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Re: TO DIVIDE AN ANGLE IN ANY NUMBER OF EQUAL PARTS
Posted:
Sep 6, 2010 2:16 PM
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Sir, You wrote:
> While I thank you for your letter posted on sept 1,
> 2010 on the subject, I fail to understand whether the
> same is your concluding letter, saying: so,I reject
> your stupid method and, don?t disturb me further with
> your idiotic ideas.
I hope I did not really give that impression!
> I am extremely sorry for the mistake I made regarding
> 60 degree and 1 radian. My apology to you for that
> mistake.
My comment was to show the difference between the angle subtended by a chord, and that subtended by an arc.
> In my previous letter posted on august,11 on the
> subject, I cited another example i.e, ?pai?. You have
> not enlightened me on that. Please do,if your time
> permits, to clear the misunderstanding regarding
> ?pai?= 22/7 or, 3.14 which is acceptably accurate,
Pi is the ratio of Circumference/Diameter. It is neither 22/7 nor 3.14 for theoretical considerations or proofs, but these values may be useful in practice for approximating calculated values.
> If my method is 100% perfect ... I would
> not have written ... : Certain constraints and its
> probable solutions ...(or) ...how to better the
> process to get acceptable accuracy. ... more
> bisection, more accuracy , if required.
I did acknowledge your method for acute angles, and I understand your approach of subdividing larger angles into smaller appropriately acute angles, but each subdivision, and later expansion, involves more operations, thus reducing the accuracy per operation achievable.
> To conclude, I would humbly request you to go through
> and not to glance through all my letters and write-up
> once again with a positive frame of mind.
It was not my intention to be critical of your method. It seems easy to understand and remember for students and artisans.
When I was at school we would construct an n-section of an angle by trial and error. Not very sophisticated, but quite practical, and not involving many operations to achieve drawing accuracy. You have given the process more structure, and that should be a help to your students provided they understand the underlying theory, incuding why it is necessary to subdivide an obtuse angle, and the difference between the accuracy theoretically achievable and that achievable in practice with a compass on paper.
I hope my comments have been of some help, and that I have now cleared up any miunderstandings.
Sincerely, Peter Scales.
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