B

A

D

Ruutjuur

Arv

Tõestus

α

α

Ruutjuure \; leidmine \; Hippokratese \; meetodiga

Allikas:
Numberphile (2020, märts 15). Mesolabe Compass and Square Roots - Numberphile. 
Vaadatud aadressil: https://www.youtube.com/watch?v=9VVPBS_flOI

n = 17 (slider from 0 to 100, step 1)
A: (n, 0)
B: ((n + 1) / 2, 0)
C: (n + 1, 0)
D = Point(xAxis)
c = Semicircle(D, C)
C' = Rotate(C, 90°, A)
α = Angle(C, A, C')
f = Ray(A, C')
E = Intersect(c, f)
RuutJuur = Segment(A, E)
h = Segment(D, E)
β = Angle(D, E, C)
i = Segment(E, C)
j = Segment(A, C)
k = Segment(D, A)
a = true
γ = Angle(C, D, E)
δ = Angle(A, E, C)
l = Line(E, k)
text1: "\sqrt{" + (LaTeX[n]) + "}=" + (LaTeX[RuutJuur]) + ""
t1, e, d, a_1 = Polygon(D, A, E)
t2, e_1, a_2, c_1 = Polygon(A, C, E)
text2: "Kolmnurgad \; ABD \; ja \; DBC \; on \; sarnased, \; s.t. \\
\frac{|AB|}{|DB|}=\frac{|DB|}{|BC|} , \; |BC|=1⇒|AB|=|DB|^2 \\" + (LaTeX[n]) + "= " + (LaTeX[RuutJuur]) + "^2"