Mark Wooding wrote:
Would the world be a better place if we had a name for 2 pi rather than
pi itself?
I don't think so. The women working in the factory in India
that makes most of the worlds 2s would be out of a job.
--
Greg
--
http://mail.python.org/mailman/listinfo/python-list
Steven D'Aprano writes:
> Well, what is the definition of pi? Is it:
>
> the ratio of the circumference of a circle to twice its radius;
> the ratio of the area of a circle to the square of its radius;
> 4*arctan(1);
> the complex logarithm of -1 divided by the negative of the complex square
> r
Steven D'Aprano writes:
> On Wed, 13 Oct 2010 21:52:54 +0100, Arnaud Delobelle wrote:
>>
>> Given two circles with radii r1 and r2, circumferences C1 and C2, one is
>> obviously the scaled-up version of the other, therefore the ratio of
>> their circumferences is equal to the ratio of their radi
Steven D'Aprano wrote:
under Euclidean
geometry, there was a time when people didn't know whether or not the
ratio of circumference to radius was or wasn't a constant, and proving
that it is a constant is non-trivial.
I'm not sure that the construction you mentioned proves that
either, becaus
On Wed, Oct 13, 2010 at 07:31:59PM +, Steven D'Aprano wrote:
> On Wed, 13 Oct 2010 16:17:19 +0200, Antoon Pardon wrote:
>
> > On Wed, Oct 13, 2010 at 01:20:30PM +, Steven D'Aprano wrote:
> >> On Tue, 12 Oct 2010 22:13:26 -0700, RG wrote:
> >>
> >> >> The formula: circumference = 2 x pi x
Steve Howell writes:
> And yet nobody can recite this equally interesting ratio to thousands
> of digits:
>
> 0.2141693770623265...
That is 1/F1 where F1 is the first Feigenbaum constant a/k/a delta.
The mathworld article is pretty good:
http://mathworld.wolfram.com/FeigenbaumConstant.html
I
On Oct 13, 12:31 pm, Steven D'Aprano wrote:
0.2141693770623265
>
> Perhaps this will help illustrate what I'm talking about... the
> mathematician Mitchell Feigenbaum discovered in 1975 that, for a large
> class of chaotic systems, the ratio of each bifurcation interval to the
> next approached a
On Wed, 13 Oct 2010 21:52:54 +0100, Arnaud Delobelle wrote:
> Steven D'Aprano writes:
>
>> On Wed, 13 Oct 2010 16:17:19 +0200, Antoon Pardon wrote:
>>
>>> On Wed, Oct 13, 2010 at 01:20:30PM +, Steven D'Aprano wrote:
On Tue, 12 Oct 2010 22:13:26 -0700, RG wrote:
>> The formula
Steven D'Aprano writes:
> On Wed, 13 Oct 2010 16:17:19 +0200, Antoon Pardon wrote:
>
>> On Wed, Oct 13, 2010 at 01:20:30PM +, Steven D'Aprano wrote:
>>> On Tue, 12 Oct 2010 22:13:26 -0700, RG wrote:
>>>
>>> >> The formula: circumference = 2 x pi x radius is taught in primary
>>> >> schools,
On Wed, 13 Oct 2010 16:17:19 +0200, Antoon Pardon wrote:
> On Wed, Oct 13, 2010 at 01:20:30PM +, Steven D'Aprano wrote:
>> On Tue, 12 Oct 2010 22:13:26 -0700, RG wrote:
>>
>> >> The formula: circumference = 2 x pi x radius is taught in primary
>> >> schools, yet it's actually a very difficult
On Wed, 13 Oct 2010 15:07:07 +0100, Tim Bradshaw wrote:
> On 2010-10-13 14:20:30 +0100, Steven D'Aprano said:
>
>> ncorrect -- it's not necessarily so that the ratio of the circumference
>> to the radius of a circle is always the same number. It could have
>> turned out that different circles had
On Wed, Oct 13, 2010 at 01:20:30PM +, Steven D'Aprano wrote:
> On Tue, 12 Oct 2010 22:13:26 -0700, RG wrote:
>
> >> The formula: circumference = 2 x pi x radius is taught in primary
> >> schools, yet it's actually a very difficult formula to prove!
> >
> > What's to prove? That's the definit
On 2010-10-13 14:20:30 +0100, Steven D'Aprano said:
ncorrect -- it's not necessarily so that the ratio of the circumference
to the radius of a circle is always the same number. It could have turned
out that different circles had different ratios.
But pi is much more basic than that, I think.
On Tue, 12 Oct 2010 22:13:26 -0700, RG wrote:
>> The formula: circumference = 2 x pi x radius is taught in primary
>> schools, yet it's actually a very difficult formula to prove!
>
> What's to prove? That's the definition of pi.
Incorrect -- it's not necessarily so that the ratio of the circum
In article
,
Peter Nilsson wrote:
> Keith Thompson wrote:
> > The radian is defined as a ratio of lengths. That ratio
> > is the same regardless of the size of the circle. The
> > choice of 1/(2*pi) of the circumference isn't arbitrary
> > at all; there are sound mathematical reasons for it.
Keith Thompson wrote:
> The radian is defined as a ratio of lengths. That ratio
> is the same regardless of the size of the circle. The
> choice of 1/(2*pi) of the circumference isn't arbitrary
> at all; there are sound mathematical reasons for it.
Yes, but what is pi then?
> Mathematicians cou
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