First PLN Reflection

Conceptua Math tweeted "Mathematicians want to say goodbye to Pi." from Yahoo! News.   

"I know it will be called blasphemy by some, but I believe that pi is wrong."

opens University of Utah mathematician Bob Palais' 2001 essay entitled, "Pi is Wrong!"

The argument is not that the current estimate of the value of pi, approximately 3.14159265...; verifiable by accurate measurement, Power Series expansions, and other processor-assisted computations; is itself incorrect.  Instead, Mr. Palais argues that that 2*pi, recently donned "tau" by his followers, is more relevant than pi.  Pi is the ratio of the circumference of a circle to its diameter.  Tau is the ratio of the circumference of a circle to its radius.  C = pi * diameter = tau * radius.  There'd have to be a similar reorientation of thinking about the formula for the area of a circle. 

But the real advantage to tau is on the unit circle:

"There are 2pi radians in a circle. This means one quarter of a circle corresponds to half of pi. That is, one quarter corresponds to a half. That's crazy. Similarly, three quarters of a circle is three halves of pi. Three quarters corresponds to three halves! Let's now use tau.  One quarter of a circle is one quarter of tau. One quarter corresponds to one quarter! Isn't that sensible and easy to remember?"

A fact which would also pay dividends when it comes time to think about graphing transformations of trigonometric functions. 

Despite the growing momentum of nascent movement, it is unlikely that the next editions of the textbooks will be rewritten to reflect this line of thought.  Indeed, tau, all of its advantages notwithstanding, is likely to lose this battle.  I am sure Betamax sympathizes. 

However, this article remains powerful for teachers.  Professor McKnight argues that breaking down the monolithic viewpoint of the textbook with supplemental materials is more engaging to students.  Moreover, giving students choice is a powerful tool of engagement.  I could envision a math teacher opening the lesson on the unit circle with a brief passage from the textbook and this news article, and then allowing the students to hash out which convention they would prefer. 

I think the example also illustrates the power of Twitter for math teachers.  It makes brand new developments and debates easily accessible to the teacher, who can introduce them to the classroom.