U.S. CitiesCity-Data Forum Index
Go Back   City-Data Forum > General Forums > Science and Technology
Please register to participate in our discussions with 2 million other members - it's free and quick! Some forums can only be seen by registered members. After you create your account, you'll be able to customize options and access all our 15,000 new posts/day with fewer ads.
View detailed profile (Advanced) or search
site with Google Custom Search

Search Forums  (Advanced)
Old 02-01-2018, 09:18 AM
100 posts, read 35,546 times
Reputation: 65


A few years ago, a lot of mathematicians started discussing an interesting proposed circle constant which has been named τ ("tau", or "tough" if you wanna use the Greek pronunciation) which has caused a lot of controversy, and the idea behind that constant is that it is based on the radius rather than the diameter, so that τ = C/r (as opposed to π = C/d).
The motivation behind using this constant is that it seems to be more intuitive in a lot of ways, and also make more sense.
It's not just about trivial arithmetic or about replacing 2π with τ, it's about the belief that τ might actually be easier to understand for beginners and that it is probably more descriptive.

One major simplification that I can see right away is that τ much more directly tells you how many revolutions you have gone around the unit circle, because the number of revolutions is directly proportional to the number of τ.
For example, if an angle has the value (2/7)τ, then you can see right away that you have gone 2/7 of one revolution, so that would be about 103.
It also appears that τ would eliminate the need to memorise exact angles - you don't need to "learn" that 45 is equal to (1/4)π radians, because if you express this in terms of τ then you will get (1/8)τ;
in other words, exactly 1/8 of one period, which you can see from inspection!
The same is also true for 60, which is of course 1/6 of a period, so that would be (1/6)τ radians.
And to be honest, I still often confuse myself when I write angles in terms of π, even though I started trigonometry almost 15 years ago in high school in 2003.
It just seems more natural to me to use τ instead, since that constant much more directly corresponds to the number of periods.
It also seems to fit better with the general formula for the area of a circle sector;
that formula is A(θ) = (1/2)θr (basically, the closed integral of a circle's arc length in terms of radians), and you can see clearly that the special case where θ = τ gives you A(θ = τ) = (1/2)τr, which does indeed give you the area for a full circle, and this might give new students some further insight.

I really like this idea, and I think that the only times when I use π nowadays are when I need to simplify an expression as much as possible and thus prefer to write π instead of τ/2, although I always think of angles in terms of τ, since it just seems simpler to me.
But I am also interested to know of your opinions as well.
Reply With Quote Quick reply to this message

Old 02-03-2018, 12:30 AM
9,087 posts, read 9,246,166 times
Reputation: 4671
Originally Posted by Markus86 View Post
But I am also interested to know of your opinions as well.
Pi was introduced in it's current definition in 1706 and popularized when it was adopted by Euler in 1737. It's pretty obvious that it is not going to be displaced.
Reply With Quote Quick reply to this message
Old 02-03-2018, 07:20 AM
5,775 posts, read 3,050,430 times
Reputation: 15139
Silliness. Mathematically no reason for it. So nr^2 becomes t/2 r^2? Not really changing anything other than rearranging deck chairs and creating confusion along the way.
Reply With Quote Quick reply to this message
Old 02-05-2018, 04:46 PM
Location: Heart of Dixie
12,448 posts, read 10,152,693 times
Reputation: 28069
To quote King Arthur in Monty Python's "The Holy Grail": "T'is a silly place".
Reply With Quote Quick reply to this message
Please register to post and access all features of our very popular forum. It is free and quick. Over $68,000 in prizes has already been given out to active posters on our forum. Additional giveaways are planned.

Detailed information about all U.S. cities, counties, and zip codes on our site: City-data.com.

Please update this thread with any new information or opinions. This open thread is still read by thousands of people, so we encourage all additional points of view.

Quick Reply

Over $104,000 in prizes was already given out to active posters on our forum and additional giveaways are planned!

Go Back   City-Data Forum > General Forums > Science and Technology
Similar Threads
Follow City-Data.com founder on our Forum or

All times are GMT -6.

2005-2018, Advameg, Inc.

City-Data.com - Archive 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35 - Top