Author: FM

meetk plaats

hulpcirkels

biljartprobleem

barrow

Moeite bij a=b

a=

b=

gelijke hoeken

Startprobleem:
Cirkelbiljart (r=1). 
A en B daarbinnen.
OA=a; OB=b; hoek a,b via alpha.
Hoe bal te A te stoten via rand 
zodat bal in B komt?

Aanpak via kijkhoeken: OA en OB 
onder dezelfde hoek te zien.

test route

hyp

theta

gamma=

tekst

b = 0.35 (slider from 0 to 1)
α = 0 rad (slider from 0 to 180°)
a = 0.71 (slider from 0 to 1)
θ = 0.767944870877505 rad (slider from 0 to 6.283185307179586)
O = Intersect(xAxis, yAxis)
A: ((-a), 0)
H: (b, 0)
B = Rotate(H, α, O)
β = Angle(H, O, B)
g = Segment(A, O)
γ = 0.3141592653589793 rad (slider from 0 to 180°)
B' = Rotate(B, 90° - γ, O)
δ = Angle(B, O, B')
i = LineBisector(B, O)
O' = Rotate(O, 90° - γ, A)
ε = Angle(O, A, O')
k = LineBisector(A, O)
h = Line(A, O')
C = Intersect(k, h)
c = Circle(C, A)
j = Line(O, B')
D = Intersect(j, i)
E = Intersect(i, j)
d = Circle(D, B)
P1, G = Intersect(c, d)
b_1 = false
e = false
l = Segment(O, P1)
m = Segment(P1, A)
n = Segment(P1, B)
ζ = Angle(A, P1, O)
η = Angle(O, P1, B)
p: x^(2) + y^(2) = 1
o = true
X = Point(p)
q = Segment(A, X)
r = Segment(X, O)
A' = Mirror(A, r)
s = Ray(X, A')
f: ((((b * a) * cos(θ - α)) * sin(θ)) + (((b * a) * cos(θ)) * sin(θ - α))) / ((a * sin(θ)) - (b * sin(θ - α)))
P: ((f * cos(θ)), (f * sin(θ)))
u = true
f_1 = Segment(O, B)
Invulvak1 = Textfield(a)
Invulvak2 = Textfield(b)
v = true
I, J = Intersect(p, s)
w = Vector(X, J)
t = false
P' = Mirror(P, p)
a_1 = false
Invulvak3 = Textfield(θ)
Invulvak4 = Textfield(γ)
c_1 = false