Re: Angle Trisection
- From: bassam king karzeddin <bassam@xxxxxxxxxx>
- Date: Wed, 15 Mar 2006 06:51:24 EST
Dear All
If Alpha and Beta are two angles in the same triangle and (n) is positive integer,(m) is positive integer less than (n) ,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 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 floor function
g (x) is a polynomial of the same kind of f (x), but, with (n-1) degree.
Reference Link, at this Site:
http://www.blogit.com/Blogs/Blog.aspx/karzeddin/
In your case (n=3), therefore, the triangle having one angle trice another angle in the same triangle will be represented in the following triangle sides (A, B, C), where :
A = 1
B = abs(x^3-2*x)
C = abs(x^2-1)
Choose any value for (x) to obtain the suitable angle and it's exact trisection angle in the same triangle
Still I didn't claim this the solution of angle trisection, and most likely you will not find this material in any book
Best Regards
Bassam King Karzeddin
Al Hussein Bin Talal University
JORDAN
.
- References:
- Angle Trisection
- From: bmaschino
- Angle Trisection
- Prev by Date: Re: sum of i.i.d. exponentially distributed random variables with geometrically distributed number of summands
- Next by Date: decomposition of polynomials
- Previous by thread: Re: Angle Trisection
- Next by thread: Re: Angle Trisection
- Index(es):
Relevant Pages
|
