Régression parabolique non triviale
Réponses à toutes vos questions après le Bac (Fac, Prépa, etc.)
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leon1789
- Membre Transcendant
- Messages: 5486
- Enregistré le: 27 Nov 2007, 15:25
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par leon1789 » 07 Juil 2023, 21:56
PS. C'est marrant, un clown (déjà mentionné durant ces pages) dont les remarques pseudo-mathématiques le rapprochent d'un simple perroquet, ne comprenant absolument rien au présent sujet, se permet comme à son habitude de critiquer des échanges sur ce forum , alors qu'il ne sait pas lire la moindre explication mathématique. Il connaîtrait même Sylvain, et le qualifie de personne "pas vraiment sympathique". C'est dire sa piètre mentalité .
Clairement incapable de tracer la moindre parabole, il se croit "meilleur que meilleur" (sic). Un vendeur d'intelligence qui n'en a pas un échantillon sur lui, disait Coluche.
Et comme on peut s'en douter, il n'a aucune idée de ce qu'est la "recherche", il n'a pas la moindre réflexion qui ne soit pas absurde à l'évidence. Quand on est d'une telle incompétence en analyse et en géométrie (*), on évite de le montrer en étalant ses bêtises... enfin, les gens normaux évitent...
(*) cf une histoire récente d'un vecteur qui n'existe pas, ou plutôt nul par permutation, etc. des démonstrations ridiculement bidons mais à mourir de rire. Bien pire que ChatGPT. Heureusement que les étudiants font nettement mieux... remarque, eux ont étudié un peu de maths, et ne prétendent pas avoir les maths infuses.
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leon1789
- Membre Transcendant
- Messages: 5486
- Enregistré le: 27 Nov 2007, 15:25
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par leon1789 » 08 Juil 2023, 07:06
Pour une branche seulement
- Code: Tout sélectionner
[206.8,298.6]
[206.9,298.6]
[207,298.6]
[207.1,298.6]
[207.2,298.6]
[207.3,298.6]
[207.4,298.6]
[207.5,298.6]
[207.6,298.6]
[207.7,298.6]
[207.8,298.6]
[207.9,298.6]
[208,298.6]
[208.1,298.6]
[208.2,298.6]
[208.3,298.6]
[208.4,298.6]
[208.5,298.6]
[208.6,298.6]
[208.7,298.6]
[208.8,298.6]
[208.9,298.6]
[209,298.6]
[209.1,298.6]
[209.2,298.6]
[209.3,298.6]
[209.4,298.6]
[209.5,298.6]
[209.6,298.6]
[209.7,298.6]
[209.8,298.6]
[209.9,298.6]
[210,298.6]
[204.3,298.7]
[204.4,298.7]
[204.5,298.7]
[204.6,298.7]
[204.7,298.7]
[204.8,298.7]
[204.9,298.7]
[205,298.7]
[212.9,298.7]
[213,298.7]
[213.1,298.7]
[213.2,298.7]
[213.3,298.7]
[213.4,298.7]
[213.5,298.7]
[213.6,298.7]
[203.2,298.8]
sommet en (200,300)


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leon1789
- Membre Transcendant
- Messages: 5486
- Enregistré le: 27 Nov 2007, 15:25
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par leon1789 » 08 Juil 2023, 08:54
leon1789 a écrit:En fait, a²+b²=1 n'est pas la bonne contrainte pour minimiser. Comme ni a ni b ne peuvent être nuls, j'ai pris ab=1 , et là, les formules sont plus simples et les résultats absolument corrects sur tous les exemples donnés par Sylvain.
Ben314 a écrit:Tu as une idée de pourquoi ça marche mieux ?
Sachant que, le cas

, signifie qu'on considère que la distance de
)
à la parabole

est

alors que le cas

signifie que la distance est

.
Dans un cas comme dans l'autre, je vois pas bien à quoi ça correspond géométriquement . . .
Une explication :
pour la parabole

et un point
)
du plan, on pose la "distance" :
 = \sqrt[3]{ \dfrac{1}{\lambda}(\lambda x^2-y)^2 })
Cette distance est compatible avec les homothéties (centrées en (0,0) ) : si on fait agir une homothétie de rapport h>0 sur le plan, alors les distances habituelles associées à une norme (dont la distance euclidienne) sont multipliées par h. Et c'est exactement ce qui ce passe avec cette distance

:
via l'homothétie, l'image du point est
=(hx, hy))
et
l'image de la parabole est

avec

.
Alors
la distance est multipliée par h.
Sauf erreur de ma part, il n'y a pas cette compatibilité avec

.
P.S Je précise pour notre clown dlz qui se complet dans son incompétence qu'on essaie de trouver une rotation et une homothétie appliquée à la parabole y=x² depuis le début de cette recherche.
Modifié en dernier par
leon1789 le 08 Juil 2023, 10:29, modifié 1 fois.
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sylvain231
- Membre Relatif
- Messages: 307
- Enregistré le: 07 Avr 2020, 12:20
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par sylvain231 » 08 Juil 2023, 10:28
vous avez vu le spam ?
Léon ta fonction à minimiser :
f := ( E40*E02 )^(1/2) - E21 :
n'est pas fonction de t ?! à moins que tu fasses une rotation sur les points avant le calcul des E est-ce le cas ?
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leon1789
- Membre Transcendant
- Messages: 5486
- Enregistré le: 27 Nov 2007, 15:25
-
par leon1789 » 08 Juil 2023, 10:30
sylvain231 a écrit:vous avez vu le spam ?
oui.
sylvain231 a écrit:Léon ta fonction à minimiser :
f := ( E40*E02 )^(1/2) - E21 :
n'est pas fonction de t ?! à moins que tu fasses une rotation sur les points avant le calcul des E est-ce le cas ?
si si bien sûr, elle est fonction de t : oui, on fait rotation sur les points avant le calcul des E, c'est écrit bien Xt et Yt... comme avec les méthodes précédentes

Et attention, on minimise pour t variant dans ] -Pi ; Pi ]
(avant, pour des raisons de symétrie, on étudiait sur ]0 ; Pi] )
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sylvain231
- Membre Relatif
- Messages: 307
- Enregistré le: 07 Avr 2020, 12:20
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par sylvain231 » 08 Juil 2023, 10:39
c'est bon entre temps je l'ai vu et codé, ça marche, bravo !
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sylvain231
- Membre Relatif
- Messages: 307
- Enregistré le: 07 Avr 2020, 12:20
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par sylvain231 » 08 Juil 2023, 10:42
C’est la meilleure méthode proposée elle a marché sur tous mes exemples cet après-midi je testerai sur plus d’exemples
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sylvain231
- Membre Relatif
- Messages: 307
- Enregistré le: 07 Avr 2020, 12:20
-
par sylvain231 » 08 Juil 2023, 11:28
ah pour une parabole avec un a très petit (ici a=0.0001) ça me met une parabole étroite au lieu de plate, voici mes points :
- Code: Tout sélectionner
points.size()=1007
[497.631, 255.157]
[503.359, 254.141]
[497.888, 253.509]
[493.589, 258.192]
[496.202, 253.424]
[495.619, 258.24]
[493.263, 256.382]
[492.04, 259.569]
[499.334, 256.74]
[497.993, 257.858]
[496.278, 258.098]
[490.201, 254.982]
[490.39, 260.723]
[488.745, 260.684]
[487.858, 260.99]
[492.606, 253.344]
[495.023, 258.722]
[485.967, 254.538]
[487.623, 262.591]
[490.908, 257.983]
[489.73, 260.827]
[489.848, 257.103]
[485.578, 256.701]
[483.454, 253.479]
[487.241, 257.117]
[488.737, 253.857]
[488.743, 261.499]
[482.733, 259.321]
[485.325, 261.037]
[489.169, 254.09]
[488.604, 260.495]
[482.177, 258.011]
[479.972, 257.468]
[484.961, 260.626]
[485.407, 258.468]
[485.073, 257.976]
[479.396, 259.544]
[475.753, 261.981]
[476.447, 261.182]
[481.505, 261.713]
[476.435, 257.573]
[474.928, 257.203]
[474.836, 256.305]
[475.103, 257.248]
[480.948, 260.885]
[471.88, 263.858]
[479.434, 254.424]
[474.246, 260.146]
[474.795, 261.384]
[472.412, 260.74]
[475.178, 256.146]
[474.859, 259.407]
[474.862, 256.752]
[469.612, 262.208]
[468.494, 261.808]
[472.239, 264.546]
[470.447, 264.177]
[473.816, 262.223]
[465.686, 256.034]
[467.863, 260.653]
[469.159, 262.53]
[471.448, 255.104]
[467.2, 256.161]
[472.352, 261.99]
[463.624, 255.364]
[468.32, 256.043]
[464.774, 260.147]
[463.431, 262.606]
[463.542, 261.522]
[464.25, 263.58]
[467.347, 261.592]
[459.016, 259.354]
[462.642, 259.838]
[457.897, 258.304]
[464.12, 264.225]
[457.009, 262.025]
[457.282, 258.723]
[465.516, 261.615]
[460.602, 264.702]
[461.331, 256.572]
[458.457, 259.011]
[461.855, 263.855]
[455.45, 258.094]
[456.225, 257.226]
[457.215, 266.391]
[454.404, 257.55]
[453.745, 261.326]
[452.627, 260.019]
[457.223, 259.364]
[453.666, 262.644]
[454.327, 259.248]
[449.301, 260.263]
[453.028, 264.459]
[453.129, 266.501]
[453.59, 266.751]
[452.022, 266.993]
[454.098, 257.682]
[452.525, 266.694]
[448.595, 257.837]
[452.26, 263.615]
[446.588, 262.454]
[449.231, 261.533]
[454.176, 266.596]
[444.016, 264.101]
[443.667, 263.491]
[451.032, 260.279]
[447.414, 264.161]
[447.37, 262.236]
[442.262, 259.315]
[443.769, 265.607]
[446.795, 266.361]
[448.584, 265.211]
[449.257, 258.104]
[444.866, 262.892]
[443.572, 264.19]
[438.898, 262.16]
[446.387, 264.191]
[444.072, 262.558]
[446.883, 265.381]
[442.308, 265.649]
[438.755, 267.014]
[442.479, 262.157]
[445.45, 267.54]
[442.284, 259.702]
[438.35, 264.076]
[443.795, 263.91]
[437.071, 264.587]
[435.785, 260.858]
[437.325, 268.283]
[437.88, 263.816]
[435.089, 264.822]
[436.971, 266.641]
[433.49, 264.572]
[435.938, 266.237]
[432.95, 267.94]
[434.897, 261.292]
[434.796, 269.459]
[433.642, 263.813]
[435.988, 261.832]
[432.175, 261.207]
[428.466, 269.174]
[428.962, 260.459]
[426.487, 262.805]
[432.739, 262.259]
[427.945, 265.562]
[429.594, 267.605]
[429.507, 263.225]
[430.774, 263.455]
[426.822, 262.091]
[432.026, 264.403]
[429.734, 267.384]
[422.577, 261.998]
[430.522, 267.878]
[422.759, 269.198]
[420.887, 267.167]
[423.908, 265.17]
[421.661, 268.841]
[421.244, 266.044]
[419.768, 270.037]
[425.89, 267.571]
[417.398, 263.353]
[420.135, 266.919]
[422.724, 262.057]
[424.606, 270.291]
[424.15, 262.176]
[424.053, 263.169]
[420.189, 270.16]
[415.028, 266.116]
[422.302, 262.151]
[415.02, 268.785]
[412.588, 271.636]
[418.992, 261.944]
[412.517, 270.564]
[413.105, 267.783]
[411.752, 264.952]
[412.671, 263.245]
[410.462, 271.85]
[413.886, 262.529]
[411.246, 270.217]
[411.043, 262.826]
[409.904, 262.916]
[406.337, 264.32]
[412.479, 268.178]
[412.387, 263.535]
[412.508, 269.3]
[409.068, 268.753]
[405.269, 264.453]
[406.624, 267.827]
[403.982, 269.881]
[411.276, 264.213]
[409.574, 271.351]
[406.509, 269.898]
[408.851, 271.963]
[405.966, 264.549]
[401.369, 272.633]
[400.077, 264.917]
[399.953, 265.036]
[399.294, 264.214]
[402.93, 273.314]
[402.908, 263.663]
[407.009, 263.773]
[403.179, 264.354]
[404.899, 268.558]
[400.427, 273.077]
[397.007, 266.176]
[398.609, 267.868]
[403.617, 265.639]
[394.716, 269.01]
[403.469, 266.225]
[393.708, 264.439]
[400.075, 273.023]
[400.888, 271.284]
[395.563, 271.106]
[398.044, 269.106]
[391.179, 272.215]
[391.278, 274.005]
[398.124, 274.527]
[389.401, 271.614]
[396.13, 273.405]
[392.194, 273.754]
[394.607, 266.944]
[390.76, 267.415]
[392.142, 271.79]
[394.387, 268.744]
[392.109, 274.064]
[386.065, 270.222]
[385.897, 266.611]
[383.394, 271.033]
[390.983, 273.764]
[383.429, 269.975]
[386.876, 266.665]
[390.576, 273.662]
[388.392, 266.791]
[386.519, 273.492]
[387.337, 273.478]
[380.119, 270.298]
[383.453, 268.92]
[384.404, 273.912]
[379.428, 266.345]
[384.215, 268.993]
[377.493, 269.139]
[381.812, 271.275]
[381.265, 270.094]
[380.849, 271.088]
[375.893, 274.659]
[382.58, 276.182]
[383.367, 268.158]
[379.259, 267.574]
[380.433, 272.983]
[381.219, 267.192]
[377.284, 275.629]
[379.319, 273.023]
[380.979, 273.302]
[379.109, 273.636]
[375.309, 271.063]
[369.978, 272.89]
[372.197, 274.35]
[370.98, 272.977]
[368.337, 275.851]
[376.807, 273.881]
[370.499, 272.878]
[373.986, 277.551]
[375.807, 275.499]
[366.809, 268.896]
[374.533, 270.19]
[367.372, 268.373]
[366.609, 276.392]
[368.374, 270.408]
[366.388, 272.002]
[363.723, 272.188]
[370.796, 270.9]
[367.637, 274.463]
[364.494, 278.072]
[360.725, 274.245]
[362.874, 269.645]
[366.19, 275.185]
[360.764, 276.279]
[359.723, 271.036]
[365.011, 269.848]
[366.72, 273.6]
[357.22, 271.33]
[356.781, 275.39]
[356.444, 269.71]
[364.52, 270.798]
[361.149, 277.38]
[361.7, 275.042]
[360.282, 275.564]
[361.373, 269.745]
[354.978, 277.93]
[360.781, 278.35]
[360.982, 273.327]
[353.306, 276.883]
[355.367, 276.872]
[357.134, 271.046]
[353.238, 279.102]
[349.437, 279.964]
[354.383, 280.587]
[347.02, 274.042]
[356.327, 278.565]
[348.264, 276.024]
[347.518, 271.173]
[351.121, 271.763]
[347.565, 279.578]
[348.119, 279.909]
[347.978, 273.406]
[349.887, 278.485]
[345.898, 280.595]
[348.57, 281.283]
[348.628, 276.215]
[341.936, 271.899]
[340.722, 276.266]
[348.777, 279.718]
[345.241, 276.223]
[347.568, 272.469]
[343.144, 276.647]
[344.331, 276.383]
[343.102, 279.756]
[341.686, 277.695]
[345.128, 272.684]
[336.269, 273.902]
[340.585, 274.137]
[336.304, 280.821]
[337.709, 273.345]
[341.032, 279.655]
[336.392, 276.457]
[337.134, 279.795]
[341.322, 281.041]
[335.057, 273.222]
[332.774, 282.665]
[333.273, 281.072]
[337.097, 278.371]
[331.536, 281.483]
[336.318, 277.07]
[330.149, 281.413]
[332.458, 281.166]
[333.246, 279.03]
[330.957, 283.038]
[332.185, 274.177]
[328.617, 282.203]
[327.832, 280.471]
[330.955, 278.49]
[329.614, 274.942]
[325.607, 275.164]
[325.97, 281.388]
[326.795, 275.108]
[326.723, 281.08]
[328.741, 283.383]
[331.548, 280.948]
[330.293, 276.055]
[322.828, 280.864]
[328.086, 283.969]
[326.083, 275.049]
[320.112, 281.085]
[324.293, 283.956]
[322.663, 280.635]
[322.726, 277.292]
[321.979, 275.578]
[319.291, 282.423]
[321.225, 283.248]
[317.928, 278.033]
[323.562, 276.614]
[323.388, 280.562]
[321.169, 282.048]
[317.454, 284.883]
[315.308, 276.196]
[322.719, 283.093]
[317.523, 284.341]
[315.273, 283.003]
[316.193, 278.469]
[317.266, 282.453]
[317.891, 278.341]
[317.266, 277.246]
[315.444, 279.247]
[316.496, 285.617]
[315.659, 277.562]
[315.262, 280.137]
[315.975, 277.686]
[309.732, 277.452]
[308.966, 279.582]
[316.611, 277.758]
[314.048, 281.151]
[309.274, 277.752]
[315.182, 277.144]
[313.307, 279.785]
[307.25, 286.623]
[309.27, 285.239]
[304.688, 285.468]
[302.512, 285.964]
[302.539, 280.845]
[301.794, 278.941]
[303.422, 279.842]
[303.756, 284.019]
[304.329, 278.525]
[302.52, 282.51]
[302.2, 283.533]
[304.546, 278.015]
[305.169, 287.229]
[306.534, 284.012]
[297.323, 285.701]
[298.562, 281.121]
[296.651, 283.33]
[299.899, 284.953]
[295.614, 287.294]
[302.793, 281.862]
[300.152, 287.036]
[298.793, 286.802]
[292.531, 284.24]
[295.013, 288.051]
[297.468, 281.56]
[300.217, 285.608]
[296.916, 284.034]
[295.84, 282.903]
[294.692, 282.679]
[291.201, 283.703]
[296.375, 287.509]
[294.132, 286.789]
[289.641, 285.81]
[288.676, 281.235]
[290.841, 287.125]
[287.236, 281.521]
[293.556, 282.446]
[286.365, 280.708]
[285.717, 281.799]
[293.038, 286.04]
[290.117, 280.83]
[292.463, 285.766]
[289.929, 282.065]
[285.481, 288.654]
[289.735, 283.368]
[289.268, 288.305]
[284.285, 288.639]
[288.277, 288.679]
[282.977, 288.604]
[281.305, 285.169]
[279.251, 284.565]
[282.598, 287.541]
[287.74, 283.338]
[278.215, 290.376]
[280.925, 281.596]
[283.871, 282.661]
[277.575, 286.993]
[280.193, 287.788]
[282.894, 290.042]
[284.05, 288.83]
[283.225, 289.175]
[275.635, 283.187]
[276.67, 290.052]
[277.953, 288.969]
[280.131, 286.733]
[273.151, 282.22]
[276.001, 288.101]
[274.428, 290.932]
[274.887, 283.078]
[273.487, 290.949]
[275.077, 283.486]
[277.222, 287.027]
[276.774, 282.91]
[273.33, 290.018]
[270.059, 289.691]
[268.483, 291.14]
[269.809, 285.497]
[272.903, 285.243]
[270.715, 286.049]
[268.695, 285.16]
[265.523, 288.479]
[266.155, 287.734]
[268.544, 283.56]
[268.833, 287.326]
[266.877, 288.085]
[268.31, 293.228]
[267.795, 292.998]
[268.811, 284.545]
[263.518, 293.096]
[266.547, 292.943]
[262.94, 287.917]
[262.3, 289.066]
[262.07, 286.228]
[262.521, 291.954]
[265.282, 291.741]
[260.711, 292.756]
[258.088, 289.377]
[265.18, 291.516]
[264.119, 287.919]
[255.933, 293.502]
[256.444, 288.39]
[259.645, 285.093]
[260.555, 292.616]
[262.139, 292.482]
[253.872, 290.828]
[262.205, 287.177]
[256.389, 291.203]
[256.552, 290.939]
[252.915, 289.815]
[260.528, 291.995]
[255.735, 293.542]
[256.026, 295.282]
[248.901, 290.7]
[251.742, 286.745]
[249.533, 286.519]
[249.203, 294.253]
[250.24, 289.024]
[254.109, 291.89]
[248.073, 292.217]
[254.669, 294.263]
[245.957, 287.527]
[253.244, 287.973]
[246.054, 295.128]
[243.919, 294.703]
[245.274, 296.551]
[247.941, 296.696]
[241.23, 288.274]
[246.899, 294.179]
[246.403, 292.614]
[247.694, 296.181]
[247.699, 297.21]
[242.744, 296.997]
[245.724, 295.613]
[243.189, 289.552]
[241.647, 297.269]
[242.147, 288.76]
[234.9, 288.645]
[235.923, 296.463]
[241.423, 296.959]
[238.467, 290.184]
[241.445, 293.258]
[232.839, 298.235]
[240.443, 291.133]
[234.002, 296.013]
[234.97, 292.953]
[231.769, 293.971]
[236.707, 298.747]
[237.015, 298.964]
[234.19, 293.119]
[231.321, 298.354]
[232.669, 296.386]
[235.427, 297.607]
[229.772, 298.567]
[226.886, 291.23]
[229.35, 291.921]
[226.034, 294.551]
[229.494, 293.682]
[226.188, 292.505]
[228.892, 294.775]
[223.063, 292.024]
[231.773, 293.839]
[223.54, 292.553]
[230.367, 291.473]
[222.405, 291.918]
[219.922, 294.888]
[221.907, 292.057]
[221.883, 300.283]
[220.547, 299.37]
[218.08, 298.288]
[225.272, 294.926]
[223.904, 292.647]
[220.027, 291.561]
[222.695, 295.582]
[223.872, 292.296]
[215.866, 299.314]
[217.52, 294.015]
[218.701, 300.741]
[217.831, 301.288]
[219.99, 299.216]
[215.778, 299.833]
[220.036, 293.037]
[212.529, 297.327]
[216.087, 301.476]
[212.583, 301.865]
[215.319, 301.993]
[214.173, 301.272]
[219.102, 300.183]
[214.073, 299.934]
[215.057, 294.462]
[208.238, 301.337]
[210.314, 300.901]
[212.679, 297.312]
[215.934, 298.285]
[207.164, 301.076]
[207.752, 297.985]
[208.949, 294.848]
[205.626, 293.968]
[213.656, 299.751]
[212.023, 300.962]
[203.773, 299.793]
[206.552, 299.158]
[206.894, 298.219]
[204.111, 297.552]
[207.105, 300.379]
[206.411, 299.217]
[202.668, 294.951]
[204.691, 296.237]
[203.909, 301.503]
[199.448, 303.709]
[203.695, 299.149]
[200.588, 295.488]
[202.491, 299.489]
[198.274, 301.105]
[198.811, 301.879]
[202.555, 295.047]
[196.095, 300.012]
[202.726, 300.641]
[195.172, 299.741]
[198.24, 299.34]
[199.084, 304.415]
[194.418, 304.741]
[195.68, 303.638]
[192.946, 296.897]
[199.259, 300.476]
[198.884, 299.933]
[192.024, 302.206]
[194.165, 305.693]
[194.129, 304.55]
[190.511, 304.009]
[197.408, 305.77]
[196.606, 300.919]
[192.403, 297.924]
[190.075, 305.991]
[190.204, 298.308]
[194.653, 304.582]
[193.791, 299.121]
[187.775, 300.926]
[193.312, 297.946]
[185.044, 303.109]
[189.226, 303.046]
[186.874, 300.468]
[191.52, 300.469]
[189.091, 303.011]
[188.621, 299.853]
[181.578, 300.184]
[188.134, 298.448]
[185.982, 305.121]
[186.938, 298.187]
[181.87, 306.011]
[178.296, 301.448]
[182.197, 303.683]
[186.677, 300.631]
[177.14, 299.456]
[182.184, 298.737]
[176.559, 302.819]
[181.026, 300.269]
[183.69, 299.819]
[174.349, 301.567]
[174.989, 301.387]
[173.672, 308.078]
[181.059, 299.695]
[172.432, 304.573]
[173.623, 300.169]
[173.329, 304.277]
[172.756, 306.935]
[170.544, 299.886]
[174.848, 303.889]
[170.274, 301.331]
[173.386, 305.904]
[171.196, 305.923]
[167.904, 300.604]
[173.793, 307.23]
[173.743, 307.117]
[170.006, 307.648]
[174.686, 302.406]
[175.032, 301.634]
[165.937, 303.499]
[169.157, 301.87]
[164.87, 307.274]
[165.166, 306.69]
[164.101, 304.368]
[164.749, 308.805]
[171.245, 309.363]
[164.972, 306.335]
[168.802, 309.187]
[168.782, 303.554]
[162.567, 308.253]
[165.898, 309.499]
[166.572, 309.18]
[161.422, 304.483]
[161.828, 305.342]
[159.357, 310.569]
[163.143, 308.136]
[160.257, 308.448]
[165.433, 304.882]
[156.511, 307.592]
[158.899, 304.331]
[163.44, 308.653]
[161.073, 308.283]
[157.694, 309.468]
[153.651, 311.176]
[155.016, 303.989]
[159.891, 304.481]
[158.206, 310.207]
[159.29, 308.651]
[153.875, 304.439]
[150.289, 309.92]
[159.701, 306.308]
[155.396, 309.84]
[157.809, 303.922]
[153.238, 307.121]
[148.596, 307.55]
[153.928, 310.61]
[154.351, 305.81]
[154.108, 305.144]
[149.882, 307.025]
[145.76, 310.494]
[154.381, 306.286]
[148.117, 305.594]
[144.704, 312.349]
[148.487, 310.777]
[153.101, 307.327]
[147.169, 307.869]
[149.116, 307.697]
[142.776, 312.026]
[151.342, 313.707]
[146.57, 309.771]
[150.176, 305.477]
[142.626, 307.567]
[147.78, 305.172]
[140.138, 310.5]
[144.054, 308.443]
[142.465, 306.778]
[141.653, 307.18]
[140.225, 309.693]
[138.653, 308.095]
[140.69, 309.515]
[144.536, 315.659]
[136.295, 311.6]
[143.803, 306.95]
[143.327, 315.957]
[135.485, 309.135]
[133.95, 310.411]
[135.52, 310.097]
[137.379, 314.692]
[140.094, 309.764]
[132.964, 313.802]
[138.651, 315.607]
[132.028, 307.958]
[137.923, 316.232]
[132.697, 316.495]
[130.471, 316.195]
[135.84, 312.906]
[131.686, 312.732]
[133.729, 310.274]
[134.136, 308.672]
[132.858, 309.724]
[135.65, 314.049]
[127.585, 307.648]
[135.95, 314.225]
[126.751, 310.522]
[134.93, 313]
[124.915, 310.035]
[132.232, 310.689]
[126.723, 314.526]
[133.67, 308.866]
[125.543, 313.661]
[127.449, 317.705]
[129.806, 313.082]
[124.244, 309.16]
[129.45, 314.393]
[130.518, 315.855]
[124.535, 309.086]
[124.616, 312.653]
[121.343, 309.791]
[120.004, 316.93]
[126.471, 315.754]
[119.561, 313.629]
[118.184, 317.861]
[124.01, 314.917]
[117.984, 310.432]
[121.818, 309.802]
[119.351, 312.069]
[116.649, 310.542]
[115.277, 314.43]
[119.154, 311.69]
[116.541, 319.53]
[114.359, 316.531]
[117.794, 311.679]
[120.485, 316.562]
[112.485, 319.86]
[113.985, 319.345]
[112.718, 320.332]
[117.431, 318.802]
[110.193, 314.975]
[114.336, 314.193]
[117.833, 317.623]
[117.695, 315.271]
[113.957, 319.917]
[111.446, 319.995]
[114.405, 312.476]
[109.935, 312.499]
[107.315, 316.192]
[108.845, 318.978]
[111.533, 320.296]
[105.667, 316.651]
[111.628, 317.524]
[107.938, 316.11]
[108.342, 318.677]
[108.425, 315.046]
[103.234, 319.434]
[107.767, 316.333]
[105.994, 322.344]
[103.985, 316.058]
[100.362, 318.537]
[106.374, 319.959]
[100.966, 314.317]
[100.493, 317.866]
[103.675, 321.839]
[103.405, 318.112]
[101.87, 317.731]
[95.7213, 319.449]
[97.4544, 323.507]
[94.5791, 315.459]
[103.536, 320.64]
[95.1441, 317.505]
[100.156, 318.855]
[102.312, 317.671]
[95.8019, 315.004]
[96.3825, 324.311]
[93.5689, 321.98]
[94.2311, 320.151]
[92.1801, 316.063]
[90.5609, 318.951]
[96.6147, 320.888]
[91.8848, 315.074]
[92.9586, 322.909]
[94.6567, 321.392]
[92.0748, 322.995]
[93.1653, 319.625]
[94.6005, 321.846]
[95.1987, 322.452]
[89.2674, 318.771]
[90.287, 324.359]
[87.3501, 316.766]
[92.1371, 317.772]
[91.5138, 317.777]
[90.726, 326.006]
[87.8356, 322.292]
[82.9778, 318.825]
[87.6078, 323.006]
[83.7911, 326.468]
[89.469, 316.642]
[79.9777, 325.603]
[86.6066, 321.784]
[85.2028, 326.22]
[80.7296, 318.53]
[78.4589, 326.166]
[80.1921, 322.819]
[86.8201, 322.774]
[80.566, 324.654]
[84.0559, 320.954]
[77.6574, 327.507]
[83.0123, 319.896]
[76.0634, 327.357]
[76.457, 324.941]
[79.961, 326.753]
[82.2491, 319.641]
[81.1173, 324.968]
[72.4473, 322.353]
[80.6788, 326.866]
[74.6171, 322.29]
[77.1891, 325.441]
[74.2966, 321.653]
[76.4072, 322.633]
[77.083, 322.899]
[76.4892, 326.363]
[69.035, 328.776]
[73.3279, 328.642]
[74.9784, 324.779]
[74.7955, 325.075]
[74.7892, 322.139]
[72.3504, 322.464]
[69.1757, 326.249]
[67.1284, 321.441]
[68.752, 322.24]
[71.27, 324.489]
[69.7961, 327.564]
[63.5517, 329.439]
[66.9211, 327.054]
[65.7198, 320.753]
[66.7986, 330.489]
[66.725, 320.836]
[60.2983, 330.088]
[65.4793, 321.058]
[63.2558, 322.606]
[59.3537, 328.471]
[59.8698, 326.392]
[63.3305, 324.363]
[65.0005, 327.815]
[62.0322, 328.016]
[66.1001, 327.292]
[63.9863, 325.565]
[56.4902, 327.06]
[55.2736, 323.026]
[55.7418, 328.456]
[59.5161, 331.124]
[61.66, 331.51]
[54.6964, 324.807]
[54.3657, 331.142]
[58.5399, 326.014]
[52.4007, 325.188]
[52.6866, 332.568]
[50.86, 324.004]
[54.1347, 330.531]
[53.013, 329.628]
[55.9176, 325.131]
[50.9013, 332.761]
[52.3734, 326.456]
[52.782, 330.984]
[56.0956, 332.737]
[52.6781, 333.131]
[47.4943, 330.713]
[50.4305, 326.658]
[46.4356, 330.796]
[53.0555, 328.652]
[48.2696, 326.925]
[52.5066, 332.563]
[44.3684, 331.067]
[46.9164, 324.859]
[51.3402, 327.499]
[50.0637, 333.048]
[41.5138, 330.175]
[44.5182, 326.418]
[45.5948, 334.592]
[49.6919, 328.22]
[43.5187, 325.401]
[44.5594, 331.235]
[41.1786, 333.006]
[46.2948, 325.572]
[37.7866, 329.591]
[37.8528, 327.161]
[41.3296, 329.282]
[39.0421, 328.528]
[35.6931, 332.517]
[42.2639, 334.275]
[44.5553, 333.232]
[39.0439, 327.077]
[40.0619, 331.302]
[33.8337, 333.217]
[37.0367, 330.14]
[41.4796, 331.251]
[39.1901, 327.864]
[34.4439, 327.27]
[37.6305, 335.006]
[31.772, 328.658]
[36.3871, 327.611]
[38.0825, 331.861]
[34.7624, 328.097]
[31.4108, 329.186]
[32.8153, 327.987]
[36.6738, 337.281]
[36.1999, 330.561]
[35.8161, 334.107]
[26.6251, 335.843]
[32.9929, 333.729]
[29.5477, 337.744]
[34.1616, 328.459]
[27.6138, 337.94]
[26.0397, 331.907]
[30.6383, 332.403]
[29.23, 336.518]
[22.552, 336.31]
[27.6321, 335.998]
[29.6213, 331.018]
[28.9953, 334.652]
[23.3733, 338.283]
[20.8113, 337.699]
[23.412, 329.411]
[19.8333, 333.944]
[19.6974, 332.62]
[19.1734, 332.337]
[24.2804, 335.029]
[24.4558, 338.107]
[23.515, 334.03]
[22.0066, 336.497]
[23.2495, 335.563]
[16.9115, 333.81]
[17.151, 332.476]
[20.8336, 338.795]
[19.182, 338.462]
[21.3213, 334.209]
[16.8254, 332.664]
[19.4921, 335.269]
[10.1489, 336.088]
[17.2006, 340.933]
[18.0415, 339.828]
[11.0189, 338.745]
[11.8319, 339.823]
[8.35535, 336.611]
[11.7628, 336.783]
[6.40407, 333.319]
[8.48504, 333.369]
[7.78602, 332.663]
[5.7849, 333.366]
[6.08961, 337.256]
[10.21, 333.42]
[8.05242, 336.467]
[3.70095, 342.045]
[4.65064, 336.056]
[11.6535, 341.707]
[6.86233, 340.934]
[7.97643, 337.075]
[6.42342, 341.378]
[4.13271, 341.827]
[1.0484, 333.816]
[1.34656, 342.23]
[-1.79737, 341.261]
[0.722635, 337.827]
[-2.26806, 340.932]
[2.12197, 341.487]
[0.504238, 342.843]
[-0.755544, 334.796]
sommet = [200, 300]
-
leon1789
- Membre Transcendant
- Messages: 5486
- Enregistré le: 27 Nov 2007, 15:25
-
par leon1789 » 08 Juil 2023, 12:08
ok, t := 0.176 "ancien" a := 0.000099
mais ton exemple est quasiment une droite...



Mais ok, tout n'est pas totalement clair encore.
Oui, avec un

grand (ie. ancien "a" proche de 0), alors pour tout

pas trop grand, le point
)
est estimé (à tort) proche de la parabole

. C'est pourquoi on observe une ligne de points derrière le sommet sur l'exemple mal traité.
-
sylvain231
- Membre Relatif
- Messages: 307
- Enregistré le: 07 Avr 2020, 12:20
-
par sylvain231 » 13 Juil 2023, 15:58
Bonjour Léon,
tu cherches encore ou tu as laissé tomber ?
Merci
Bonne soirée
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