TAU DAY - 'What's the big deal'pdf
TAU DAY - 'What's the big deal'pdf
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  1. TAU DAY: What’s the big deal?!(6.28/2015, or June 28, by swami_mathtraveler)(FYI, this piece is lite on math, and heavy on concept.)(thx, xkcd!) Tau time!So, does it matter? Well, at least for the fun of it!:) Let’s explore a bit...For the record, the “circle constant” (CC) is a basic property of any circle. It is simply the ratio of the “around” divided by the “across”. This number never changes, hence, a “constant”. In fact, other regular shapes have their own “shape constant”! The circle is just a special case. Check out this insightful video to grok what this means.PI (π), or TAU (τ )? Any symbol can be used to represent any thing. It’s your choice! In the case of the CC, the symbol is a stand in referring to the concept of a constant property of a shape. But our “problem” arises when choosing how to represent this property. “Around by across” naturally suggests “circumference by diameter”. So, let’s take a look...whereC = circumference (i.e. “around”)D = diameter (i.e. “across”; also = 2r, as in the substitution above)r = radius (i.e. “across”; well half way)
  2. What all of this simply means is that it takes 2 times π radius lengths to make one turn around the circle, or 2(~3.14) radii, which is ~6.28 radii. Hey, wait, isn’t that τ !?:)So, all the “fuss” is over a simple substitution: τ = 2π, meaning τ = one “turn”. That’s it; just a matter of how you want to look at it. The important thing is not to lose sight of the underlying meaning of the “circle constant”: it is the unchanging relation between the around and the across.Learn more about this “fascination” aspect of math (and humans) from Michael Hartl’s “Tau Manifesto” and his Tau Day website here, including some nice videos, plus details on when it makes sense to use τ. (FYI, not always!) BTW, he’s kinda the guy who started it all! Also, here is a brief historical note on tau as it relates to the circle.OK, now you know what the “big deal” is. So, go out and tell all your friends. Post it to facebook. Start a global chain letter. Go nuts! Or not. But at least take joy in knowing what π (& τ) is really about:)--------------------Epilogue: GOING DEEPER...Being that the “radian” is central to the story of the circle constant, I’d be remiss not to mention it. Well, like the degree, it’s simply the measure of an angle. It’s almost 60 times as big as a degree. But don’t worry, that’s easily explained:)...Basically, the radian gets around the arbitrary nature of the degree: Why 360 degrees in the circle? How about 300? Or, say, 400 (see gradian/gon)? These have no intrinsic connection to the circle (dejined as the collection of points in a plane that are the same distance from a point called the center). We know this distance as the radius.
  3. Now, take the radius and wrap it around the circle. Of course, it only goes part of the way. The angle made by this pie piece is a radian. Note I said “pie”, not “pi”!:) In fact, it goes approximately 1/6th of the way around the circumference (which means 360 ̊/6 which is 60 ̊: “mystery” solved).This natural way of representing the angle of, or distance around, a circle has proven to be very handy in many instances. That said, it is not the only way (take the degree, for example!). And, in the end, math is a way of thinking. So, to the extent that a representation helps you think mathematically, including conceptually, that is what gives value to the representation.AND LASTLY...To explore more of this different way of looking at math, including philosophical excursions, plus some intellectual socializing, check out my math/philosophy group, the Wing Circle.
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