Sunday, October 8, 2017

Ok, to answer you, if I have a brilliant idea, about an animation decrypter for the ellipt curve, in corel...just follow the white rabbit of this math law "If the successive sides of a cyclic hexagon are a, b, c, d, e, f, then the three main diagonals concur at a single point if and only if ace = bdf"


If you want a math quiz : A hexagon with consecutive sides of lengths 2, 2, 7, 7, 11, and 11 is inscribed in a circle.  Find the radius of the circle.

http://www.qbyte.org/puzzles/p063s.html

Trigonometric Solution

Three chords of lengths 2, 7, and 11, inscribed in a semicircle of radius r. The angle subtended at the center of the circle by each chord is, respectively, 2a, 2b, 2c. Angle d is complementary to c, so that d is the angle between a radius and the chord of length 11.
We can drop a perpendicular from the center of the circle to each of the chords, bisecting the isosceles triangles, as shown.
We have a + b + c = pi/2, and c + d = pi/2.
Hence a + b = d < pi/2.
We also have
a = arcsin(1/r), b = arcsin(7/2r), d = arccos(11/2r)
Taking the cosine of both sides of a + b = d, and using trigonometric identities cos(x + y) = cosx cosy − sinx siny, and sin2x + cos2x = 1, we get
sqrt(1 - 1/r^2) * sqrt(1 - 49/4r^2) - 7/2r^2 = 11/2r
Adding 7/2r2 to both sides of the equation, squaring, and multiplying by 2r3, we obtain
2r3 − 87r − 77 = 0
This easily factorizes, giving (r − 7)(2r2 + 14r + 11) = 0.
The quadratic factor has negative real roots.  Hence r = 7 is the only positive real root.
Therefore the radius of the circumscribing circle of the original hexagon is 7 units.

Elsa David hey...i think is even more complicated math problem than the ellipt curve it self




No comments: