Now here is a campaign of which I approve: the outdated and outmoded pi deserves to be replaced by the intrinsically more useful tau (= 2 * pi).
Why is that you ask, because pi is the ratio of the circumference to the diameter of a circle and the area is pi*(radius)^2, which is pretty straightforward.
Maybe, but the area formula (tau/2)*(radius)^2 shows us that the area of a circle is the sum of a series of infinitessimally sectors (ie. very thin triangles). The tau form of the formula is much more like all those other quadratic formulae for energy (1/2*m*v^2), distance (1/2*a*t^2), etc etc, because what is really going wrong is that pi is only half the value it needs to be. The circuumference of a circle is pi*diameter but that is 2*pi*radius, or tau*radius.
As Leonnard Euler would have told us exp(i*tau)=1, which is just too cool for words.
1 comment:
Mathematically yes, but in the real world, i.e., engineering or practical science, Pi is better.
Just try to (or imagine) measuring the radius of a circular object, e.g., a pipeline. Diameter & circumference are measurable, radius is not.
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