|
|
Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
Posted:
Oct 8, 2010 9:47 PM
|
|
To: Peter Scales
From: Shyamal Kumar Das
Sir,
Long time, no see ???.i mean no response. Hope , this e-mail finds you in good health and spirit.
Now, I am writing you this letter because of the following reasons:
1) I ?ve realized that again I ?ve made mistake applying unitary method which is not correct . Again sorry sir.
2) Any way, what is very much annoying me is the drawback of my method. The difference between arc length and chord length and how to overcome that have spoilt my sleep at night.
3) I ?ve calculated out something which ,according to me, is very much interesting and
relevant.
CALCULATION :
A) When , the angle subtended at the center= 180 deg.,
The difference between arc length and chord length= pi*R-2R=R( pi-2 ) =R ( 3.14-2) = 1.14R
B) When , the angle subtended at the center= 90 deg.,
The difference between arc length and chord length= pi/2*R- v2R= R( 1.571-1.414)= 0.16R
C) When , the angle subtended at the center= 60 deg.,
The difference between arc length and chord length= pi/3*R- R = R( 1.047-1 ) =0.047R
D) When , the angle subtended at the center= 30 deg.,
The difference between arc length and chord length= pi/6*R-2Rsin15 deg
= R(0.5233- 2*0.2588) = =0.0057R
E) When , the angle subtended at the center= 22.5 deg.,
The difference between arc length and chord length= pi/8*R- 2Rsin11.25deg =R(0.3925- 2*0.1951)= =0.0023R
F) When , the angle subtended at the center= 1/5 of 22.5deg = 4.5deg
The difference between arc length and chord length= pi/40- 2Rstn2.25deg
=R( 0.0785-2*0.0393 ) ???
OBSERVATION & INFERENCE :
Hence, it is observed that, when angle subtended at the center tends to zero, the difference between arc length and chord length also tends to zero. Thus, we can infer that when angle subtended at the center is 4.5deg, the arc and chord lengths are almost same. In my previous letter where I took the example of 180deg., to be divided into 5 equal parts, the cut-off arc / chord length has been taken for graduation, against subtended angle = 4.5deg. at the center.
Please correct me ,if I am wrong. I am eagerly waiting for your reply on this. If you are O.K with my calculation, observation and inference, then I shall only hope that you will approve my method which is almost correct. Thanks and regards. Shyamal Kumar Das 09.10.2010
|
|
