (e^x + 1 / e^x - 1)  dx = L^2

And I could go on and on.

In my view, the only serious contender to being more simple is V = pi / 4,
but never the hideous tau = 2 * pi.

The only problem is that on L day you get a quarter of a pizza  
instead of a whole pie.

Y(J)S

-----Original Message-----
From: 86attendees-bounces@ietf.org [mailto:86attendees-bounces@ietf.org] On Behalf Of Tim Shepard
Sent: 14 March, 2013 16:22
To: Andrew Mcgregor
Cc: Stephane Bortzmeyer; Robin Wilton; Jon Hudson; Scott Brim; 86attendees@ietf.org
Subject: Re: [86attendees] Pie?

The natural constant is the ratio of the circumference to the
radius. That we wound up with pi which is the ratio of the
circumference to the diameter was a mistake.

If you're not already aware of this, read the Tau Manifesto at:

      http://tauday.com/tau-manifesto

(And if that is tl;dr for you, just skip to section 3 that discusses 
 the formula for area of the circle.) 

(Be glad that we got the definition of a radian right.)

You still have more than 3 months left to make plans for your
celebration of this natural constant on June 28.

			-Tim Shepard
			 shep@alum.mit.edu
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