redefining pi

[calvin]

Why not define pi to be the area of a unit circle?
That doesn't change the value of pi, but changes
our way of looking at it.

Currently we look at a circle and try to wrap its diameter
around its circumference, and see that it takes about 3
diameters to do the job, but we are not perceiving pi
directly or exactly.

With the proposed definition, we see pi whenever we see
a circle, and we see it instantly and perfectly. Pi then might
become the central symbol of mathematics, matching
its myriad mathematical and physical applications.

[david petry]

On Sunday, May 5, 2013 2:35:19 PM UTC-7, calvin wrote:

> Why not define pi to be the area of a unit circle?
> That doesn't change the value of pi, but changes
> our way of looking at it.

> Currently we look at a circle and try to wrap its diameter
> around its circumference, and see that it takes about 3
> diameters to do the job, but we are not perceiving pi
> directly or exactly.

Just something to consider: when I was a very young child, it occurred to me to ask the question of how far a wheel goes each time it rolls around once, but it didn't occur to me to ask what the area of a circle is. So for me at least, the usual way of thinking about pi is the natural way.

[JT]

You need Pi to calculate the area so i do not see the point, if you
can calculate the circumreference and area without use of radius, you
can get rid of Pi.

[William Elliot]

On Sun, 5 May 2013, david petry wrote:

> Just something to consider: when I was a very young child, it occurred
> to me to ask the question of how far a wheel goes each time it rolls

> around once.

pi.d where d is the diameter of the circle.

[JT]

And one way to go at it would be using polygons and the ratios of
their sides, the six sided polygon have very nice features, but there
may be better ones.

[William Elliot]

On Sun, 5 May 2013, calvin wrote:

> Why not define pi to be the area of a unit circle?

Because then the circumference of a circle would
be C = 2.pi.sqr A and the radius r = sqr A.

[Timothy Murphy]

calvin wrote:

> Why not define pi to be the area of a unit circle?
> That doesn't change the value of pi, but changes
> our way of looking at it.
>
> Currently we look at a circle and try to wrap its diameter
> around its circumference, and see that it takes about 3
> diameters to do the job, but we are not perceiving pi
> directly or exactly.

I agree with you.
The length of a path is a much more complicated concept
than the area of an open set (in the plane).

What does the teacher say to the school pupil who asks,
"What do you mean by the circumference of a circle?"

--
Timothy Murphy
e-mail: gayleard /at/ eircom.net
tel: +353-86-2336090, +353-1-2842366
s-mail: School of Mathematics, Trinity College Dublin

[Bill Taylor]

The mathematically best way to define pi
is as the appropriate zero of certain parts
of the complex exponential function.

But I guess that's well outside the intended
scope of the question...

-- Baffling Bill

** What if all circles do not have the same
** ratio of circumference to diameter?
**
** Eh? What then? Eh? Eh!!

[J.B. Wood]

On 05/05/2013 05:35 PM, calvin wrote:
> Why not define pi to be the area of a unit circle?
> That doesn't change the value of pi, but changes
> our way of looking at it.
>

Hello. That would make Pi have the dimensions of squared units. And
what do we use for units? Meters, feet, inches,...? Pi shows up in
lots of things (especially in applied math) where it must be taken as a
dimensionless constant. To do otherwise just doesn't make sense.
Sincerely,

--
J. B. Wood e-mail: arl_1...@hotmail.com

[Richard Tobin]

In article <km82vq$a57$1...@ra.nrl.navy.mil>,

J.B. Wood <john...@nrl.navy.mil> wrote:

>> Why not define pi to be the area of a unit circle?

>Hello. That would make Pi have the dimensions of squared units.

A unit circle has radius 1. Not 1 inch, or 1 centimetre, or 1 anything.

-- Richard

[Barry Schwarz]

By this reasoning, the unit sphere has a radius of 1 also and a volume
of 4pi/3. The amount of liquid to fill the cube can't have units
either so its density is irrelevant and it will have no weight.

And since both the area and volume have no units, we can subtract the
two to get V-A = pi/3.

Just think how much easier all those engineering courses would be now.

--
Remove del for email

[J.B. Wood]

Area is measured in square somethings. Otherwise it isn't an area. You
can't have a dimensionless area. Sincerely,

[J.B. Wood]

On 05/06/2013 08:29 AM, Richard Tobin wrote:

Area is measured in square somethings. Otherwise it isn't an area. You

can't have a dimensionless area. Sincerely,

[1treePetrifiedForestLane]

if the diameter is unit, the area is pi dd,
the circumference is pi d, and the volume is pi ddd/6,
the inherent octahedroness of the sphere.

can then use diadians for circumferential angle and
for areal (sterdiadians?)

[1treePetrifiedForestLane]

here is a puzzle. I have changed two of the variables:

K/(fourthroot(vv/2)) = (fourthroot(vv/2)/M

[Richard Tobin]

In article <a8rfo8hcqj7a63lri...@4ax.com>,

Barry Schwarz <schw...@dqel.com> wrote:

>Just think how much easier all those engineering courses would be now.

I don't think you can have unit circles in engineering.

-- Richard

[konyberg]

Would it. In my mathematics a unit circle has defined its radius as 1. The perimeter would be 2*pi.

KON

[konyberg]

And of course the area of a unit circle equals to pi. However, area has a measurement, pi does not.

KON

[david petry]

On Monday, May 6, 2013 3:01:53 AM UTC-7, Timothy Murphy wrote:

> What does the teacher say to the school pupil who asks,
> "What do you mean by the circumference of a circle?"

It can be explained intuitively in terms of wrapping a string around a cylinder.

[JT]

Circumreference can be explained *exactly* by adding together all
sidelengths of a uniform polygon where vertices approach a limit.
It is easiest to start with a polygon because it is built by isoceles.
Basicly you just go for an adequate smoothness and end up with giving
the sidelengths as a fraction relation to the vertice of the hexagon.
So 1/x * distance between center of polygon and vertex.

[JT]

Multiplied by number of sides/vertices of course.

[JT]

On 7 Maj, 03:08, david petry <david_lawrence_pe...@yahoo.com> wrote:

And the number you get by recursively split the sides of polygon into
two will never reach infinity, because geometry can not handle circles
with polygons where the connecting vertices between lines is 180
degrees.
So is there something wrong with geometry no infinity is simply
inadequate in math since 1/0 have no solution.

[JT]

On 7 Maj, 03:08, david petry <david_lawrence_pe...@yahoo.com> wrote:

0.5=(n/2-1)/n
http://www.wolframalpha.com/input/?i=0.5%3D%28n%2F2-1%29%2Fn

[JT]

Why do you people suggest that a perfect smooth circle has no
solution?

[1treePetrifiedForestLane]

as has been said,
some one around here doesn't know **** from Shinola --
one of the most respected brands!