On March 14th this year, much attention was focused on the movement to eradicate π (pi) as the fundamental mathematical constant, and replace it with τ (tau), numerically equivalent to 2*π. In his 2001 piece "π Is Wrong!", Bob Palais lists reasons why τ is the better choice. This past week on June 28th, attention was focused again on this movement to adopt the new constant, which approximates to 6.28.
Viewing from the mathematical and physics perspective, using τ as the fundamental constant makes intuitive sense. There should be little dissent in the notion that radian expression, which currently equates a whole turn to 2*π, is the formal convention in academia when it comes to circles. Redefining that whole turn to τ instead, and getting rid of the 2 term, would simplify expressions such as the equation relating linear and angular frequency (ω = τf instead of ω = 2πf) and most noticeably, the equation relating circumference and radius. One equation that would seemingly get more complicated is the area formula. Instead of A= π*r^2, it would have the additional half term, A = (1/2)*τ*r^2. However, Palais compares this new formulas to many commonly used quadratic formulas that encompasses the half term: K=(1/2)*m*v^2 or d=(1/2)*g*t^2.
Unfortunately in many instances, deriving the mathematical logic is simply not sufficient to make appreciable impact. Just like the imperial system used in here United States, it makes logical sense to adopt the metric system and avoid the costly errors in miscommunication and mixes. However, one obstacle is the short-term cost. It would be enormously expensive to replace all signs and regulations with the metric system. While replacing π in academia is not as great of a challenge (many modern academic writing still refer to archaic conventions), the bigger hurdle here comes down to uprooting the tradition. Every year, students chant the digits of π and bring circular items on March 14th. Mathematicians and physicists have dealt with calculations for centuries with π. Just because there is logic behind new and effective changes, doesn't mean that people will relinquish the old ways, even if those old ways may be somewhat more inconvenient. That degree of logical improvement, together with the degree of attachment to the tradition, will ultimately dictate whether changes can be implemented.
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