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Topic: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
Replies: 23   Last Post: Mar 4, 2013 4:05 AM

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Peter Scales

Posts: 140
From: Australia
Registered: 4/3/05
Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
Posted: Jul 25, 2010 7:04 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

SHYAMAL KUMAR DAS wrote:

> Respected Sirs,
>
> I would like to inform you that most probably I have
> invented a geometrical method / construction, by
> which any angle can be divided into any number of
> equal parts.
> So far I know, a few people had tried to trisect an
> angle, but failed to do so. My method can not only
> trisect but divide any angle into any no. of equal
> parts.
>
> Please be kind enough to look into my method.


Sir,

The method you propose does give a reasonable approximation to the 1/n th value of an acute angle for reasonably large n, but unfortunately it is not a valid method for exact angle division.

The flaw is that it equates the base (chord) of an isosceles triangle with the corresponding arc of a sector, which is simply not true.

This leads to an error in your construction. When you use a compass to lay off a length, it is a chord you lay off, not an arc. There is no unique arc associated with a chord, and in your example two different arcs occur: arc DM with r=1 and arc HI (=IJ etc) with r=5. The chords are identical, but the arcs are not.

Your comment on page 3 regarding 60degrees being an approximation for 1 radian arises from the same error. In an isosceles triangle, a side of unity subtends 60 degrees at the apex whereas an arc of unity subtends 1 radian = 57.296 degrees. This is not an approximation, but a different value from a different figure.

As an example, use your method to bisect a right angle:
BD=1, chordBE=sqrt2, BA=2, CF=FG=sqrt2
.: your approx to the bisected angle, theta, has
sin(theta/2)=1/4*sqrt2 .: theta/2=20.7deg theta=41.4deg
and the discrepancy is 90-2*41.4=7.2deg

It is even more obvious if you use your method to bisect a straight angle=180 BD=1 DE=2 and the resultant approx bisected angle is 60deg, not 90deg.

I hope this has been of some help to you.

Since you have access to the Internet you could Google angle division and explore the extensive existing literature.

Regards, Peter Scales.


Date Subject Author
7/21/10
Read TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
shyamal kumar das
7/25/10
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
Peter Scales
8/11/10
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
shyamal kumar das
8/11/10
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
Avni Pllana
11/1/10
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
shyamal kumar das
11/2/10
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
Avni Pllana
11/3/10
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
shyamal kumar das
8/13/10
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
shyamal kumar das
8/24/10
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
shyamal kumar das
8/24/10
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
Peter Scales
9/1/10
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
Peter Scales
9/3/10
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
shyamal kumar das
9/6/10
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
Peter Scales
9/18/10
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
shyamal kumar das
10/8/10
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
shyamal kumar das
10/8/10
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
shyamal kumar das
10/9/10
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
Peter Scales
10/14/10
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
shyamal kumar das
10/19/10
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
shyamal kumar das
11/3/10
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
shyamal kumar das
9/10/11
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
shyamal kumar das
3/2/13
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
Doctor Nisith Bairagi
3/4/13
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
shyamal kumar das
3/4/13
Read Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
shyamal kumar das

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