Tau VS Pi
Pi
 44%  [ 17 ]
Tau
 23%  [ 9 ]
Both
 26%  [ 10 ]
Neither
 2%  [ 1 ]
Other, please post.
 2%  [ 1 ]
Total Votes : 38

_iPhoenix_ wrote:
Lemme restate my solution:

Use them when they are more useful.

You (JWinslow) described numerous formulae with 2π and, yes, you admitted that although not all formulae use it, most do.

I think tau should be taught/used where it is more efficient/makes more sense logically, and pi used where is would be more efficient/makes more sense.

There are 2 ways such a solution could go
    A) Students learn about how the circle constants relate to their maths more clearly, and are able to see why sometimes one is preferred over the other.

    B) Students try to memorize which one to use in which scenario rather than thinking of what it means, and end up getting them mixed up and being thoroughly confused.
mr womp womp wrote:
_iPhoenix_ wrote:
Lemme restate my solution:

Use them when they are more useful.

You (JWinslow) described numerous formulae with 2π and, yes, you admitted that although not all formulae use it, most do.

I think tau should be taught/used where it is more efficient/makes more sense logically, and pi used where is would be more efficient/makes more sense.

There are 2 ways such a solution could go
    A) Students learn about how the circle constants relate to their maths more clearly, and are able to see why sometimes one is preferred over the other.

    B) Students try to memorize which one to use in which scenario rather than thinking of what it means, and end up getting them mixed up and being thoroughly confused.


I vote A Razz

But the students should be taught that they have a simple conversion.
Well, I kinda disagree with the "simple conversion" thing. Sure, at first, the fact that there needs to be a conversion, however simple, from pi to tau is unavoidable. However, my own goal with this is for the correct convention (which I believe is tau) to be collectively set in the minds of students, teachers, mathematicians, and the like. This is only possible if there are people that are willing to go the extra mile with this idea, e.g. using it in a high-profile mathematical paper, or teaching a class with it. Tau isn't only reserved to a passing mention in any class.

It took quite a long time even for the convention of pi to be used and accepted by many. Some people used pi, but some people used pi/delta, some used p, some used c, and some even used a weird curly symbol to express the same quantity, C/D. And even after pi became standard, people still used 2pi as a separate symbol (i.e. always writing 2pi/4 instead of pi/2). Pi has been around for about 300 years, and only now is it as famous and popular as it is today, so I wouldn't hold my breath that we'd change immediately, of course. But the great thing is, it doesn't need to happen all at once.
My algebra teacher introduced it as an alternative.

(And I showed him it Razz)

Also, weren't there several petitions to make pi equal to exactly 3 in some areas
"And he [Hiram] made a molten sea, ten cubits from the one rim to the other it was round all about, and...a line of thirty cubits did compass it round about....And it was an hand breadth thick...." First Kings, chapter 7, verses 23 and 26

One of my all time favorite passage from teh bibble Evil or Very Mad
mr womp womp wrote:
"And he [Hiram] made a molten sea, ten cubits from the one rim to the other it was round all about, and...a line of thirty cubits did compass it round about....And it was an hand breadth thick...." First Kings, chapter 7, verses 23 and 26

One of my all time favorite passage from teh bibble Evil or Very Mad

Hm, there might be a couple explanations for this:

1. It wasn't exactly round, but slightly elliptical.
2. There was an error in measurement.
3. The bowl was not a "bowl" in the hemispherical sense, but rather a cylinder that was flared at the top (as this verse seems to suggest).
4. My favorite explanation: the measurement is exactly correct.

Let me explain:

The passage says that the measurement "from one rim to the other" (or outer diameter) is 10 cubits (180 inches), meaning it has an outer radius of 90 inches. It also says that it had a circumference of 30 cubits (540 inches) (unspecified whether outer or inner, but because using the outer circumference would give us a bowl with no thickness, let's use inner). And finally, it says the bowl was a handbreadth (4 inches) thick.

This gives us an inner radius of 90 - 4 = 86 inches. Plugging this into the formula for circumference of a circle, τr, gives us 540 = 86τ, or τ = 540 / 86, which is equal to 6.279069767441860465116 repeating, or ~6.28. Since 6.28 is the most common approximation for τ, maybe those measurements are pretty accurate after all.
Bump.

Happy Tau Day, everyone! I hope you all take the time to read The Tau Manifesto today! It might convince some of the unconvinced here Wink
JWinslow23 wrote:
Bump.

Happy Tau Day, everyone! I hope you all take the time to read The Tau Manifesto today! It might convince some of the unconvinced here Wink

Oh my, I didn't even notice! As a converted tauist, I should pay more attention to tau day Razz
I think a fun thing to do for pi day would be to bake half a pie, and make a bunch of half-circle related things, rather than the full-circle things that the un-converted usually (and wrongfully) make.
mr womp womp wrote:
JWinslow23 wrote:
Bump.

Happy Tau Day, everyone! I hope you all take the time to read The Tau Manifesto today! It might convince some of the unconvinced here Wink

Oh my, I didn't even notice! As a converted tauist, I should pay more attention to tau day Razz
I think a fun thing to do for pi day would be to bake half a pie, and make a bunch of half-circle related things, rather than the full-circle things that the un-converted usually (and wrongfully) make.

Heh, yeah. Maybe try and see how well a car drives with semicircle-shaped wheels. Laughing
JWinslow23 wrote:
mr womp womp wrote:
"And he [Hiram] made a molten sea, ten cubits from the one rim to the other it was round all about, and...a line of thirty cubits did compass it round about....And it was an hand breadth thick...." First Kings, chapter 7, verses 23 and 26

One of my all time favorite passage from teh bibble Evil or Very Mad

Hm, there might be a couple explanations for this:

1. It wasn't exactly round, but slightly elliptical.
2. There was an error in measurement.
3. The bowl was not a "bowl" in the hemispherical sense, but rather a cylinder that was flared at the top (as this verse seems to suggest).
4. My favorite explanation: the measurement is exactly correct.

Let me explain:

The passage says that the measurement "from one rim to the other" (or outer diameter) is 10 cubits (180 inches), meaning it has an outer radius of 90 inches. It also says that it had a circumference of 30 cubits (540 inches) (unspecified whether outer or inner, but because using the outer circumference would give us a bowl with no thickness, let's use inner). And finally, it says the bowl was a handbreadth (4 inches) thick.

This gives us an inner radius of 90 - 4 = 86 inches. Plugging this into the formula for circumference of a circle, τr, gives us 540 = 86τ, or τ = 540 / 86, which is equal to 6.279069767441860465116 repeating, or ~6.28. Since 6.28 is the most common approximation for τ, maybe those measurements are pretty accurate after all.


I'm no historian, but the ancients considered the ratio of diameter to circumference to be exactly 3. (Isaac Asimov wrote a beautiful essay called "A piece of pi" and I highly, highly, highly recommend it, as it delves into the history of the current circle constant, and explains that passage wonderfully.)

Here's an alternative explanation, using pi (I have nothing against tau, just I'm approaching the same problem from a different perspective)


I will be using cubits as my unit of measurement but it doesn't really matter.



To find how far off a circumference (c) is (in percent) when given diameter (d) and use the following equation.

f(c, d) = 100(1 - (c / πd))

We simply plug in c and d to get:

f(30, 10) = 100 - 300/π
f(30, 10) = 4.507034144862798538669741976491382779324212555726130751399...%

That's acceptable, small scale.

I'm still not sure what I achieved through all this... Cool

Oh yeah, I flooded SAX with !calc commands...
_iPhoenix_ wrote:
JWinslow23 wrote:
mr womp womp wrote:
"And he [Hiram] made a molten sea, ten cubits from the one rim to the other it was round all about, and...a line of thirty cubits did compass it round about....And it was an hand breadth thick...." First Kings, chapter 7, verses 23 and 26

One of my all time favorite passage from teh bibble Evil or Very Mad

Hm, there might be a couple explanations for this:

1. It wasn't exactly round, but slightly elliptical.
2. There was an error in measurement.
3. The bowl was not a "bowl" in the hemispherical sense, but rather a cylinder that was flared at the top (as this verse seems to suggest).
4. My favorite explanation: the measurement is exactly correct.

Let me explain:

The passage says that the measurement "from one rim to the other" (or outer diameter) is 10 cubits (180 inches), meaning it has an outer radius of 90 inches. It also says that it had a circumference of 30 cubits (540 inches) (unspecified whether outer or inner, but because using the outer circumference would give us a bowl with no thickness, let's use inner). And finally, it says the bowl was a handbreadth (4 inches) thick.

This gives us an inner radius of 90 - 4 = 86 inches. Plugging this into the formula for circumference of a circle, τr, gives us 540 = 86τ, or τ = 540 / 86, which is equal to 6.279069767441860465116 repeating, or ~6.28. Since 6.28 is the most common approximation for τ, maybe those measurements are pretty accurate after all.


I'm no historian, but the ancients considered the ratio of diameter to circumference to be exactly 3. (Isaac Asimov wrote a beautiful essay called "A piece of pi" and I highly, highly, highly recommend it, as it delves into the history of the current circle constant, and explains that passage wonderfully.)

Here's an alternative explanation, using pi (I have nothing against tau, just I'm approaching the same problem from a different perspective)


I will be using cubits as my unit of measurement but it doesn't really matter.



To find how far off a circumference (c) is (in percent) when given diameter (d) and use the following equation.

f(c, d) = 100(1 - (c / πd))

We simply plug in c and d to get:

f(30, 10) = 100 - 300/π
f(30, 10) = 4.507034144862798538669741976491382779324212555726130751399...%

That's acceptable, small scale.

I'm still not sure what I achieved through all this... Cool

Oh yeah, I flooded SAX with !calc commands...

Do you think they would have calculated the circumference of the bowl, instead of actually measuring it somehow?

I'm under the belief that they measured the bowl's diameter and circumference, but the discrepancy in measurement is due to the difference in outer and inner circumference and diameter.
Apparently there are other examples of pi being equal to three to the ancients.
JWinslow23 wrote:
mr womp womp wrote:
JWinslow23 wrote:
Bump.

Happy Tau Day, everyone! I hope you all take the time to read The Tau Manifesto today! It might convince some of the unconvinced here Wink

Oh my, I didn't even notice! As a converted tauist, I should pay more attention to tau day Razz
I think a fun thing to do for pi day would be to bake half a pie, and make a bunch of half-circle related things, rather than the full-circle things that the un-converted usually (and wrongfully) make.

Heh, yeah. Maybe try and see how well a car drives with semicircle-shaped wheels. 0x5

EDIT: This half-pie thing appears to already be a thing Razz
  
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