Klein Ray

KleinRay[ <Point>, <Point> ]

JunkTool1

No Help Available

JunkTool2

No Help Available

JunkTool3

No Help Available

JunkTool4

No Help Available

JunkTool5

No Help Available

Klein Angle Bisector

KleinAngleBisector[ <Point>, <Point>, <Point> ]

Klein Midpoint

Klein Perpendicular Bisector

Klein Point Reflection

Klein Circle Center And Point

KleinCircleCenterAndPoint[ <Point>, <Point> ]

Klein Circle Center And Radius

Klein Distance

Klein Angle Measure

a = Ray(A, B)
C, D = Intersect(Circle[(0, 0), (1, 0)], a)
b = Segment(A, C)
C, a = KleinRay(A, B)
D, b = KleinRay(B, A)
d = Segment(D, C)
a = Segment(A, B)
a, C, D = JunkTool1(A, B)
b = Segment((0, 0), C)
c = Segment((0, 0), D)
d = OrthogonalLine(C, b)
e = OrthogonalLine(D, c)
P = Intersect(d, e)
C = JunkTool3(A, B)
a = Line(C, B)
D, E = Intersect(Circle[(0, 0), (1, 0)], a)
b = Segment(D, E)
C = JunkTool3(A, B)
a, D, E = JunkTool1(A, B)
b = Line(C, F)
G = Intersect(b, a)
H, I = Intersect(Circle[(0, 0), (1, 0)], b)
c = Segment(H, I)
D, a = KleinRay(C, A)
E, b = KleinRay(C, B)
P = JunkTool3(D, E)
c = Line(P, C)
F, G = Intersect(Circle[(0, 0), (1, 0)], c)
d = Segment(F, G)
P = JunkTool3(A, B)
b = Ray(P, A)
c = Ray(P, B)
E, F = Intersect(Circle[(0, 0), (1, 0)], b)
G, H = Intersect(Circle[(0, 0), (1, 0)], c)
d = Segment(E, H)
e = Segment(G, F)
I = Intersect(e, d)
E = KleinMidpoint(A, B)
d = JunkTool4(A, E)
a, B, C = JunkTool1(A, M)
Q = JunkTool3(A, M)
b = Ray(Q, A)
D, E = Intersect(Circle[(0, 0), (1, 0)], b)
c = Ray(Q, M)
F, G = Intersect(Circle[(0, 0), (1, 0)], c)
d = Segment(G, M)
H = Midpoint(d)
P = JunkTool3(H, M)
e = Ray(P, D)
f = Ray(P, E)
I, J = Intersect(Circle[(0, 0), (1, 0)], f)
T = If(E ≠ I, I, J)
K, L = Intersect(Circle[(0, 0), (1, 0)], e)
T' = If(K ≠ D, K, L)
g = Line(T, T')
N = Intersect(a, g)
P' = KleinPointReflection(P, O)
b = JunkTool4(P, O)
C, D = Intersect(Circle[(0, 0), (1, 0)], b)
c = Segment(D, O)
E = Midpoint(c)
d = KleinAngleBisector(P, O, E)
F, G = Intersect(Circle[(0, 0), (1, 0)], d)
e = Segment(O, F)
H = Midpoint(e)
f, I = JunkTool5(O, H, P)
P'' = Intersect(f, b)
P''' = KleinPointReflection(P'', O)
g = KleinAngleBisector(P, O, H)
J, K = Intersect(Circle[(0, 0), (1, 0)], g)
h = Segment(O, J)
L = Midpoint(h)
i, M = JunkTool5(O, L, P)
P'''' = Intersect(i, d)
k = Conic(P, P'', P''', P'''', P')
C, b = KleinPerpendicularBisector(O, A)
D, E = Intersect(Circle[(0, 0), (1, 0)], b)
c = Segment(C, E)
F = Midpoint(c)
d, M = JunkTool5(C, F, B)
G = KleinPointReflection(B, M)
e = KleinCircleCenterAndPoint(O, G)
a = Line(A, B)
C, D = Intersect(Circle[(0, 0), (1, 0)], a)
b: abs(log(Distance[A, C] / Distance[A, D] / (Distance[B, C] / Distance[B, D]))) / 2
E = Midpoint(A, B)
Name[A] + (Name[B]) + "=" + b
text1, a = KleinDistance(B, C)
text2, b = KleinDistance(A, C)
text3, c = KleinDistance(A, B)
α = Angle(acos((cosh(c) - (cosh(a) * cosh(b))) / (((-sinh(a)) * sinh(b)))))
"∡" + (Name[A]) + (Name[C]) + (Name[B]) + "=" + α
d = AngularBisector(A, C, B)
e = Segment(A, B)
D = Intersect(d, e)
E = Midpoint(Segment[C, D])