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)
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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******
