« la science qui mesure et représente la surface terrestre »

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1 « la science qui mesure et représente la surface terrestre »

2 1- Thalès Mesure de la tour Gilles Aycelin à Narbonne.

3 2- Eratosthène Mesure du rayon de la terre.

4 2- Eratosthène

5 Résultats des mesures HeureOmbreObjetTangenteAngle 11:435380,131578957,49585764 11:571387800,1769230810,0331206 11:428380,2105263211,888658 11:58321310,2442748113,7270966 12:01512030,2512315314,1026348 12:00512030,2512315314,1026348 11:39341350,2518518514,1360618 11:4019740,2567567614,4000213 11:58451750,2571428614,4207731 11:5818680,2647058814,82648 11:5444016600,2650602414,8454521 11:43692590,2664092714,9176475 11:44692590,2664092714,9176475 11:48692590,2664092714,9176475 11:52732730,2673992714,9705982 12:0044016400,2682926815,0183606 11:5444016400,2682926815,0183606 11:55501860,268817215,0463918 11:57853140,2707006415,1469844 11:57853140,2707006415,1469844 11:4127,51000,27515,3762512 11:49501800,2777777815,524111 12:0046516400,2835365915,8299735 11:402173,50,2857142915,9453959 11:412173,50,2857142915,9453959 11:3717,5610,2868852516,0074043 11:4274,52590,2876447916,0476054 11:45501630,3067484717,0533148 11:501858,50,3076923117,102729 11:4839,50,3157894717,5255684 11:5039,50,3157894717,5255684 11:4539,50,3157894717,5255684 11:5512380,3157894717,5255684 11:5626810,3209876517,7959889 11:3520620,3225806517,8786966 11:4120610,3278688518,1527059 11:4120610,3278688518,1527059 11:3824730,3287671218,1991651 11:4224730,3287671218,1991651 11:4117500,3418,7780332 11:4414400,3519,2900462 11:4121600,3519,2900462 11:4414,5400,362519,9255807 11:4631840,3690476220,2564622 11:4512320,37520,5560452 12:006160,37520,5560452 11:44641700,3764705920,6298799 11:37772030,3793103420,7722547 11:44631620,3888888921,2505055 11:4334840,404761922,0362269 11:40721730,4161849722,5963445 11:431032000,51527,2484674 11:551052000,52527,6994728 11:4625450,5555555629,0546041 11:477931,32,5239616668,3864038

6 Résultats des mesures HeureOmbreObjetTangenteAngle 11:435380,131578957,49585764 11:571387800,1769230810,0331206 11:428380,2105263211,888658 11:58321310,2442748113,7270966 12:01512030,2512315314,1026348 12:00512030,2512315314,1026348 11:39341350,2518518514,1360618 11:4019740,2567567614,4000213 11:58451750,2571428614,4207731 11:5818680,2647058814,82648 11:5444016600,2650602414,8454521 11:43692590,2664092714,9176475 11:44692590,2664092714,9176475 11:48692590,2664092714,9176475 11:52732730,2673992714,9705982 12:0044016400,2682926815,0183606 11:5444016400,2682926815,0183606 11:55501860,268817215,0463918 11:57853140,2707006415,1469844 11:57853140,2707006415,1469844 11:4127,51000,27515,3762512 11:49501800,2777777815,524111 12:0046516400,2835365915,8299735 11:402173,50,2857142915,9453959 11:412173,50,2857142915,9453959 11:3717,5610,2868852516,0074043 11:4274,52590,2876447916,0476054 11:45501630,3067484717,0533148 11:501858,50,3076923117,102729 11:4839,50,3157894717,5255684 11:5039,50,3157894717,5255684 11:4539,50,3157894717,5255684 11:5512380,3157894717,5255684 11:5626810,3209876517,7959889 11:3520620,3225806517,8786966 11:4120610,3278688518,1527059 11:4120610,3278688518,1527059 11:3824730,3287671218,1991651 11:4224730,3287671218,1991651 11:4117500,3418,7780332 11:4414400,3519,2900462 11:4121600,3519,2900462 11:4414,5400,362519,9255807 11:4631840,3690476220,2564622 11:4512320,37520,5560452 12:006160,37520,5560452 11:44641700,3764705920,6298799 11:37772030,3793103420,7722547 11:44631620,3888888921,2505055 11:4334840,404761922,0362269 11:40721730,4161849722,5963445 11:431032000,51527,2484674 11:551052000,52527,6994728 11:4625450,5555555629,0546041 11:477931,32,5239616668,3864038 HeureOmbreObjetTangenteAngle 11:48692590,2664092714,9176475 11:52732730,2673992714,9705982 12:0044016400,2682926815,0183606 11:5444016400,2682926815,0183606 11:55501860,268817215,0463918 11:57853140,2707006415,1469844 11:57853140,2707006415,1469844 11:4127,51000,27515,3762512 11:49501800,2777777815,524111 12:0046516400,2835365915,8299735 11:402173,50,2857142915,9453959 11:412173,50,2857142915,9453959 11:3717,5610,2868852516,0074043 11:4274,52590,2876447916,0476054 11:45501630,3067484717,0533148 11:501858,50,3076923117,102729 11:4839,50,3157894717,5255684 11:5039,50,3157894717,5255684 11:4539,50,3157894717,5255684 11:5512380,3157894717,5255684 11:5626810,3209876517,7959889 11:3520620,3225806517,8786966 11:4120610,3278688518,1527059 11:4120610,3278688518,1527059 11:3824730,3287671218,1991651 11:4224730,3287671218,1991651 11:4117500,3418,7780332 11:4414400,3519,2900462 11:4121600,3519,2900462 Moyenne série :16,7564254

7 Résultats des mesures HeureOmbreObjetTangenteAngle 11:435380,131578957,49585764 11:571387800,1769230810,0331206 11:428380,2105263211,888658 11:58321310,2442748113,7270966 12:01512030,2512315314,1026348 12:00512030,2512315314,1026348 11:39341350,2518518514,1360618 11:4019740,2567567614,4000213 11:58451750,2571428614,4207731 11:5818680,2647058814,82648 11:5444016600,2650602414,8454521 11:43692590,2664092714,9176475 11:44692590,2664092714,9176475 11:48692590,2664092714,9176475 11:52732730,2673992714,9705982 12:0044016400,2682926815,0183606 11:5444016400,2682926815,0183606 11:55501860,268817215,0463918 11:57853140,2707006415,1469844 11:57853140,2707006415,1469844 11:4127,51000,27515,3762512 11:49501800,2777777815,524111 12:0046516400,2835365915,8299735 11:402173,50,2857142915,9453959 11:412173,50,2857142915,9453959 11:3717,5610,2868852516,0074043 11:4274,52590,2876447916,0476054 11:45501630,3067484717,0533148 11:501858,50,3076923117,102729 11:4839,50,3157894717,5255684 11:5039,50,3157894717,5255684 11:4539,50,3157894717,5255684 11:5512380,3157894717,5255684 11:5626810,3209876517,7959889 11:3520620,3225806517,8786966 11:4120610,3278688518,1527059 11:4120610,3278688518,1527059 11:3824730,3287671218,1991651 11:4224730,3287671218,1991651 11:4117500,3418,7780332 11:4414400,3519,2900462 11:4121600,3519,2900462 11:4414,5400,362519,9255807 11:4631840,3690476220,2564622 11:4512320,37520,5560452 12:006160,37520,5560452 11:44641700,3764705920,6298799 11:37772030,3793103420,7722547 11:44631620,3888888921,2505055 11:4334840,404761922,0362269 11:40721730,4161849722,5963445 11:431032000,51527,2484674 11:551052000,52527,6994728 11:4625450,5555555629,0546041 11:477931,32,5239616668,3864038 HeureOmbreObjetTangenteAngle 11:48692590,2664092714,9176475 11:52732730,2673992714,9705982 12:0044016400,2682926815,0183606 11:5444016400,2682926815,0183606 11:55501860,268817215,0463918 11:57853140,2707006415,1469844 11:57853140,2707006415,1469844 11:4127,51000,27515,3762512 11:49501800,2777777815,524111 12:0046516400,2835365915,8299735 11:402173,50,2857142915,9453959 11:412173,50,2857142915,9453959 11:3717,5610,2868852516,0074043 11:4274,52590,2876447916,0476054 11:45501630,3067484717,0533148 11:501858,50,3076923117,102729 11:4839,50,3157894717,5255684 11:5039,50,3157894717,5255684 11:4539,50,3157894717,5255684 11:5512380,3157894717,5255684 11:5626810,3209876517,7959889 11:3520620,3225806517,8786966 11:4120610,3278688518,1527059 11:4120610,3278688518,1527059 11:3824730,3287671218,1991651 11:4224730,3287671218,1991651 11:4117500,3418,7780332 11:4414400,3519,2900462 11:4121600,3519,2900462 Moyenne série :16,7564254   16,7564254°

8 Au même moment à La Paz…   42,1°

9 Résultats : Angle à Caracas : 16,8° Angle à La Paz : 42,1° Différence des angles (angle au centre de la terre) : 42,1 – 16,8 = 25,3° Soit la relation de proportionnalité : Soit une erreur de 5,3%

10 3 - Triangulation Mesure de la distance du Collège Marcelin Albert (St Nazaire d’Aude) au collège Joseph Anglade (Lézignan). Octobre 2007 – juin 2008

11 Collège Marcelin ALbert Collège Joseph Anglade

12 Collège Marcelin ALbert Collège Joseph AngladeEoliennes

13 Collège Marcelin ALbert Collège Joseph Anglade

14 Les triangles Le premier triangle et la base.

15 La base.

16 Le premier triangle

17 83°30 ' 27' 83°27 '

18

19 180° – (46°05’ + 83°30’) 180° – 129°35’ 50°25’ Formule des sinus

20

21

22

23 Calcul des angles et côtés des triangles conservés.

24 AF² = DF² + AD² – 2  DF  AD  cos AF² = 467² + 1003² – 2  467  1003  sin 126° AF  1331 m Formule d'Al Kashi

25 6772 m

26 9156 m

27 Nous utilisons la formule d’Al Kashi et obtenons 13196 m. (La valeur réelle est de 13077 m soit une erreur de 0,9%)

28

29 Traitement de l'erreur.

30 3 ème rang : Jean Charles Cros (entre les deux filles), Jimmy Sylvestre, Delphine Sauzède, Aurélie Magnez (cachée). 2 ème rang : Sarah Pramayon, Christy Mounié, Julie Delmas, Alison Richebusch, Roxane Pilat et Caroline Taudière. 1 er rang, les professeurs : Didier Aribaud, Christophe Monié, Marc Amiel, Pierre-Yves Gouiffes.