No, the culprit is not truncation. Pi has a definite value and it is
not your fraction. You are trying to change the value of a mathematical
constant and you do not have the power to do that, any more than you can
change the charge on an electron.
Your statement that "either radian or pi MUST be defined" is completely
wrong. "Pi" is a *name* for a specific number just like "five". Its
value is fixed and not subject to definition (or redefinition). If I
ask you how many times a line the length of the diameter of a circle
will fit around the circumference the answer is "pi" times. Not 3 or 4
or 22/7 or 100000/31831 or 216 or any other quantity, just pi.
Look at the issue this way. There are two numbers, pi and the Brij
fraction. They are different. They cannot be forced to the same value
any more than you can make 7 and 44 the same.
Brij Bhushan Vij wrote:
Jon:
.....as the number of terms (n) grows indefinitely.
So the culprit is TRUNCATION!
Your number is NOT pi.
My value is YET another approximation, like any other value - that
satisfy most solutions.
I do say, if a circle is to have *2 Pi Radians*; either radian or Pi
MUST be defined. If not, how canscience assign Radian a value of
57*17'44".88, which cab be deduced from MY value.
Brij Bhushan Vij
(Tuesday, Kali 5106-W41-02)/D-026 (Thursday, 2006 January
26H15:87(decimal) ET
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda
Jan:31; Feb:29; Mar:31; Apr:30; May:31; Jun:30
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(365th day of Year is World Day)
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Telephone: +001(201)684-0191
From: Jon Saxton <[EMAIL PROTECTED]>
Reply-To: [EMAIL PROTECTED]
To: "U.S. Metric Association" <[email protected]>
Subject: [USMA:35867] RE: NEW Yard (yd') or Metre New (m') RE: Re:
decimal time
Date: Thu, 26 Jan 2006 14:44:55 -0500
I am sure you will agree that any arc cut from a circle does have a
definite length. OK, so it is curved rather than straight. That
doesn't matter. Just choose an arc such that the length (of the arc,
not the secant) is the same length as the radius of the circle. Then
join the ends of the arc to the centre with straight lines. The
angle so formed is, by definition, a radian.
A bit (actually quite a lot) of mathematical deduction shows that pi,
the ratio of the circumference of a circle to its diameter is given
by (the FORTRAN style notation):
sqrt(6 * (1/1**2 + 1/2**2 + 1/3**2 + 1/4**2 + ... + 1/n**2))
as the number of terms (n) grows indefinitely. This series converges
on the value of pi and not on 100000/31831 or any other rational number.
Your number is NOT pi. It is something else. It has no relationship
to the ratio of the circumference of a circle to its diameter other
than being an approximation accurate to about one part in 300 000 -
not terribly close by measurement standards.
The ratio of the circumference to the radius is fixed for all time.
It is not something which you or I or the government of Indiana can
change at will.
Anyway, if you are assuming the power to change the mathematical and
physical properties of the universe, why would you choose a horrible
fraction such as 100000/31831? Why not pick 3.2 or 3.6 instead?
They'd be much nicer.
Brij Bhushan Vij wrote:
Jon:
On the same line, a radian is the angle subtended at the centre of
a circle by an arc equal to the >radius.
HOW do you cut the arc EQUAL to the radius of circle - arc length is
greater than the side cutting it? My value for Pi, in the form
(a/b=100000/31831) is YET another value for Pi that satisfy ALL
operations equally.
Brij Bhushan Vij
(Tuesday, Kali 5106-W41-02)/D-026 (Thursday, 2006 January
26H13:08(decimal) ET
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda
Jan:31; Feb:29; Mar:31; Apr:30; May:31; Jun:30
Jul:30; Aug:31; Sep:30; Oct:31; Nov:30; Dec:30
(365th day of Year is World Day)
******As per Kali V-GRhymeCalendar******
2108 Henry Court, MAHWAH NJ 07430 (USA)
Telephone: +001(201)684-0191
From: Jon Saxton <[EMAIL PROTECTED]>
Reply-To: [EMAIL PROTECTED]
To: "U.S. Metric Association" <[email protected]>
Subject: [USMA:35855] RE: NEW Yard (yd') or Metre New (m') RE: Re:
decimal time
Date: Wed, 25 Jan 2006 21:49:41 -0500
You CANNOT arbitrarily declare the value of pi to be 100000/31831
no matter how convenient you might think it would be. The
mathematics just doesn't work like that. It is like saying the
square root of 2 is exactly 1.4.
On the same line, a radian is the angle subtended at the centre of
a circle by an arc equal to the radius. You can't redefine that to
suit your purposes either, any more than you can arbitrarily say
that a right angle is a fifth of a full circle.
There is no controversy to discuss.
Brij Bhushan Vij wrote:
Phillip Hall & friends:
I can't quite work this out. If we take the Earth radius as 6371
km, and assume a perfect sphere, >I get 40030.1735920411 km
(rounded to 10 dp) when I multiply 6371 by 2 * pi (using pi =
>3.1415926535 ... from windows calculator)
This small difference is due to the Pi value you use from
computer; and I use MY rationalised value for Pi of ratio:
100000/31831 that FIXES 'Radian at 57*.2958 =57*17'44".88.
Thus, Earth circumference is 2*Pi*radius =2x100000/31831x6371
=40030.1592786906 (to 10th decimal) Km. I choose THIS value for Pi
since NO OTHER value for Pi defines *either Pi or Radian -
eaxactly*. This is a deviation of 0.01431335051535 (or 14.3133505
cm).
I have discussed Pi controversy at length, and my views are stored
in the archieves. The point is its TRUNCATION that evaluate ANY
two values differently.
Regards,
Brij Bhushan Vij
(Monday, Kali 5106-W41-01)/D-025 (Wednesday, 2006 January
25H15:14(decimal) ET
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda
Jan:31; Feb:29; Mar:31; Apr:30; May:31; Jun:30
Jul:30; Aug:31; Sep:30; Oct:31; Nov:30; Dec:30
(365th day of Year is World Day)
******As per Kali V-GRhymeCalendar******
