prueba
Author: José Luis Álvarez

x² = p x + q

p

q

Término

Valor

Cociente

Término general:

Número metálico:

Razón entre términos
     consecutivos:

Potencias de Φ

Sucesión generalizada de Fibonacci

Expresión general

Φ^n=a_{n} ·Φ+a_{n-1}

q = 1 (slider from 1 to 5, step 1)
p = 1 (slider from 1 to 5, step 1)
g = Function((p * x) + q, 0, Infinity)
f(x) = x^(2)
a: y = (p * x) + q
E_1, E_2 = Intersect(f, g)
E: E_2
F: (x(E), 0)
polígono1, b, f_1, c, d = Polygon((0, 0), F, (x(F), 1), (0, 1))
texto1: "x² = " + (If[p ≠ 1, p + "x", "x"]) + " + " + q
texto3: "x =  \frac{ " + p + "+ \sqrt{ " + (p^(2) + (4 * q)) + " }  }{2 }=" + (p / 2) + "+ \sqrt{ " + (p^(2) / 4 + q) + " } "
texto4: "" + (x(F))
texto5: "" + (x(F))
e = Segment(F, F - (0, 0.6))
g1 = Segment(E, F)
A = Intersect(f, a, 1)
x1: (p + sqrt(p^(2) + (4 * q))) / 2
texto2: "x =  \frac{ " + p + "+ \sqrt{ " + (p^(2) + (4 * q)) + " }  }{2 }"
texto9: "x =  \frac{ " + p + "+ \sqrt{ " + (p^(2) + (4 * q)) + " }  }{2 }=" + x1
B1: p
B2: q
A4 = 1
A5 = 2
A6: (2 * A5) - A4
A7: (2 * A6) - A5
A8: (2 * A7) - A6
A9: (2 * A8) - A7
A10: (2 * A9) - A8
A11: (2 * A10) - A9
A12: (2 * A11) - A10
A13: (2 * A12) - A11
A14: (2 * A13) - A12
A15: (2 * A14) - A13
A16: (2 * A15) - A14
A17: (2 * A16) - A15
A18: (2 * A17) - A16
A19: (2 * A18) - A17
A20: (2 * A19) - A18
A21: (2 * A20) - A19
A22: (2 * A21) - A20
A23: (2 * A22) - A21
A24: (2 * A23) - A22
A25: (2 * A24) - A23
A26: (2 * A25) - A24
A27: (2 * A26) - A25
A28: (2 * A27) - A26
B4 = 1
B5 = 1
B6: (p * B5) + (q * B4)
B7: (p * B6) + (q * B5)
B8: (p * B7) + (q * B6)
B9: (p * B8) + (q * B7)
B10: (p * B9) + (q * B8)
B11: (p * B10) + (q * B9)
B12: (p * B11) + (q * B10)
B13: (p * B12) + (q * B11)
B14: (p * B13) + (q * B12)
B15: (p * B14) + (q * B13)
B16: (p * B15) + (q * B14)
B17: (p * B16) + (q * B15)
B18: (p * B17) + (q * B16)
B19: (p * B18) + (q * B17)
B20: (p * B19) + (q * B18)
B21: (p * B20) + (q * B19)
B22: (p * B21) + (q * B20)
B23: (p * B22) + (q * B21)
B24: (p * B23) + (q * B22)
B25: (p * B24) + (q * B23)
B26: (p * B25) + (q * B24)
B27: (p * B26) + (q * B25)
B28: (p * B27) + (q * B26)
C5: B5 / B4
C6: B6 / B5
C7: B7 / B6
C8: B8 / B7
C9: B9 / B8
C10: B10 / B9
C11: B11 / B10
C12: B12 / B11
C13: B13 / B12
C14: B14 / B13
C15: B15 / B14
C16: B16 / B15
C17: B17 / B16
C18: B18 / B17
C19: B19 / B18
C20: B20 / B19
C21: B21 / B20
C22: B22 / B21
C23: B23 / B22
C24: B24 / B23
C25: B25 / B24
C26: B26 / B25
C27: B27 / B26
C28: B28 / B27
texto7: "p = " + p
texto8: "q = " + q
ldivy = Sequence(Segment[(-0.05, k), (0.05, k)], k, -2, 8)
i = Segment((0, -2.1), (0, 8.1))
h = Segment((-6.1, 0), (7.1, 0))
ldivx = Sequence(Segment[(k, -0.05), (k, 0.05)], k, -6, 7)
lrotx = Sequence(Text[k, (If[k  <  0, k - 0.15, k - 0.05], -0.4)], k, -6, 7)
lroty = Sequence(Text[k, (If[k  <  0, -0.4, -0.3], k - 0.1)], k, -2, 8)
Lfibo: B4:B28
Lcoc: C5:C28
j = 19 (slider from 1 to 19, step 1)
texto10: "\frac{ a_{" + (19 - j + 2) + "} }{a_{" + (19 - j + 1) + "} } \; = \;  " + (Element[Lcoc, 19 - j + 1])
texto11: "a_{n+2} = " + p + "·a_{n+1}+" + q + "·a_{n}"
B = (10.826187500000001, 1.2314999999999994)
pot = false
suc = false
Lfibo1: {1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765}
n = 2 (slider from 2 to 9, step 1)
texto18: "Φ^" + n + " \; = \; Φ+1"
for1 = false
razon = true
metal = false
texto12: "\sigma_{" + p + "," + q + "} \; = \; " + (x(F))
texto13: "\sigma_{1,1}=Φ = " + (x(F))
texto17: "Φ^" + (LaTeX[n]) + " \; = \; " + (LaTeX[Element[Lfibo1, n]]) + "·Φ \; + \; " + (LaTeX[Element[Lfibo1, n - 1]]) + ""
Ltabx = Sequence(Text["a_{" + (k) + "}=", (7.5, 7 - (0.6 * k))], k, 1, 10)
Ltaby = Sequence(Text[Element[Lfibo, k], (8.5, 7 - (0.6 * k))], k, 1, 10)
Ltaby1 = Sequence(Text[Element[Lfibo1, k], (8.5, 7 - (0.6 * k))], k, 1, 10)