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]]>As noted in the last page of the pdf, I suggest calling the alternate constant 2 π=6.283… `1 turn’, so that 90 degrees is `a quarter turn’, just as we would say in natural language. The main point is that the historical choice of the value of π obscures the benefit of radian measure. It is easy to see that 1/4 turn is more natural than 90° , but π/2 seems almost as arbitrary. It is apparent that we can’t eliminate π but it is to be aware of its pitfalls, and introduce an alternative for those who might wish to use one.

— Bob Palais

Palais then goes on to define a “newpi” symbol through a TeX macro, which resembles the fusion of two π:

The aforementioned article has been in print since 2001, and very little has changed on this front since then. The ideas it put forth are an amusing opinion that many of us tend to agree with, but 2π has not been adopted by the mathematical community.

Today Michael Hartl announced “The Tau Manifesto” on what he calls Tau Day (6/28 for 6.28…). In this document, Hartl echoes the good points that Palais made and builds upon them to construct a strong case in favor of adopting a circle constant which is the ratio of a circle’s circumference to its radius, not its diameter. Inspired by Palais’ use of the word “turn”, he proposes calling this constant τ (tau).

As Hartl argues, this symbol already exists (unlike the odd symbol that Palais introduced), it’s still generally available in mathematics, and it resembles π.

This new constant would not only be an improvement from a pedagogical standpoint (as shown in the diagram above), but would also “improve” several formulas. For example, Euler’s identity:

[tex]\displaystyle e^{i\pi} + 1 = 0[/tex]

Or:

[tex]\displaystyle e^{i\pi} = -1[/tex]

Which would become neater as:

[tex]\displaystyle e^{i\tau} = 1[/tex]

This makes sense intuitively (a rotation in the complex plane by one turn is 1).

(The Tau Manifesto addresses the issue of how this too can relate to the “five most important numbers in mathematics” with a slight rearrangement.)

What are your thoughts on this? As mathematics evolves, is it time to start using “Let τ = 2π” as a means of adopting a better circle constant?

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]]>The post Discussing Research Level Mathematics Online appeared first on Math ∞ Blog.

]]>With endorsements from star programmers and its unique user interface (UI), this site is very community oriented and aimed at highlighting the best answers and questions through a voting system. As such it has quickly become the number one programming forum, overshadowing the dreaded – and much shadier – Experts-Exchange.

However, what not everyone may know is that Joel and Jeff have made the platform available to others for a non-negligible monthly fee, at StackExchange. Over the course of the last few months several communities have grown out of this service, some more successfully than others.

The most successful of these sites is called MathOverflow. It currently has the largest number of active participants and voters on its posts. The site offers the same UI as StackOverflow, but adds in support for LaTeX formulas. Here at Math-Blog.com we feel it’s important to promote such nice initiatives.

From the look of things (such as the existing questions and answers), it’s clear that there is some serious mathematics going on at the site. If you’re looking for interesting discussions on topics at a graduate/research level, head over to MathOverflow – you won’t be disappointed. However, please keep in mind that the aim of the site is to target those with an interest in advanced math. If you’re seeking a more basic (read undergraduate) level of math assistance, you should probably look elsewhere.

That said, what are some the other graduate level forums and mailing lists that you find useful when it comes to your mathematical research? One of my favorites is the Number Theory List.

PS: I hope you like our new look. Be sure to drop by Math Blog this coming Monday, as we’ll be publishing a really interesting post that I’m sure you’ll love. In order not to miss it, you can also grab our feed.

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