41–50 of 54 posts
Can anyone defend Pi on grounds other than that's the way it's always been , or introducing a new constant is hard ?
> The mathematical world is as full of lonely pi's, as it is of 2*pi's. Now we need to move to tau/2 and tau, only to get a pi-manifesto in a couple of decades.
Earlier quoted context omitted.
"The fact is that making things easier doesn't necessarily mean improvement." Untrue, and if you're a programmer you ought to know better. Making something that works the exact same way, only easier, is definitely an improvement. Now it takes less of your finite mental reserves to accomplish a task, and you can now go further in the same amount of time. Making something that abstracts away some things and makes the r…
Okay, I failed to properly address "improvement". By "improvement" I mean the time required to develop something new. Of course everything improves, simply because it's built on top of the base of an older version. A simple example, it took months to write a simple browser with a little less features than the browsers available during the Win 9x era. Does it take weeks now? I doubt so. Ok, to put it more simply, what…
Ooooo, bad choice of example. It takes a day or so now, since WebKit is embeddable.
You're trying to separate something that can't be separated. You can't separate "making things take less time" from "making better things possible", because the bound in all cases is time. If you have to spend less time on X, then you've got more to spend on Y; if you can't spend less time on X you'll never reach Y. It's the rare improvement that can only improve quality, but doesn't in any way permit you to instead trade that for time.
Earlier quoted context omitted.
Okay, I failed to properly address "improvement". By "improvement" I mean the time required to develop something new. Of course everything improves, simply because it's built on top of the base of an older version. A simple example, it took months to write a simple browser with a little less features than the browsers available during the Win 9x era. Does it take weeks now? I doubt so. Ok, to put it more simply, what…
"Does it take weeks now? I doubt so." Ooooo, bad choice of example. It takes a day or so now, since WebKit is embeddable. You're trying to separate something that can't be separated. You can't separate "making things take less time" from "making better things possible", because the bound in all cases is time . If you have to spend less time on X, then you've got more to spend on Y; if you can't spend less time on X y…
However this is drawn too far from the topic of Tau, what I'm trying to imply is that science and maths has work centuries with Pi, we've found many great theories with it as well. But in the modern era (quantum), Tau seems irrelevant (okay, I haven't studied too much about quantum, but I've read on articles and there's no mention on Pi either, correct me if I'm wrong).
What's the use of making things simple at the same time confusing people? Things have always worked out, and it should continue to work on.
Earlier quoted context omitted.
It is not an exercise worth ignoring: I had also once thought that pi should be replaced. Slightly different motivation, though, as it seemed to me that pi/2 was really more interesting, and anyway it is really much easier to write multiplication than fractions when you run into a discrepancy. Here the roots of the sine are at even multiples and the roots of the cosine are at odd multiples, and e^(i pi/2) = i is more…
You got a good case with pi/2, it's truly useful, as it represents the angle between 3d axes, the boundaries of the tangent and inverse trigonometric functions, the monotonic regions of cosine and sine etc. It will even make spherical coordinates easier to visualize mentally. (It will also make a two-digit number, 16, a common resident in lots of formulas). I vouch for it, and i call for a move to name it, confusingl…
Earlier quoted context omitted.
You got a good case with pi/2, it's truly useful, as it represents the angle between 3d axes, the boundaries of the tangent and inverse trigonometric functions, the monotonic regions of cosine and sine etc. It will even make spherical coordinates easier to visualize mentally. (It will also make a two-digit number, 16, a common resident in lots of formulas). I vouch for it, and i call for a move to name it, confusingl…
pi-bar? Nooooo, you'll make the Statistics community members' heads explode!
Is this going to get posted every year?
The most compelling argument for me in using tau, (and I have started trying to think in tau when it comes up) is the radians argument: one quarter of a circle is tau/4, or pi / 8, you pick. I am certain my kids will have an easier time remembering tau/4, as I do myself. The other compelling thing for me came from remembering just how many integrals from 0 to 2pi I wrote over my freshman complex analysis class. A lot…
I am not particularly well versed in mathematics but isn't 1/4 of a circle pi/2 radians?
The mathematical world is as full of lonely pi's, as it is of 2*pi's. Now we need to move to tau/2 and tau, only to get a pi-manifesto in a couple of decades. Previous discussions: http://news.ycombinator.com/item?id=1468341 http://news.ycombinator.com/item?id=2322666
I like the compromise of using Tau and its fractions when it makes sense and using a single Pi when it's not so intuitively-connected with a circle. e.g. \int_{-\infty}^{\infty} e^{−x^2} dx = \sqrt{\pi}. Plus Tau Day's a fun excuse to eat two pies.
One could always celebrate 2\pi day. ;)