- #1

ebits21

- 46

- 0

https://www.youtube.com/watch?v=jG7vhMMXagQ

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter ebits21
- Start date

- #1

ebits21

- 46

- 0

https://www.youtube.com/watch?v=jG7vhMMXagQ

- #2

disregardthat

Science Advisor

- 1,866

- 34

- #3

Anonymous217

- 355

- 2

- #4

Mensanator

- 105

- 0

Pi turns up in places that have nothing to do with circles.

- #5

spamiam

- 360

- 0

- #6

Anonymous217

- 355

- 2

- #7

ebits21

- 46

- 0

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" [Broken]

@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.

Last edited by a moderator:

- #8

- 22,178

- 3,317

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...

- #9

myth_kill

- 19

- 0

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...

why do u consider it to be a mistake ?

you ought to read this :

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Pi_through_the_ages.html

- #10

jhae2.718

Gold Member

- 1,182

- 20

...Other unfortunate mistakes are the definition of the gamma function...

For some reason I am reminded of the joke where a math professor is giving a lecture to freshman and brings up factorials (n! is of course N!), and when no one knows what they are exclaims "But it's only a special case of the gamma function!"

Back on topic, I say stick with [tex]\pi[/tex].

- #11

- 22,178

- 3,317

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!"

That made my day

- #12

jhae2.718

Gold Member

- 1,182

- 20

- #13

- 22,178

- 3,317

That reminds me of an oral exam that I once had. The professor asks something very complicated using terms that I had never heard of before. So I say: "I'm pretty sure we have never seen those things." The professor just answered: "True, but I have seen them before." And I had to answer the question...

- #14

jhae2.718

Gold Member

- 1,182

- 20

Doesn't sound very fun. Did you get it right?

- #15

- 22,178

- 3,317

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."

It wasn't funny then, but we can laugh with it right now...:tongue2:

- #16

jhae2.718

Gold Member

- 1,182

- 20

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."

I would have drawn a circle of radius

- #17

Dickfore

- 2,988

- 5

- #18

Mensanator

- 105

- 0

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.

- #19

- 12,167

- 185

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/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.

That being said, we might as well stick with the system we have. If we Americans aren't willing to change over to metric units, I can't imagine people adopting

- #20

Dickfore

- 2,988

- 5

[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?!

I think the author of the video should start memorizing formulas instead of 'thinking critically'.

Also:

Imagine you have a pipe with a circular opening or a ball. Is it easier to measure the radius or the diameter?

- #21

- 12,167

- 185

Since when does easier-to-measure matter in mathematics?Imagine you have a pipe with a circular opening or a ball. Is it easier to measure the radius or the diameter?

- #22

jhae2.718

Gold Member

- 1,182

- 20

Imagine you have a pipe with a circular opening or a ball. Is it easier to measure the radius or the diameter?

Whoa! This is

- #23

ebits21

- 46

- 0

Whoa! This ismathematics. You can't just start bringing up practical examples like that!

I think the point is that the radius is the fundamental unit. Diameter can always be broken down into radius.

Plus.. in real life you can't just take a tape measure and hope to find the absolute value of the diameter. This is because you can't be sure you're going through the center of the pipe exactly. You would have to know the center exactly (and the radius, by definition, relates to the center).

If you use a metal wedge with a known angle to find the diameter of a pipe, you geometrically find the radius of the pipe, then multiply by two to find the diameter.

Edit: Okay, I forgot about calipers. :P

Last edited:

- #24

Dickfore

- 2,988

- 5

You might want to double check that area formula.

I thought the whole point of the vid was that [itex]\tau = 2\pi[/itex].

Since when does easier-to-measure matter in mathematics?

Since when is not being able to remember formulas considered being a mathematician?

- #25

jhae2.718

Gold Member

- 1,182

- 20

I personally say stick with [tex]\pi[/tex]. Far too late to change anything.

- #26

ebits21

- 46

- 0

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?!

Seems equally easy to remember as with pi to me. That is, if you were a person learning from scratch.

- #27

spamiam

- 360

- 0

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."

All right you jokesters, enough of that!

But seriously, the section of the manifesto on quadratic forms was quite persuasive. It compared

[itex]\frac{1}{2}gt^2[/itex], [itex]\frac{1}{2}kx^2[/itex], and [itex]\frac{1}{2}mv^2[/itex], concluding with [itex]\frac{1}{2}\tau r^2[/itex] for the area of a circle. I was pretty impressed.

Last edited:

- #28

HallsofIvy

Science Advisor

Homework Helper

- 43,017

- 973

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.

Last edited by a moderator:

- #29

- 12,167

- 185

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.I thought the whole point of the vid was that [itex]\tau = 2\pi[/itex].

- #30

- 22,178

- 3,317

- #31

Dickfore

- 2,988

- 5

Well, they wouldn't have been so advanced to not recognize we were sending [itex]\tau/2[/itex].

- #32

- 12,167

- 185

Especially if we send in binary, you'd really have to be an idiot not to recognize it.

- #33

TylerH

- 729

- 0

Since when are logs circular? :tongue:Of course, thereasonthe 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 thediameterof a log than the radius.

- #34

Dickfore

- 2,988

- 5

Since when are logs circular? :tongue:

By right about the same time cows became spherical.

- #35

jhae2.718

Gold Member

- 1,182

- 20

By right about the same time cows became spherical.

Wait...cows aren't really spherical?

Share:

- Replies
- 35

- Views
- 1K

- Last Post

- Replies
- 7

- Views
- 817

- Replies
- 56

- Views
- 3K

- Replies
- 14

- Views
- 481

- Last Post

- Replies
- 2

- Views
- 758

- Last Post

- Replies
- 4

- Views
- 841

- Last Post

- Replies
- 5

- Views
- 525

- Replies
- 66

- Views
- 2K

- Last Post

- Replies
- 3

- Views
- 2K

MHB
Pi

- Last Post

- Replies
- 3

- Views
- 2K