"Conceived principally as a social hack, Tau Day and the number τ = C/r have struck a chord (sometimes literally), leading to multiple newspaper, TV, and radio interviews, and hundreds of thousands of hits."
...
I might ask, when was the last time you needed to calculate something using Pi and did remembering the extra 2 that you always need help or not?
Well if we used Tau (T) then the area of a circle would be T/2*r2. Which then extends to the volume of a cylinder H*T/2*r2. I would probably forget to divide by 2. Danged if you do, danged if you don't.
I really don't think Tau -vs- PI is so important as it's just a matter of convention unless you drag out some proof (and more than half the audience disappears).
@Rick, my wife makes great Pecan PI, but my doctor told me to avoid nuts .... (rim shot symbol crash).
mindrobots,
Fair enough. If you never think about it then it matters not what it is.
I might ask, when was the last time you needed to calculate something using Pi and did remembering the extra 2 that you always need help or not?
We could be at the root of the problem here....I can't remember the last time I used Pi for much more than the circumference of a circle. My day to day need for math beyond what I learned in 6th or 7th grade is rare. When needed, I usually have to look something up. All those brain cells after 7th grade lived and learned and died for naught!!
I'm not sure what a "social hack" might be. What is the difference between a "social hack" and a good idea?
I would say the French obsessing over metric units during the french revolution was a social hack. They even wanted metric time.
Or perhaps Sweden deciding to drive on the right in 1963 was a social hack. Even 80% of the population did not want the change.
Karl Marx sitting in the British Museum library and writing "Das Kapital" was a social hack.
The constitution of the United States of America is a social hack.
dot, dot, dot...
@Jazzed,
The area of a circle is about the ony place you see a Pi standing on it's own. So we are more "danged" if we use Pi.
Why would you forget the 2 there? Presumably the 2 in the area of a triangle is not forgotten. The Tauists will argue that the 2 in the area of a circle when using Tau actually exposes meaning that is hidden when using Pi. (See paper)
Of course there is no "proof" that Tau is more or less "true" than Pi, as you say. But it does have a very compelling simplicity which is something mathematicians usually admire. So it's odd that they let Pi stand for so long.
The title of this thread isn't correct. Pi .... Tau... It still deals with the same ratio data set.
Pi = 3.1415926535897932384626433832795
Pi x 2 is.... T
T = 6.283185307179586476925286766559
If Pi was wrong, Tau would also be wrong.
I say they are both wrong... Hmm ... im going to make up a new division, and try to create a new geek culture from the same set of data, just magnitudally different...
let seee... how about .... PI multiplied by 3 spatial dimensions...
Pi = 3.1415926535897932384626433832795 x 3
I will call it .. Spi
Spi = 9.4247779607693797153879301498385
Or we can shorten it to just S
S = 9.4247779607693797153879301498385
Ready... set... GEEK....
Time to call all the scientists and tell them they are all wrong... errr. wait...
Given my mechanical CAD background, I find myself thinking in terms of radii constantly. To me, that's a fundamental thing. Arcs have radii and circles are simply closed arcs, and additionally, circles DO have a start and end point, coincident, where with the arc they simply are not coincident.
Even before that, I kind of fixated on the radius as a core thing. Either there is one, or there isn't, and that defines arcs and circles as one thing apart from lines, points, the conic sections and non-analytic curves (Bezier, NURBS, etc...)
(Goes off to watch the videos in the hopes of some GREAT chatter at work Monday morning)
My calculator cares not a jot, if it is fed Pi, 2*pi, or of I define Tau = 2*pi and use that.....or even Omega = 2*pi*f
However, ask someone to accurately measure the radius of any object and you will find they cannot do it directly.
Instead, they will measure the diameter, and divide by 2.
So you cannot avoid that 2, all you have done, is moved it somewhere else...
I'll stick with the real world, where we measure diameters, and let the calculators manage the details, they do that stuff well.
Well, one measures diameters in the case of what fits into the hole, but most other cases are best done with a radius.
Hole to edge? You want the radius of the hole so that you can measure from a point on that radius to the edge. Hole centers are more difficult to measure with simple tools.
My calculator cares not a jot, if it is fed Pi, 2*pi, or of I define Tau = 2*pi and use that.....or even Omega = 2*pi*f
Quite true. Users of calculators and computers hardly have to worry about this at all. Want a Fourier Transform of you signal? Just get a program to do it or use a library that does it in your own code. Hence this is not an argument for or against either notation.
However, I just happened to be thinking about that last case : Omega = 2*pi*f
Sometimes we like to work with frequency "f" which is expressed in Hertz or cycles per second.
Sometimes we like to work in angular velocity "Omega" which is expressed in radians per second.
Of course these are different ways of say the same thing as one cycle around a circle is an angle of about about 6.28318 radians so:
Omega = 6.28318 * f
Bingo, there is our Tau again. Why are we always complicating things and using two times some other number to represent that 6.28...?
However, ask someone to accurately measure the radius of any object and you will find they cannot do it directly. Instead, they will measure the diameter, and divide by 2.
In general most curves don't have a diameter. When is the last time you tried to measure the diameter of the curvature of a lens?
So you cannot avoid that 2, all you have done, is moved it somewhere else...
Does it not make more sense to introduce the two when you need it, for example getting the radius from the diameter, rather than having it hanging around all throughout your work.
I'll stick with the real world, where we measure diameters...
In the real world, for example, if you want to make a round pond in your lawn I bet you are going to bang a stake in the ground and trace out a circle of some radius. Having removed the redundant two from the problem by dividing the desired diameter by two.
At the end of the day Pi or Tau makes no odds if you are using a calculator. As you say. It makes a lot of odds for kids in school learning maths where we should be presenting things as clearly and simply as possible.
Quickly now, how many radians is one third of a revolution around a circle?
I find myself thinking in terms of radii constantly. To me, that's a fundamental thing.
It's not just you. After all the very definition of a circle is:
A circle is a simple shape of Euclidean geometry that is the set of all points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius.
No mention of diameter there. Given that fundamental definition it's obviously nuts to define your circle constant in terms of the non-fundamental diameter.
Even before that, I kind of fixated on the radius as a core thing. Either there is one, or there isn't, and that defines arcs and circles as one thing apart
from lines, points, the conic sections and non-analytic curves (Bezier, NURBS, etc...)
This might seem a bit of an esoteric nitpick here but all lines have a radius. The radius of a straight line being infinite. The radius of other curves, ellipse parabola, whatever, obviously changes as you move along the curve. See "radius of curvature" here: http://en.wikipedia.org/wiki/Radius_of_curvature_(mathematics)
As I said above, In general not all curves have a diameter. They clearly do have a radius.
In fact, using the NURBS model, they are all just curves. Lines are curves, arcs are curves, splines, conics, etc... all just curves and they all have curvature and it's either constant or variable...
Lines just do not have enough definition to demonstrate variations in curvature taken to an extreme.
Radii versus circumferences... the arguments are simply circular. How can pi be wrong without tau being wrong as well?
In electronics, I am not certain that either matters so much as sin x cos x (or should that be sin x + cos x = 1), which is an expression of position within a cycle. Why radius?, the radius is always considered to be 1 for sine wave and phase calculations......
It is so odd that so many geeks are hung up on maths while not understanding that the actual use of the maths is what is important. Floating point to infinite decimal places and other such oddities are merely oddities.
Radii versus circumferences... the arguments are simply circular
"...simply circular...", I get it:)
How can pi be wrong without tau being wrong as well?
Clearly neither are wrong as defined. Don't be misled by the title of this thread, no one want to suggest a new value for Pi.
The statement here is simply that the radius is the more fundamental property of a circle. After all the fundamental definition of a circle is in terms of radius. Therefore C/R is a more fundamental way to look at the "circle constant" than "C/D". Turns out then when you work with it in trigonometry upwards it gets rid of a lot of clutter in the equations and exposes the meaning of what you are doing more clearly.
In electronics, I am not certain that either matters so much as sin x cos x, which is an expression of position within a cycle.
Yes, perhaps. Those x's there are angles and we like to work in terms of radians. I think if you continue your chain of thought you will end up liking Tau as well. For example:
"position within a cycle" as you say. Well:
What is one complete cycle? 2 * Pi radians.
What is position halfway through a cycle? Pi radians.
What is a quarter or three quarters of a cycle? Pi / 2 or 3 * Pi / 2
Would it not be clearer to have half cycle represented by 1/2 and a quarter cycle represented by 1/4 and so on as one might expect?
And we end up with answers of Tau, Tau/2, Tau/4, 3*Tau/4
Think of Tau as "turn".
It is so odd that so many geeks are hung up on maths while not understanding that the actual use of the maths is what is important. Floating point to infinite decimal places and other such oddities are merely oddities.
I probably agree there, but I'm not quite sure what you mean yet.
Euler's identity, e^(i*pi)+1 = 0, would change to e^(i*tau)-1 = 0.
Since the original form combines 0,1,i,e,pi with addition, multiplication and exponentiation is a tad more elegant
that the one with subtraction.
This decides it for me!
Also e^(i*tau)-1 = 0 allows tau to be zero, which is a trivial solution, Euler's identity can be treated as a
definition of pi, all the solutions are non-trivial (being (2n+1)pi)
[ addition is repeated increment, multiplication repeated addition, exponentiation repeated multiplication - the Euler
identity neatly combines them - subtraction would spoil the pattern ]
Wait a minute, don't you mean Euler's identity becomes e^(i*tau) = 1
It's an aesthetic point, as maths often is, but that seems even more elegant to me. Given that 1 is the multiplicative identity it is directly telling you that e^(i*tau) is the multiplicative identity for complex numbers.
I might say "That decides it for me!"
If you object that zero is missing from the identity I can only suggest that it is appropriate, what with zero being nothing and all that.
Anyway, by way of a balanced view here is the response from the Piists: http://www.thepimanifesto.com/
Rather than worrying about the Pi(e) for dessert, or the Pi / Tau debate, I am more concerned with the Pii / P2
When I need a formula I usually derive it from first principles as my memory of lots of unused formulae from over 40 years ago is no longer the best.
The area of a rectangle is L*B. The area of a circle is a little less than L*B where L=B=diameter. Since Pi = 3.141592.. then the area of a circle must be Pi/4*L*B or put more simply Pi*R*R = Pi*R^2 because R=L/2 (because I recall that Pi is the circle constant).
The perimeter of a rectangle is L+B+L+B = 2*(L+B). For a circle it is a little less.. so it must be Pi/4*2*(L+B) = Pi/4*2*2*D (since diameter D = L = = Pi*D = 2*Pi*R (radius = diameter/2)
On this basis, I think Pi/4 would have been a better constant.
I asked the AI Siri inside the iPhone by speaking, "What is the value of pi?"
It gave the correct number out to 20 places. However, the real value
of pi could also mean "cherry." The AI made a correct assumption based
on my question. However, with tau, it thinks "tile" and did not produce a
correct response.
In the good old days, there were no good communications other than snail mail. So no debates. What was decided by the few had to be used by the majority. Nowadays, we can rant so easily on forums or facebook etc. So everyone can input their opinion easily, but with so many with different views of the situation, someone has to take control and make the decisions.
The internet is absolutely life changing. Most of it is good, but there are a few downsides such as internet fraud, flaming, etc, etc.
On this basis, I think Pi/4 would have been a better constant.
Funny you should say that. You are not the first:
[url]
[/url]
Loopy and Cluso
Does the internet breed these problems?
I believe it does.
In the extreme, all traditional sources are gone and only the net remains.
News papers all bankrupt and out when all advertising is web based.
Paper books no longer produced as e-books take over.
Universities replaced by on line academies ans such resources.
And so on.
At that point it becomes impossible to have "true" and "false" any more.
Any view of anything can and will be expressed by anyone on the planet.
How we will ever get a grip on what is real in that soup of incorrect, un-vetted, un-verifiable, infinitely malleable information is a mystery to me.
As Cluso says "..someone has to take control and make the decisions" except that frightens me. Historically the some ones who do that kind of thing have been quite dangerous. Giving them that power on a global scale is mind boggling.
The reason they chose 3.14 not 6.28 is because a circle is oval. To find the area of a oval is pi*r1*r2. With you "Tua" or whatever you said it would be (Tua/2)*r1*r2. Which one would you like? To find the area of a circle is pi*r1*r1
The reason they chose 3.14 not 6.28 is because a circle is oval. To find the area of a oval is pi*r1*r2. With you "Tua" or whatever you said it would be (Tua/2)*r1*r2. Which one would you like? To find the area of a circle is pi*r1*r1
The oval thing makes sense.
The tau as number of turns makes sense.
In which cases do we use one or the other, which comes up more often? (Neither comes up very often for me)
Pi having an endless row of non-repeating numbers can contain any or all sequences of numbers, like in 'Contact' it contained a bitmap of a circle. Does that mean that Tau would contain a bitmap of two circles? And what would the implications of that be?
That is easy to answer. If I wanted to make a bit map from Pi I would express it in binary. That immediately gives me a nice monochrome bit map. Or really an infinite number of bit maps depending how I want to chop it up.
Anyway we then have:
Pi = 11.00100100 00111111 01101010 10001000 10000101 10100011 00001000 11010011...
Tau = 110.0100100 00111111 01101010 10001000 10000101 10100011 00001000 11010011...
As you see in binary the numbers are the same except for the position of the binary point.
I conclude that we have the same bit maps available in both assuming we are prepared to adjust our bit map chopping by one bit appropriately. So if there are circles in one there are the same circles in the other.
But, what does it mean to have a bit map of a circle?
The smallest one might look like this:
00000
01110
01010
01110
00000
Which is the binary sequence 0000001110010100111000000, in only 25 bits we can draw a line of ones around a zero with radius about equal one.
Not much of a circle though is it, at what resolution would you be happy and say "that is a circle not just some jaggy line"?
I conclude that there are no circles in the bit maps you can pull out of Pi or Tau.
P.S. Given that 25 bits is 33,554,432 we would expect to see that little circle once in every next 33 million binary digits of Pi. Bigger ones will be a bit harder to find...
Comments
From: http://www.michaelhartl.com/about
"Conceived principally as a social hack, Tau Day and the number τ = C/r have struck a chord (sometimes literally), leading to multiple newspaper, TV, and radio interviews, and hundreds of thousands of hits."
C.W.
Well if we used Tau (T) then the area of a circle would be T/2*r2. Which then extends to the volume of a cylinder H*T/2*r2. I would probably forget to divide by 2. Danged if you do, danged if you don't.
I really don't think Tau -vs- PI is so important as it's just a matter of convention unless you drag out some proof (and more than half the audience disappears).
@Rick, my wife makes great Pecan PI, but my doctor told me to avoid nuts .... (rim shot symbol crash).
Bummer! Must really impact your time on the forum! :0)
We could be at the root of the problem here....I can't remember the last time I used Pi for much more than the circumference of a circle. My day to day need for math beyond what I learned in 6th or 7th grade is rare. When needed, I usually have to look something up. All those brain cells after 7th grade lived and learned and died for naught!!
http://www.conted.ox.ac.uk/courses/details.php?id=G100-29
Only 60 quid !
@ctwardel,
I'm not sure what a "social hack" might be. What is the difference between a "social hack" and a good idea?
I would say the French obsessing over metric units during the french revolution was a social hack. They even wanted metric time.
Or perhaps Sweden deciding to drive on the right in 1963 was a social hack. Even 80% of the population did not want the change.
Karl Marx sitting in the British Museum library and writing "Das Kapital" was a social hack.
The constitution of the United States of America is a social hack.
dot, dot, dot...
@Jazzed,
The area of a circle is about the ony place you see a Pi standing on it's own. So we are more "danged" if we use Pi.
Why would you forget the 2 there? Presumably the 2 in the area of a triangle is not forgotten. The Tauists will argue that the 2 in the area of a circle when using Tau actually exposes meaning that is hidden when using Pi. (See paper)
Of course there is no "proof" that Tau is more or less "true" than Pi, as you say. But it does have a very compelling simplicity which is something mathematicians usually admire. So it's odd that they let Pi stand for so long.
https://en.wikipedia.org/wiki/Order_of_magnitude
https://en.wikipedia.org/wiki/Scalar_multiplication
Different ways of looking at the same data...
The title of this thread isn't correct. Pi .... Tau... It still deals with the same ratio data set.
Pi = 3.1415926535897932384626433832795
Pi x 2 is.... T
T = 6.283185307179586476925286766559
If Pi was wrong, Tau would also be wrong.
I say they are both wrong... Hmm ... im going to make up a new division, and try to create a new geek culture from the same set of data, just magnitudally different...
let seee... how about .... PI multiplied by 3 spatial dimensions...
Pi = 3.1415926535897932384626433832795 x 3
I will call it .. Spi
Spi = 9.4247779607693797153879301498385
Or we can shorten it to just S
S = 9.4247779607693797153879301498385
Ready... set... GEEK....
Time to call all the scientists and tell them they are all wrong... errr. wait...
Yes indeed Pi and Tau are expressing the same idea. No one is saying the actual value of Pi is wrong.
The issue is, why defined your circle constant in a more clumsy way than you have to? Why not go for the more basic definiton?
Your spi example neatly sums up the issue. For example:
The resonant frequency of an inductor and capacitor in parallel is 1 / (2 * Pi * sqrt(L * C))
If we use your spi we would have 3 / (2 * spi * sqrt(L * C))
We immediately see that the three you have introduced is redundant and a pain in the ***. Let's get back to using Pi.
But wait, that two in there is also redundant and a pain in the ***, lets's get rid of that as well.
And then there was Tau.
Given my mechanical CAD background, I find myself thinking in terms of radii constantly. To me, that's a fundamental thing. Arcs have radii and circles are simply closed arcs, and additionally, circles DO have a start and end point, coincident, where with the arc they simply are not coincident.
Even before that, I kind of fixated on the radius as a core thing. Either there is one, or there isn't, and that defines arcs and circles as one thing apart from lines, points, the conic sections and non-analytic curves (Bezier, NURBS, etc...)
(Goes off to watch the videos in the hopes of some GREAT chatter at work Monday morning)
My calculator cares not a jot, if it is fed Pi, 2*pi, or of I define Tau = 2*pi and use that.....or even Omega = 2*pi*f
However, ask someone to accurately measure the radius of any object and you will find they cannot do it directly.
Instead, they will measure the diameter, and divide by 2.
So you cannot avoid that 2, all you have done, is moved it somewhere else...
I'll stick with the real world, where we measure diameters, and let the calculators manage the details, they do that stuff well.
Hole to edge? You want the radius of the hole so that you can measure from a point on that radius to the edge. Hole centers are more difficult to measure with simple tools.
However, I just happened to be thinking about that last case : Omega = 2*pi*f
Sometimes we like to work with frequency "f" which is expressed in Hertz or cycles per second.
Sometimes we like to work in angular velocity "Omega" which is expressed in radians per second.
Of course these are different ways of say the same thing as one cycle around a circle is an angle of about about 6.28318 radians so:
Omega = 6.28318 * f
Bingo, there is our Tau again. Why are we always complicating things and using two times some other number to represent that 6.28...? In general most curves don't have a diameter. When is the last time you tried to measure the diameter of the curvature of a lens? Does it not make more sense to introduce the two when you need it, for example getting the radius from the diameter, rather than having it hanging around all throughout your work. In the real world, for example, if you want to make a round pond in your lawn I bet you are going to bang a stake in the ground and trace out a circle of some radius. Having removed the redundant two from the problem by dividing the desired diameter by two.
At the end of the day Pi or Tau makes no odds if you are using a calculator. As you say. It makes a lot of odds for kids in school learning maths where we should be presenting things as clearly and simply as possible.
Quickly now, how many radians is one third of a revolution around a circle?
A circle is a simple shape of Euclidean geometry that is the set of all points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius.
No mention of diameter there. Given that fundamental definition it's obviously nuts to define your circle constant in terms of the non-fundamental diameter. This might seem a bit of an esoteric nitpick here but all lines have a radius. The radius of a straight line being infinite. The radius of other curves, ellipse parabola, whatever, obviously changes as you move along the curve. See "radius of curvature" here: http://en.wikipedia.org/wiki/Radius_of_curvature_(mathematics)
As I said above, In general not all curves have a diameter. They clearly do have a radius.
In fact, using the NURBS model, they are all just curves. Lines are curves, arcs are curves, splines, conics, etc... all just curves and they all have curvature and it's either constant or variable...
Lines just do not have enough definition to demonstrate variations in curvature taken to an extreme.
In electronics, I am not certain that either matters so much as sin x cos x (or should that be sin x + cos x = 1), which is an expression of position within a cycle. Why radius?, the radius is always considered to be 1 for sine wave and phase calculations......
It is so odd that so many geeks are hung up on maths while not understanding that the actual use of the maths is what is important. Floating point to infinite decimal places and other such oddities are merely oddities.
The statement here is simply that the radius is the more fundamental property of a circle. After all the fundamental definition of a circle is in terms of radius. Therefore C/R is a more fundamental way to look at the "circle constant" than "C/D". Turns out then when you work with it in trigonometry upwards it gets rid of a lot of clutter in the equations and exposes the meaning of what you are doing more clearly. Yes, perhaps. Those x's there are angles and we like to work in terms of radians. I think if you continue your chain of thought you will end up liking Tau as well. For example:
"position within a cycle" as you say. Well:
What is one complete cycle? 2 * Pi radians.
What is position halfway through a cycle? Pi radians.
What is a quarter or three quarters of a cycle? Pi / 2 or 3 * Pi / 2
Would it not be clearer to have half cycle represented by 1/2 and a quarter cycle represented by 1/4 and so on as one might expect?
And we end up with answers of Tau, Tau/2, Tau/4, 3*Tau/4
Think of Tau as "turn".
I probably agree there, but I'm not quite sure what you mean yet.
Since the original form combines 0,1,i,e,pi with addition, multiplication and exponentiation is a tad more elegant
that the one with subtraction.
This decides it for me!
Also e^(i*tau)-1 = 0 allows tau to be zero, which is a trivial solution, Euler's identity can be treated as a
definition of pi, all the solutions are non-trivial (being (2n+1)pi)
[ addition is repeated increment, multiplication repeated addition, exponentiation repeated multiplication - the Euler
identity neatly combines them - subtraction would spoil the pattern ]
Also, if it ain't broke, don't fix it!
Wait a minute, don't you mean Euler's identity becomes e^(i*tau) = 1
It's an aesthetic point, as maths often is, but that seems even more elegant to me. Given that 1 is the multiplicative identity it is directly telling you that e^(i*tau) is the multiplicative identity for complex numbers.
I might say "That decides it for me!"
If you object that zero is missing from the identity I can only suggest that it is appropriate, what with zero being nothing and all that.
Anyway, by way of a balanced view here is the response from the Piists: http://www.thepimanifesto.com/
When I need a formula I usually derive it from first principles as my memory of lots of unused formulae from over 40 years ago is no longer the best.
The area of a rectangle is L*B. The area of a circle is a little less than L*B where L=B=diameter. Since Pi = 3.141592.. then the area of a circle must be Pi/4*L*B or put more simply Pi*R*R = Pi*R^2 because R=L/2 (because I recall that Pi is the circle constant).
The perimeter of a rectangle is L+B+L+B = 2*(L+B). For a circle it is a little less.. so it must be Pi/4*2*(L+B) = Pi/4*2*2*D (since diameter D = L =
On this basis, I think Pi/4 would have been a better constant.
Does the internet breed these problems?
It gave the correct number out to 20 places. However, the real value
of pi could also mean "cherry." The AI made a correct assumption based
on my question. However, with tau, it thinks "tile" and did not produce a
correct response.
http://humanoidolabs.blogspot.tw/2013/01/big-brain-new-ai-friend-siri.html
The internet is absolutely life changing. Most of it is good, but there are a few downsides such as internet fraud, flaming, etc, etc.
[url]
[/url]
Loopy and Cluso I believe it does.
In the extreme, all traditional sources are gone and only the net remains.
News papers all bankrupt and out when all advertising is web based.
Paper books no longer produced as e-books take over.
Universities replaced by on line academies ans such resources.
And so on.
At that point it becomes impossible to have "true" and "false" any more.
Any view of anything can and will be expressed by anyone on the planet.
How we will ever get a grip on what is real in that soup of incorrect, un-vetted, un-verifiable, infinitely malleable information is a mystery to me.
As Cluso says "..someone has to take control and make the decisions" except that frightens me. Historically the some ones who do that kind of thing have been quite dangerous. Giving them that power on a global scale is mind boggling.
The oval thing makes sense.
The tau as number of turns makes sense.
In which cases do we use one or the other, which comes up more often? (Neither comes up very often for me)
What is a simplest way to capture them both?
Whose name would translate to what, 1.5tau? I think not.
I'm sticking with pi.
Rather than calling it Tau, perhaps they should call it Taz?
http://www.youtube.com/watch?v=nAU_IQgiggM
That is easy to answer. If I wanted to make a bit map from Pi I would express it in binary. That immediately gives me a nice monochrome bit map. Or really an infinite number of bit maps depending how I want to chop it up.
Anyway we then have:
Pi = 11.00100100 00111111 01101010 10001000 10000101 10100011 00001000 11010011...
Tau = 110.0100100 00111111 01101010 10001000 10000101 10100011 00001000 11010011...
As you see in binary the numbers are the same except for the position of the binary point.
I conclude that we have the same bit maps available in both assuming we are prepared to adjust our bit map chopping by one bit appropriately. So if there are circles in one there are the same circles in the other.
But, what does it mean to have a bit map of a circle?
The smallest one might look like this:
Which is the binary sequence 0000001110010100111000000, in only 25 bits we can draw a line of ones around a zero with radius about equal one.
Not much of a circle though is it, at what resolution would you be happy and say "that is a circle not just some jaggy line"?
I conclude that there are no circles in the bit maps you can pull out of Pi or Tau.
P.S. Given that 25 bits is 33,554,432 we would expect to see that little circle once in every next 33 million binary digits of Pi. Bigger ones will be a bit harder to find...
Martin, I cannot die happy until I do that with a Scribbler, even at significantly reduced RPM. That is, in a word, bitchin'.
BTW, what is the approximate RPM there, in PI RADIANS per second?