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tech / sci.math / Re: Exact Trisecting

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* Re: Exact Trisectingbassam karzeddin
`- Re: Exact TrisectingChris M. Thomasson

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Re: Exact Trisecting

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Subject: Re: Exact Trisecting
From: b.karzed...@yahoo.com (bassam karzeddin)
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 by: bassam karzeddin - Thu, 10 Aug 2023 02:03 UTC

On Tuesday, July 19, 2005 at 1:09:47 PM UTC+3, Robert Israel wrote:
> In article <dbgogh$679$1...@dizzy.math.ohio-state.edu>,
> bassam king karzeddin <bas...@ahu.edu.jo> wrote:
> >I will be glad to know if I wrote nonsence mathematics or something
> >useful.here is the problem.
> >An arbitrary angle and its exact trisection angle fits exactly in the
> >following symbolic triangle with the following sides:
> > a^3 , a*(b^2-a^2) , b*(b^2-2*a^2)
> >Where : 2 >= b/a >= sqrt(2)
> > (a,b):are positive real numbers
> I think you mean: if theta is an angle between 0 and pi/4,
> a triangle with angles theta, 3 theta and pi - 4 theta
> has sides with the ratios a^3 :: a*(b^2-a^2) :: b*(b^2-2*a^2)
> where cos(theta) = b/(2*a).
> Yes, that's true, and elementary to verify using the Law of Sines
> and addition formulas for the sine function.
> Robert Israel isr...@math.ubc.ca
> Department of Mathematics http://www.math.ubc.ca/~israel
> University of British Columbia Vancouver, BC, Canada

Re: Exact Trisecting

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https://www.novabbs.com/tech/article-flat.php?id=144432&group=sci.math#144432

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: Exact Trisecting
Date: Thu, 10 Aug 2023 09:12:35 -0700
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 by: Chris M. Thomasson - Thu, 10 Aug 2023 16:12 UTC

On 8/9/2023 7:03 PM, bassam karzeddin wrote:
> On Tuesday, July 19, 2005 at 1:09:47 PM UTC+3, Robert Israel wrote:
>> In article <dbgogh$679$1...@dizzy.math.ohio-state.edu>,
>> bassam king karzeddin <bas...@ahu.edu.jo> wrote:
>>> I will be glad to know if I wrote nonsence mathematics or something
>>> useful.here is the problem.
>>> An arbitrary angle and its exact trisection angle fits exactly in the
>>> following symbolic triangle with the following sides:
>>> a^3 , a*(b^2-a^2) , b*(b^2-2*a^2)
>>> Where : 2 >= b/a >= sqrt(2)
>>> (a,b):are positive real numbers
>> I think you mean: if theta is an angle between 0 and pi/4,
>> a triangle with angles theta, 3 theta and pi - 4 theta
>> has sides with the ratios a^3 :: a*(b^2-a^2) :: b*(b^2-2*a^2)
>> where cos(theta) = b/(2*a).
>> Yes, that's true, and elementary to verify using the Law of Sines
>> and addition formulas for the sine function.
>> Robert Israel isr...@math.ubc.ca
>> Department of Mathematics http://www.math.ubc.ca/~israel
>> University of British Columbia Vancouver, BC, Canada

90 / 3 = 30 degrees = pi*2 / 12 radians = pi / 6 radians = 30 degrees

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