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ebits21
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Curious on people's thoughts. Especially since most people here are a lot better at math than me!
https://www.youtube.com/watch?v=jG7vhMMXagQ
https://www.youtube.com/watch?v=jG7vhMMXagQ
ebits21 said:Curious on people's thoughts. Especially since most people here are a lot better at math than me!
Pi turns up in places that have nothing to do with circles.
Mensanator said:ebits21 said:Curious on people's thoughts. Especially since most people here are a lot better at math than me!
Pi turns up in places that have nothing to do with circles.
Tau would be 2pi, so I don't really see your point. It just makes more intuitive sense for students trying to make sense of fractions and the unit circle. You could integrate tau into any equation that uses pi.
The link in the video shows modifications in many well known formulae: http://www.tauday.com"
@Anonymous217
The video isn't really about celebrating pi day so much as suggesting a clearer way (as in clearer and more consistent) to formulate trigonometry.
micromass said:Well I certainly consider pi to be an unfortunate historic mistake. Math would be slightly more beautiful with tau. But this is the way it is and we need to stick with it.
Other unfortunate mistakes are the definition of the gamma function and the notation [tex]\subset[/tex] to mean subset or equal. But there's nothing we can do about those now...
micromass said:...Other unfortunate mistakes are the definition of the gamma function...
jhae2.718 said:For some reason I am reminded of the joke where a math professor is giving a lecture to freshman and brings up factorials, and when no one knows what they are exclaims "But it's only a special case of the gamma function!"
jhae2.718 said:I also like the joke where a visiting professor gives a lecture about Bessel functions to a group of students. When he realizes it's mostly undergrads, he asks if anyone hasn't seen a Bessel function before. When one student finally says no, the professor replies, "Well, you have now," and continues on with the lecture.
micromass said:To one student he asked: "draw a circle on the board with radius 1." The student was quite confused, but did it anyway. Then he said: "this is your score, see you next year."
ebits21 said:Mensanator said:Tau would be 2pi, so I don't really see your point. It just makes more intuitive sense for students trying to make sense of fractions and the unit circle. You could integrate tau into any equation that uses pi.ometry.
And such integration automatically makes it less intuitive for those applications not involving unit circles. And as far as intuition goes, everyone knows that if your garden hose won't reach to your rose bed, you buy an extension and make it longer. But if your hose stetches 30
feet beyond, you don't cut off the excess and attach a new nozzle.
That sums up my thoughts pretty well. In math, it is the radius of the circle that turns up in many equations, more so than the diameter. So why not define the ratio circumerence/radius as a fundamental mathematical constant, and voila! You have 6.283185...micromass said:Well I certainly consider pi to be an unfortunate historic mistake. Math would be slightly more beautiful with tau. But this is the way it is and we need to stick with it.
Since when does easier-to-measure matter in mathematics?Dickfore said:Imagine you have a pipe with a circular opening or a ball. Is it easier to measure the radius or the diameter?
Dickfore said:Imagine you have a pipe with a circular opening or a ball. Is it easier to measure the radius or the diameter?
jhae2.718 said:Whoa! This is mathematics. You can't just start bringing up practical examples like that!
Redbelly98 said:You might want to double check that area formula.
Redbelly98 said:Since when does easier-to-measure matter in mathematics?
Dickfore said:So, it's simpler to remember:
[tex]
A = 2 \tau r^{2}
[/tex]
and
[tex]
V = \frac{2 \tau}{3} r^{3}
[/tex]
for surface area and volume of a sphere?!
To one student he asked: "draw a circle on the board with radius 1." The student was quite confused, but did it anyway. Then he said: "this is your score, see you next year."
My mistake, I was thinking of the area of a circle, but you did say in the post you meant the surface area of a sphere.Dickfore said:I thought the whole point of the vid was that [itex]\tau = 2\pi[/itex].
micromass said:Just imagine that advanced civilizations in space have missed us because we've been sending pi into space, and not tau
Since when are logs circular? :tongue:HallsofIvy said:Of course, the reason the Greek's chose to give a symbol for [itex]\pi[/itex] rather than [itex]2\pi[/itex] is that the cirumference of a circle is [itex]2\pi r[/itex] or [itex]\pi d[/itex] and it is much easier to measure the diameter of a log than the radius.
TylerH said:Since when are logs circular? :tongue:
Dickfore said:By right about the same time cows became spherical.