Η σκιά της πυραμίδας αποτελείται από ένα προσιτό τμήμα το ΑΒ και ένα απρόσιτο μέρος το ΟΑ.

Πώς ο Θαλής μέτρησε το απρόσιτο τμήμα ΟΑ ;

ΟΑ=\frac{α}{2}

Ο Θαλής μέτρήσε το ύψος της πυραμίδας χρησιμοποιώντας :
∙το ύψος του
∙τον ήλιο
Πως;

πυραμίδα

Θαλής

σκιά Θαλή

απρόσιτο μήκος σκιάς

προσιτό μήκος σκιάς

Θαλής

κύκλος Θαλή

σκιά

ακτίνες ήλιου

Α_1 = (-8.047738648947956, -3.2394342092016544)
Β_1 = (-3.307433001107423, -3.2394342092016544)
α = Segment(Α_1, Β_1)
c = Circle(Β_1, α)
Γ_1 = Point(c)
b = Segment(Β_1, Γ_1)
d = Line(Γ_1, α)
e = Line(Α_1, b)
Δ_1 = Intersect(d, e)
f = Segment(Δ_1, Γ_1)
g = Segment(Δ_1, Α_1)
h = Segment(Δ_1, Β_1)
i = Segment(Α_1, Γ_1)
Ε = Intersect(h, i)
j = OrthogonalLine(Ε, α)
K = Point(j)
υ = Segment(K, Ε)
l = Segment(K, Γ_1)
m = Segment(K, Β_1)
n = Segment(K, Δ_1)
p = Segment(K, Α_1)
q = Line(Ε, α)
B = (1.5743743078626773, -1.7536667673411879)
r_2 = Ray(K, B)
s = Segment(K, B)
t = Segment(Β_1, B)
a_1 = Segment(Γ_1, B)
b_1 = Segment(Ε, B)
Α_2 = Intersect(b, b_1)
c_1 = Segment(Ε, Α_2)
Θ = (-1.557957918050941, -4.00804550488272)
Η = (-0.7861306755260244, -2.432231551394345)
O = Intersect(υ, c_1)
Κ = (-9.639632336655593, 4.684658814054167)
Λ = (-6, 8)
Μ = (-4.4040708748615724, -2.991806302224909)
n_1 = false
o_1 = false
p_1 = false
q_1 = false
r_1 = true
c_2 = Circle(O, υ)
a_2 = OrthogonalLine(O, υ)
Γ = Point(a)
Δ = Point(a)
k = Segment(Γ, Δ)
d_1 = Circle(Γ, k)
e_1 = OrthogonalLine(Γ, a)
Ζ = Intersect(d_1, e_1, 2)
θ = Segment(Ζ, Γ)
r = 1.2 (slider from 0 to k, step 0.1)
g_1 = Circle(Γ, r)
Ι = Intersect(g_1, k, 1)
h_1 = Segment(Γ, Ι)
i_1 = Ray(Ι, Ζ)
r1: ((υ * r)) / θ
f_1 = Circle(O, r1)
Β = Intersect(f_1, a_2, 2)
j_1 = Segment(O, Β)
Α = Intersect(b, j_1)
s_1 = Ray(Β, K)
t_1 = Line(Β, Ι)
Ν = (7.482068660022147, -5.043580388603649)
d_2 = Ray(Ι, Ν)
e_2 = Circle(Ι, 1)
Ξ = Intersect(e_2, d_2, 1)
f_2 = Circle(Ξ, 1)
Ο = Intersect(f_2, d_2, 2)
g_2 = Circle(Ο, 1)
Π = Intersect(g_2, d_2, 2)
h_2 = Circle(Π, 1)
Ρ = Intersect(h_2, d_2, 2)
p_2 = Circle(Ρ, 1)
Σ = Intersect(p_2, d_2, 2)
q_2 = Circle(Σ, 1)
Τ = Intersect(q_2, d_2, 2)
i_2 = Segment(Τ, Β)
j_2 = Line(Σ, i_2)
l_2 = Line(Ρ, j_2)
m_2 = Line(Π, l_2)
n_2 = Line(Ο, m_2)
s_2 = Line(Ξ, n_2)
Υ = Intersect(t_1, s_2)
Φ = Intersect(n_2, t_1)
Χ = Intersect(t_1, m_2)
Ψ = Intersect(t_1, l_2)
Ω = Intersect(t_1, j_2)
t_2 = Line(Ω, s_1)
a_3 = Line(Ψ, t_2)
b_3 = Line(Χ, a_3)
c_3 = Line(Φ, b_3)
d_3 = Line(Υ, c_3)
Ε_1 = Point(d_3)
Ζ_1 = Point(c_3)
Η_1 = Point(b_3)
Θ_1 = Point(a_3)
Ι_1 = Point(t_2)
e_3 = Ray(Ω, Ι_1)
f_3 = Ray(Ψ, Θ_1)
g_3 = Ray(Χ, Η_1)
h_3 = Ray(Φ, Ζ_1)
i_3 = Ray(Υ, Ε_1)
Κ_1 = Point(i_3)
Λ_1 = Point(i_3)
j_3 = Ray(Κ_1, Λ_1)
Ν_1 = Point(h_3)
Ξ_1 = Intersect(b, g_3)
Ο_1 = Point(p)
l_3 = Line(Ο_1, f_3)
Π_1 = Point(l_3)
m_3 = Ray(Ο_1, Π_1)
πολύγ3, β, β_2, γ_1 = Polygon(Β_1, Γ_1, Β)
πολύγ1 = If(x(Α) < x(Β), Polygon[Β_1, Γ_1, Β])
Μ_1 = (-6.951100775193803, -8.899500654384383)
Ρ_1 = (-5.429957918050945, -6.246344508204979)
Σ_1 = (-8.932124031007756, -4.442198328802984)
Τ_1 = Point(p)
k_1 = Line(Τ_1, m_3)
l_1 = Line(Σ_1, k_1)
m_1 = Line(Ρ_1, i_1)
b_2 = Line(Μ_1, m_1)
Υ_1 = Point(m_1)
Φ_1 = Point(k_1)
Χ_1 = Point(b_2)
Ψ_1 = Point(l_1)
k_2 = Ray(Ρ_1, Υ_1)
k_3 = Ray(Τ_1, Φ_1)
n_3 = Ray(Μ_1, Χ_1)
p_3 = Ray(Σ_1, Ψ_1)
Ω_1 = (-3.9088150609080876, -7.2722315513943485)
q_3 = Segment(O, Α)
r_3 = Segment(Α, Β)
Β_2 = Point(h_1)
Γ_2 = Point(a)
Δ_2 = Mirror(Γ_2, θ)
s_3 = Ellipse(Δ_2, Γ_2, Δ)
t_3 = Segment(Γ, Δ)
v = false
w = false
u = false
v_1 = false
z = false
Ε_2 = Point(p)
Ζ_2 = Point(p)
Η_2 = (-5.253080841638987, -6.9184773985704275)
Θ_2 = (-7.941612403100781, -7.236856136111957)
Ι_2 = (-2.3522967884828403, -6.2109690929225865)
a_4 = Line(Ι_2, i_1)
b_4 = Line(Ζ_2, i_1)
c_4 = Line(Ε_2, a_4)
d_4 = Line(Θ_2, c_4)
e_4 = Line(Η_2, c_4)
Κ_2 = (1.326746400885931, 3.411143863888052)
f_4 = Line(Κ_2, s_1)
Λ_2 = Point(f_4)
Μ_2 = Point(b_4)
Ν_2 = Point(a_4)
Ξ_2 = Point(c_4)
Ο_2 = Point(e_4)
Π_2 = Point(d_4)
g_4 = Ray(Κ_2, Λ_2)
h_4 = Ray(Ζ_2, Μ_2)
i_4 = Ray(Ι_2, Ν_2)
j_4 = Ray(Ε_2, Ξ_2)
k_4 = Ray(Η_2, Ο_2)
l_4 = Ray(Θ_2, Π_2)
u_1 = false