Ποια σχέση μπορεί να έχουν οι καρδιές 
που βλέπετε με τις συναρτήσεις;
Κλικ στο κουμπί δίπλα από κάθε 
καρδιά για να την ανακαλύψετε.

καρδιά 1

καρδιά 2

καρδιά 3

1

$ \frac{π}{2} $

2

$ -\frac{π}{2} $

3

1. Γραφική παράσταση της f(x)=ημx , 0<x<π/2

2. Στροφή αυτής κατά 90°

3. Ανάκλαση.

4. Δυο ημικύκλια.

Αρχή

Συναρτήσεις της καρδιάς

1. Γραφική παράσταση της f(x)=ημx , -π/2<x<π/2

2. Στροφή αυτής κατά 90°

3. Ανάκλαση.

4. Δυο ημικύκλια.

1. Γραφική παράσταση της συνάρτησης
   $ p(x)=\sqrt{|x|} + \sqrt{1 - x²}$

2. Γραφική παράσταση της συνάρτησης
   $ q(x)=\sqrt{|x|} - \sqrt{1 - x²}$

Σούφαρη Αθανασία

Πηγή:http://www.mathematische-basteleien.de/heart.htm

Ω = (1.5707963267948966, 0)
f = Function(sin(x), 0, 1.5707963267948966)
Χ = Intersect(yAxis, xAxis)
n = Vector(Χ, Ω)
Α = Intersect(xAxis, yAxis)
f_1 = Rotate(f, 90*°, Α)
a = Mirror(f_1, yAxis)
Β: (π / 2, f(π / 2))
Β' = Rotate(Β, 90*°, Α)
Β'' = Mirror(Β', yAxis)
b = Segment(Β', Β'')
Γ = Midpoint(Β', Β'')
c = Semicircle(Β', Γ)
d = Semicircle(Γ, Β'')
πολύγ1, α, β', β'' = Polygon(Β', Β'', Α)
Δ = (5.820665561365071, -4.4708298041230945)
Ε = (7.71611661518927, -4.4708298041230945)
e = Segment(Δ, Ε)
g = LineBisector(e)
Ζ = Point(g)
Θ = (3.1548030465068577, -1.505913327647303)
g_1 = Function(sin(x) - 4, -1.5708, 1.5708)
Ξ: (((-π)) / 2, g_1(((-π)) / 2))
Ο: (π / 2, g_1(π / 2))
Π: Intersect[g_1, yAxis, (0, -4)] - (1, 0)
Ξ' = Rotate(Ξ, 90*°, Π)
d_1 = OrthogonalLine(Ξ', xAxis)
p_1 = Function(asin(x) - 4, -1.5708, 1.5708)
q_1(x) = p_1((-x) - 2)
Ρ: (π / 2, p_1(π / 2))
Σ: (((-π)) / 2, g_1(((-π)) / 2))
Σ' = Mirror(Σ, e_1)
Υ = (0, -4)
Σ'' = Mirror(Σ', Υ)
Σ''' = Mirror(Σ'', h_1)
j_1: y = y(Σ'')
Φ = Midpoint(Σ''', Σ'')
k_1 = Semicircle(Σ''', Φ)
r_1 = Semicircle(Φ, Σ'')
o(x, y) = y ≤ j_1(x)
u(x, y) = y ≥ p_1(x)
v(x, y) = y ≥ q_1(x)
w(x, y) = o(x, y) ∧ u(x, y)
z(x, y) = o(x, y) ∧ v(x, y)
s_1(x) = sqrt(abs(x - 3)) + sqrt(1 - (x - 3)^(2)) - 2
f_2(x) = sqrt(abs(x - 3)) - sqrt(1 - (x - 3)^(2)) - 2
l_1(x, y) = y ≤ s_1(x)
m_1(x, y) = y ≥ f_2(x)
n_1(x, y) = l_1(x, y) ∧ m_1(x, y)
g_2(x) = sin(x)
h_2 = Function(sin(x), 0, 1.5708)
o_1 = Rotate(h_2, 90*°, Χ)
u_1 = Mirror(o_1, yAxis)
v_1 = 0 (slider from 0 to 5, step 0.001)
Ψ: (π / 2, h_2(π / 2))
a_2 = false
Ψ'_1 = Rotate(Ψ, 90*°, Χ)
Α_1 = Mirror(Ψ'_1, yAxis)
z_1: (-floor(v_1)) + v_1
w_1 = Rotate(h_2, ((z_1 * 90))°, Χ)
Ψ' = Rotate(Ψ, ((z_1 * 90))°, Χ)
Β_1 = Midpoint(Ψ'_1, Α_1)
c_2 = Semicircle(Ψ'_1, Β_1)
d_2 = Semicircle(Β_1, Α_1)
b_2 = true
p_2 = Function(sin(x), -1.5708, 1.5708)
Η: (π / 2, p_2(π / 2))
Ι: (p_2(π / 2), π / 2)
Κ: ((-p_2(π / 2)) + 4, π / 2)
Λ = Midpoint(Κ, Ι)
i = 5 (slider from 0 to 5, step 0.01)
Μ = (-1.5707963267948966, 0)
j = false
p(x) = sqrt(abs(x)) + sqrt(1 - x^(2))
q(x) = sqrt(abs(x)) - sqrt(1 - x^(2))
l = 0 (slider from 0 to 2, step 0.01)
m = Segment(Χ, Ω)
Χ' = Translate(Χ, Vector[(z_1 * n)])
Ν: (x(Χ'), h_2(x(Χ')))
Τ: (y(Ν), x(Ν))
s(x) = sqrt(0.25 - (x + 0.5)^(2)) + y(Β_1)
t(x) = sqrt(0.25 - (x - 0.5)^(2)) + y(Β_1)
Γ_1 = Intersect(a_1, xAxis)
b_1 = Segment(Γ_1, Χ)
r = Segment(Γ_1, Χ)
c_1 = Vector(Γ_1, Χ)
Δ_1 = Translate(Γ_1, Vector[(z_1 * c_1)])
Ε_1: (x(Δ_1), s(x(Δ_1)))
Χ'_1 = Translate(Χ, Vector[(z_1 * c_1)])
Ζ_1: (x(Χ'_1), t(x(Χ'_1)))
t_1 = Segment(Ψ'_1, Α_1)
u_2 = Vector(Μ, Ω)
e_2: (-floor(i)) + i
Μ' = Translate(Μ, Vector[(e_2 * u_2)])
Η_1: (x(Μ'), p_2(x(Μ')))
Θ_1: (x(Κ), 0)
t_2(x) = sqrt(1 - x^(2)) + y(Β_1)
j_2 = Rotate(p_2, 90*°, Χ)
s_2(x) = sqrt(1 - (x - 2)^(2)) + y(Β_1)
k_2 = Rotate(p_2, ((e_2 * 90))°, Χ)
i_2 = Segment(Ψ'_1, Κ)
Ι_1 = Intersect(h, xAxis)
k = Vector(Ι_1, Θ_1)
Κ_1 = Translate(Ι_1, Vector[(e_2 * k)])
Λ_1: (p_2(x(Μ')), (-x(Μ')))
Μ'_1 = Translate(Μ, Vector[(e_2 * (-u_2))])
l_2 = Mirror(j_2, h)
Ν_1 = Translate(Γ_1, Vector[(e_2 * k)])
v_2 = Vector(Γ_1, Ι_1)
m_2: (-floor(l)) + l
Π_1 = Translate(Γ_1, Vector[(m_2 * v_2)])
Σ_1 = Translate(Γ_1, Vector[(m_2 * v_2)])
Τ_1: (x(Σ_1), q(x(Σ_1)))
q_2 = Function(h_2, 0, x(Χ'))
o_2 = Mirror(q_2, n_2)
r_2 = Function(s, x(Γ_1), x(Δ_1))
f_3 = Function(t, x(Χ), x(Χ'_1))
g_3 = Function(g_2, -1.5707963267948966, x(Μ'))
h_3 = Function(g_2, -1.5708, 1.5707963267948966)
p_3 = Function(p, -1.5708, x(Π_1))
q_3 = Function(q, -1.5708, x(Τ_1))
r_3 = Function(t_2, -1.5708, x(Ν_1))
s_3 = Function(s_2, -1.5708, x(Κ_1))
t_3 = Function(g_2(x - 2), 0.4292, 3.5708)
z_2 = Vector((1, 0), (3.5708, 0))
Φ_1 = Translate(Ι_1, Vector[(e_2 * z_2)])
f_4 = Function(t_3, 0.4292, x(Φ_1))
w_2 = Mirror(f_4, a_3)
b_3 = Segment(Σ''', Σ'')
c_3 = Segment(Β', Α)
d_3 = Segment(Β', Β'')
e_3 = Segment(Α, Β'')