81–90 of 128 posts
Using tau would uglify euler's equation, wouldn't it?
Seems pretty comparable to me: this one elegantly demonstrates the full periodicity of complex exponentials, while the original elegantly demonstrates how complex exponentials can produce pure negative numbers.
I have found the idea of tau useful even though I have never used it in writing. One argument in favor of tau is that in many formulas pi often has the multiplier 2 in front of it. If these formulas are written in terms of tau, they may become slightly easier to memorize and manipulate. Perhaps so, but I don't really care about this. It’s not a big difference. Besides, there are also lots of formulas that are easier…
One argument in favor of tau is that in many formulas pi
often has the multiplier 2 in front of it.
Of course you can construct infinitely many formulas, but most of those are used a vanishingly small number of times. The question is what common formulas use pi or tau. How often would people actually have to write, read or say a factor?
Earlier quoted context omitted.
Treating 2π as a single entity is probably the best option for now. Not sure if formulas like 1/2 (2π) r^2 will ever catch on, but in more complicated formulas it's probably better to not simplify things like (2π)^4 / 6 to 2^3 π^4 / 3.
The idea of 2π as symbolic entity in its own right, should be easier to accept than τ. Introduce a single symbol that joins 2 and π, a bit like the Jupiter symbol ( http://unicode-table.com/en/2643/ ), and pronounced 'two-pi'. Like τ it also starts with a T, for turn. That would be totally backward compatible in reading, writing and speech.
Okay, tau is a little better. Meanwhile, millions of lines of code are written in languages with no type system to speak of, millions of Americans use imperial measurements, billions worldwide speak languages that are inefficient and ambiguous, and many many people aren't even educated enough to know about pi or tau. We have much more damaging problems than multiplying by 2. Given the gigantic amount of effort it wou…
> millions of Americans use imperial measurements There are two types of countries: those using 'metric' units, and those who have been to the Moon. There's absolutely nothing fundamentally wrong with standard units (indeed, they are better for concrete manipulation). One can do science and engineering just as well with grains as with grams, with cups as with litres, with inches as with centimetres. They could do wit…
If mathematics has a bikeshed, this is it. I enjoy the ridiculousness of it all, but people who consider this anything other than a well-executed joke really should get a hold of themselves.
Really? This seems very similar to problems with variable naming and magic numbers, which are far from bike shedding.
https://en.wikipedia.org/wiki/Angular_frequency
Note how convenient ω is when squared, in the expression of angular acceleration, eliminating a ridiculous 4 factor.
I have found the idea of tau useful even though I have never used it in writing. One argument in favor of tau is that in many formulas pi often has the multiplier 2 in front of it. If these formulas are written in terms of tau, they may become slightly easier to memorize and manipulate. Perhaps so, but I don't really care about this. It’s not a big difference. Besides, there are also lots of formulas that are easier…
One argument in favor of tau is that in many formulas pi often has the multiplier 2 in front of it. And an argument in favor of pi is that many formulas do not have that any multiplier in front it. So this cannot be resolved without quantitative evidence of the number of formulas using either one, including their frequency of use. Of course you can construct infinitely many formulas, but most of those are used a vani…
Also, when counting formulas don't forget to expand "angular frequency" ω to the 2πf it denotes.
Using tau would uglify euler's equation, wouldn't it?
You be the judge of that. Compare e^(iπ) = -1 to e^(iτ) = 1. The whole business of re-writing the identity as e^(iπ) + 1 = 0 is nothing but a hack to get around the weirdness of π as a constant.
In the case of Euler's identity, what we're really asking is "what values of x make e^(ix) + 1 = 0 true?" and the answer is "every multiple of π". Using τ instead hides half of the answers.