Le\; plus\; grand\; rectangle\;  (2)

On \;définit \;le \;point \;V\left( x=d\;,\;S(x)  \right) 

N

P

Q

M

C

B

A

H

Le \;pas\;de\;la\;colonne\;d=x\;dans\;le\;tableur\
est\;10^{-1}:\;c'est\;l'incrément\;du\;curseur\;d

Conjecture:\
1^{ère}\;Méthode:\;d'après\;les\;traces\;de\;V\;on\;a:\
\;\;\;\;\;\;\;\;\;S(x)=18\;\;\;et\;\;x=4\
2^{ème}\;Méthode:\;d'après\;le\;tableur\
*\;Ovrir\;le\;menu\;''Affichage''\
*\;Désactiver\;l'option:\;Graphique\;2\
*\;Actver\;l'option:\;Tableur\
A\;la\;ligne\;42\;de\;ce\;tableur,\;on\;lit:\
\;\;\;\;\;\;\;S(x)=18\;\;et\;\;x=4

On\;définit\;le\;point\;V\left(x=d\;,\;S(x)   \right) 

d = 3.8 (slider from 0 to 8, step 0.1)
A = (0, 0)
B = (12, 0)
C = (8, 6)
H = (8, 0)
poly1, b, a, c = Polygon(A, C, B)
d_2 = Segment(A, H)
M: (d, 0)
e = OrthogonalLine(M, c)
N = Intersect(e, b)
f = OrthogonalLine(N, e)
P = Intersect(f, a)
g = OrthogonalLine(P, f)
Q = Intersect(g, c)
poly2, m, d_1, e_1, f_1 = Polygon(M, N, P, Q)
V: (d, poly2)
texte2: "V\left(  " + (LaTeX[d]) + "\;,\;" + (LaTeX[poly2]) + " \right) "
A1 = Name(d)
B1 = Name(poly2)
A2 = 0
B2 = 0
A3 = 0.1
B3 = 0.8887500000000002
A4 = 0.2
B4 = 1.7550000000000003
A5 = 0.3
B5 = 2.59875
A6 = 0.4
B6 = 3.420000000000001
A7 = 0.5
B7 = 4.21875
A8 = 0.6
B8 = 4.994999999999999
A9 = 0.7
B9 = 5.748749999999999
A10 = 0.8
B10 = 6.48
A11 = 0.9
B11 = 7.188750000000002
A12 = 1
B12 = 7.875
A13 = 1.1
B13 = 8.53875
A14 = 1.2
B14 = 9.18
A15 = 1.3
B15 = 9.798750000000002
A16 = 1.4
B16 = 10.395
A17 = 1.5
B17 = 10.96875
A18 = 1.6
B18 = 11.520000000000001
A19 = 1.7
B19 = 12.048749999999998
A20 = 1.8
B20 = 12.555
A21 = 1.9
B21 = 13.03875
A22 = 2
B22 = 13.5
A23 = 2.1
B23 = 13.938749999999999
A24 = 2.2
B24 = 14.355000000000002
A25 = 2.3
B25 = 14.748749999999998
A26 = 2.4
B26 = 15.120000000000001
A27 = 2.5
B27 = 15.46875
A28 = 2.6
B28 = 15.794999999999998
A29 = 2.7
B29 = 16.098750000000003
A30 = 2.8
B30 = 16.379999999999995
A31 = 2.9
B31 = 16.638749999999998
A32 = 3
B32 = 16.875
A33 = 3.1
B33 = 17.088749999999997
A34 = 3.2
B34 = 17.28
A35 = 3.3
B35 = 17.448749999999997
A36 = 3.4
B36 = 17.595000000000002
A37 = 3.5
B37 = 17.71875
A38 = 3.6
B38 = 17.82
A39 = 3.7
B39 = 17.898750000000003
A40 = 3.8
B40 = 17.955
A41 = 3.9
B41 = 17.988750000000003
A42 = 4
B42 = 18
A43 = 4.1
B43 = 17.98875
A44 = 4.2
B44 = 17.955000000000002
A45 = 4.3
B45 = 17.898749999999996
A46 = 4.4
B46 = 17.820000000000004
A47 = 4.5
B47 = 17.71875
A48 = 4.6
B48 = 17.59499999999999
A49 = 4.7
B49 = 17.448750000000004
A50 = 4.8
B50 = 17.28
A51 = 4.9
B51 = 17.08875
A52 = 5
B52 = 16.875
A53 = 5.1
B53 = 16.638749999999995
A54 = 5.2
B54 = 16.380000000000003
A55 = 5.3
B55 = 16.098749999999995
A56 = 5.4
B56 = 15.795000000000002
A57 = 5.5
B57 = 15.46875
A58 = 5.6
B58 = 15.120000000000001
A59 = 5.7
B59 = 14.748750000000001
A60 = 5.8
B60 = 14.354999999999997
A61 = 5.9
B61 = 13.938750000000002
A62 = 6
B62 = 13.5
A63 = 6.1
B63 = 13.038749999999999
A64 = 6.2
B64 = 12.555000000000001
A65 = 6.3
B65 = 12.048749999999998
A66 = 6.4
B66 = 11.520000000000003
A67 = 6.5
B67 = 10.96875
A68 = 6.6
B68 = 10.395
A69 = 6.7
B69 = 9.798749999999998
A70 = 6.8
B70 = 9.179999999999996
A71 = 6.9
B71 = 8.53875
A72 = 7
B72 = 7.875
A73 = 7.1
B73 = 7.188749999999999
A74 = 7.2
B74 = 6.479999999999993
A75 = 7.3
B75 = 5.748750000000005
A76 = 7.4
B76 = 4.994999999999994
A77 = 7.5
B77 = 4.21875
A78 = 7.6
B78 = 3.4200000000000017
A79 = 7.7
B79 = 2.598749999999999
A80 = 7.8
B80 = 1.755000000000006
A81 = 7.9
B81 = 0.8887499999999946
A82 = 7.9
A83 = 7.9
A84 = 8
B82 = 0
B83 = 0.8887499999999946
B84 = 1.755000000000006
texte12: "d=AM=x=" + (LaTeX[d]) + ""
h = OrthogonalLine(V, yAxis)
i = OrthogonalLine(V, xAxis)
D = Intersect(h, yAxis)
E = Intersect(i, xAxis)
texte13: "S(x)=" + (LaTeX[poly2]) + ""
texte14: "x=" + (LaTeX[d]) + ""
j = Segment(V, D)
k = Segment(V, E)
texte16: "Pour \;x=" + (LaTeX[d]) + ",\;on\;a:\;S(x)=" + (LaTeX[poly2]) + ""