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Hellow All I have provided a symbolic triangle of...

<< Back to: sci.math FAQ: The Trisection of an Angle

Question by Bassam Karzeddin
Submitted on 1/30/2007
Related FAQ: sci.math FAQ: The Trisection of an Angle
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Hellow All

I have provided a symbolic triangle of constructible length (where you can choose) in sci.math - thread of mine-
(alpha - beta) triangle that possess an arbitrary angle and it's exact n'th division angle

kindly see the subject below:

If Alpha and Beta are two angles in the same triangle and (n) is positive integer,(m) is integer >= 0,such that:
n*Alpha = Beta Mod (PI) OR:

n*Alpha - m*(PI) = Beta

Where, Angle (PI) = 180 degree OR:
(PI) = 3.14159265...

Then, the sides of (Alpha-Beta) Triangle are of the ratio:

1 :: absolute value of f(x)
::absolute value of g(x)

Where, f (x) and g (x) are two polynomial equations of degrees (n) and (n-1) successively in any real variable (x) such that the sum of smaller sides is grater or equal than the larger side.

And f (x) is defined as the following:

f (x) = Sum {from i=0,to, i=[n/2]}
(-1)^i*(n-i)! *x^(n-2*i)/{(n-2*i)! *i!}
Where,
! denotes the factorial of a number,and,
[..] denotes the least integer

g (x) is a polynomial of the same kind of f (x), but, with (n-1) degree.

Example:

Assuming n=3, m=0, and applying in the above equations will give you a triangle with an arbitrary angle and it's exact trisection angle in the same triangle, with the following sides

1, x, (x-1)*seqrt(x+1), where, (3>x>1), and x  is any constructible length



Thanking You All for your patience.

Best Regards

Bassam King Karzeddin

Al Hussein Bin Talal University

JORDAN


My question : is this an addition to divisible angles or nonsence as I'm a civil engineer and don't belong to the mathematician cateogry


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