Geometric Properties of the Normal Curve and it's Deviation
Some Geometric Properties; Type in [ .2222] ; [ 1/2.53 ] ; [ .45 ] ; [ 1] ; and [ 1.5 ] into the Sigma Box to see the Three relationships. The value of my two constants in my equation will be given. ( see Red equation ) Line segment U2T2 and the value of Sigma at 1/2.53. The Green reference line goes through point M at Sigma = 1.5. Also interesting is Sigma =.45 which gives Z = 2.2222 while the Green Line goes through point " U " The input Box " N " moves the ( Red Curve ) I would like to point out that the number in my equation " 2.23 " makes for an interesting relationship. The Green reference line is Tangent to point " U " which is at the end of the Blue Arc with a radius of 1. While at Sigma = 1 ; Point " U " is a point on the Z triangle. Additionally, Line Segment U2T2 has a length of .3909. Then at Sigma = .2222 ; U2T2 has a length = .8414 1 / 2.53 is = to the constant 1 / (2*pi)^.5 which is the constant in the Normal Probability equation, which in fact I knew because that is equal to: [1 / ( Integral of the equation - 2^x(x-1) = .3953 )] from minus infinity to positive infinity. At Sigma equals [.2222] you can see the distance between the two hypotenuses is .8414; segment ( U2T2 in Red ) which is equal to about my other constant in the denominator of my equation RV Sigma.
Please explore the geometric relationship between values