So, after reading the opposition, Im still pretty sure Im a τist. thepimanifesto/ The πists main points seem to be: 1. π is cleaner for areas than τ 2. τ is just a multiple of π 3. Heres a bunch of other formulas with pi instead of tau. See! I can play that game too. Point 2 is spurious. The reverse is also true: π is just a multiple of τ. Hes starting with the assumption that π is the number to use, then saying, And tau is just riding on its coattails, see? Point 3 is somewhat more legitimate. If the question were simply Which symbol and value for the circle constant gives us the fewest fractions? then it would be a fairly even race. But that *isnt* the fundamental point of the Tau Manifesto. The πist doesnt address the big benefit of τ-it implies more meaningful geometric content by itself. That makes it much more useful for teaching and in general. τ is a turn all the way around the circle. The πist returns, Well, π is the area of a unit circle (a circle with a radius of 1)! And look at all these other area formulas that make use of pi! See? Pi makes much more sense in two dimensions. What s/hes missed here is that having divide by 2 in area equations actually tells us something very important. When you move from one dimension into two dimensions (that is, you were measuring lines, but now youre measuring areas), smaller numbers actually represent more stuff. The diameter of a circle is a distance; the area of a circle is a whole bunch of infinitesimal distances in one dimension summed up over another dimension. The fact that the magnitude of the area of the unit circle is half the magnitude of its circumference alludes to deeper truths about circles, and the nature of one-number measurements in many dimensions (such as area, volume, hypervolume, etc.). It sets geometry students up for future understanding of the divide by the exponent operation that they will perform when they move on to Calculus. In brief, it tells students, When youre dealing with areas, less is more (compared to distances). Smaller numbers dont mean anything was lost-square meters just cover more than plain ol meters. A little with them goes a long way. In short, the πist failed to grasp the Tau Manifestos main point, and thus, failed to refute it.
Posted on: Mon, 02 Dec 2013 04:17:04 +0000
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