Interesting idea! What do you guys think about it?
And with this I've thought of this: Different by an obvious reason but it's new.
Pi (≈3.14159265)
Tau (≈6.2831853)

Interesting idea! What do you guys think about it?
And with this I've thought of this: Different by an obvious reason but it's new.
I always try to argue that Tau is the better choice, it makes many results and formulas look a little more transparent IMO. I don't think making the shift is very practical at this point though.
Much like how the conventional direction of current in circuit diagrams remains from positive to negative, despite the fact that negative charge is what moves.
I meant to start a poll, but forgot when I initiated the thread. But it's added now.
Here's a doublecolumn list of the geometric relationships of a circle's radius, diameter, circumference, and area in terms of each other in contrasting ratios of pi or tau.
(left in pi, right in tau) Neither much of a big nor significant difference, IMO. So there's not much argument there.
However, when it comes to trigonometry, I believe it's much better to use Tau, since the unit circle relationship depends on its radius, and not the diameter, for the trigonometric functions. As described well in the video, it's periodic by Tau because in radians a full circle represents a whole Tau, instead of 2pi. And a quarter of the turn is a quarter Tau, not a half pi, etc. Which would be much, much easier to learn in school, IMO also.
I also think is much more elegant and beautiful than . Also showing the true relationship between the complex exponential function and the trigonometric functions.
Last edited by brody; April 3rd, 2012 at 03:11 PM. Reason: Fixed image
I like the area formulas because they end up looking more like standard calculus formulas. The one half tau r squared in particular.
TheObserver, I disagreed with your statement exp(i*tau/2)=1 for several reasons but you've edited so nevermind Did you see your mistake?
And I agree on the formulas thing, beauty in complexity. It turns out Tau actually made most of the equations a little more complex, but the concept is still better.
Yeah I noticed that you had switched it to the one, my bad!
To answer seriously, the impact of any such change has to be weighed against its merits. QWERTY remains the standard keyboard layout even though many analyses have shown there are better ones, but it is too much trouble to change.
True for keyboards, but for this: maybe not. As with anything, only future products have to be changed. Which is a problem depending on how the new feature is used in life. For example, in keyboards, most people are used to using QWERTY, and changing the typing patterns they've used all their lives would be very difficult. But if 2pi were to change to Tau, then all you have to do is substitute anywhere you see 2pi for tau, which isn't something you have to gradually transition to. It's merely an idea and a symbol, not a skill, nor habit.
And that's one of the things we have to deal with if we are going to change. Should we replace all pi's with Tau/2, or should we just use both Pi (since we're used to it) and Tau where it's best needed like trigonometry (and it's a better representation of certain concepts)?
As long as we're hoping to change things, lets shift the USA over to the metric system.
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