Making a Strip of Isosceles Trapezoids
Making a Strip of Isosceles Trapezoids
Suppose the angle measures . The line bisects , so . The line bisects , so triangle is isosceles and is congruent to , which measures . Then and . So the angles converge to . In this way the trapezoids converge to an isosceles trapezoid congruent to the trapezoid consisting of three sides and of a diagonal of a regular pentagon. Isosceles trapezoids are obtained immediately when . Otherwise, the isosceles condition is approached as the number of repeats, . Visually, however, the result appears to be satisfied with . Use the bottom scroll bar to view extended regions of the diagram.
D
1
A
1
B
1
2π/5+ϵ
A
1
C
1
∠D
1
A
1
B
1
|∠|=π/5+ϵ/2
D
1
A
1
C
1
C
1
D
1
∠
A
1
C
1
D
1
A
1
D
1
C
1
∠A
1
D
1
C
1
∠B
2
C
1
D
1
2π/5-ϵ/4
||=π/5-ϵ/8
∠B
2
C
1
A
2
|∠|=1/2(π-(π/5-ϵ/8))=2π/5+ϵ/16
D
2
A
2
B
2
D
n
A
n
B
n
2π/5
A
n
D
n
C
n
D
n
ϵ=0
m∞
m≈5