2017-2018/3e/Geometrie/Triangle_rectangle/E5_rayon_terre.svg

278 lines
15 KiB
XML

<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!-- Created with Inkscape (http://www.inkscape.org/) -->
<svg
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:cc="http://creativecommons.org/ns#"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
width="210mm"
height="148mm"
viewBox="0 0 210 148"
version="1.1"
id="svg8"
inkscape:version="0.92.2 5c3e80d, 2017-08-06"
sodipodi:docname="E5_rayon_terre.svg">
<defs
id="defs2">
<marker
inkscape:stockid="Arrow1Mstart"
orient="auto"
refY="0"
refX="0"
id="marker1344"
style="overflow:visible"
inkscape:isstock="true">
<path
id="path1342"
d="M 0,0 5,-5 -12.5,0 5,5 Z"
style="fill:#000000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:1.00000003pt;stroke-opacity:1"
transform="matrix(0.4,0,0,0.4,4,0)"
inkscape:connector-curvature="0" />
</marker>
<marker
inkscape:isstock="true"
style="overflow:visible"
id="marker1286"
refX="0"
refY="0"
orient="auto"
inkscape:stockid="Arrow1Mstart"
inkscape:collect="always">
<path
transform="matrix(0.4,0,0,0.4,4,0)"
style="fill:#000000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:1.00000003pt;stroke-opacity:1"
d="M 0,0 5,-5 -12.5,0 5,5 Z"
id="path1284"
inkscape:connector-curvature="0" />
</marker>
<marker
inkscape:stockid="Arrow1Mstart"
orient="auto"
refY="0"
refX="0"
id="Arrow1Mstart"
style="overflow:visible"
inkscape:isstock="true"
inkscape:collect="always">
<path
id="path996"
d="M 0,0 5,-5 -12.5,0 5,5 Z"
style="fill:#000000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:1.00000003pt;stroke-opacity:1"
transform="matrix(0.4,0,0,0.4,4,0)"
inkscape:connector-curvature="0" />
</marker>
<filter
inkscape:collect="always"
style="color-interpolation-filters:sRGB"
id="filter986"
x="-0.20633045"
width="1.412661"
y="-0.15405296"
height="1.3081059">
<feGaussianBlur
inkscape:collect="always"
stdDeviation="0.42599431"
id="feGaussianBlur988" />
</filter>
</defs>
<sodipodi:namedview
id="base"
pagecolor="#ffffff"
bordercolor="#666666"
borderopacity="1.0"
inkscape:pageopacity="0.0"
inkscape:pageshadow="2"
inkscape:zoom="1.0935553"
inkscape:cx="134.35387"
inkscape:cy="314.68683"
inkscape:document-units="mm"
inkscape:current-layer="layer1"
showgrid="false"
inkscape:object-paths="true"
inkscape:snap-intersection-paths="true"
inkscape:snap-global="true"
showguides="false"
inkscape:window-width="1680"
inkscape:window-height="1022"
inkscape:window-x="1366"
inkscape:window-y="0"
inkscape:window-maximized="1">
<sodipodi:guide
position="-12.831221,220.52593"
orientation="1,0"
id="guide1898"
inkscape:locked="false" />
</sodipodi:namedview>
<metadata
id="metadata5">
<rdf:RDF>
<cc:Work
rdf:about="">
<dc:format>image/svg+xml</dc:format>
<dc:type
rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
<dc:title></dc:title>
</cc:Work>
</rdf:RDF>
</metadata>
<g
inkscape:label="Calque 1"
inkscape:groupmode="layer"
id="layer1"
transform="translate(0,-149)">
<g
id="g2026"
transform="translate(0,-0.48389562)">
<g
transform="matrix(0.79531276,0,0,0.79531276,81.254333,81.589449)"
id="g1917">
<g
id="g842"
style="stroke-width:0.79374999;stroke-miterlimit:4;stroke-dasharray:none">
<path
id="path815"
style="opacity:1;vector-effect:none;fill:none;fill-opacity:1;fill-rule:nonzero;stroke:#000000;stroke-width:0.79374999;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
sodipodi:type="arc"
sodipodi:cx="56.852383"
sodipodi:cy="148.5"
sodipodi:rx="37.638245"
sodipodi:ry="37.638245"
sodipodi:start="0.036596929"
sodipodi:end="6.2452096"
sodipodi:open="true"
d="M 94.465425,149.87714 A 37.638245,37.638245 0 0 1 56.176671,186.13218 37.638245,37.638245 0 0 1 19.214147,148.52595 37.638245,37.638245 0 0 1 56.124785,110.86879 37.638245,37.638245 0 0 1 94.46349,147.071" />
<g
transform="translate(-48.147618)"
id="g836"
style="stroke-width:0.79374999;stroke-miterlimit:4;stroke-dasharray:none">
<path
style="fill:none;stroke:#000000;stroke-width:0.79374999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
d="m 103.97172,147.47172 2.05656,2.05656"
id="path817"
inkscape:connector-curvature="0" />
<path
style="fill:none;stroke:#000000;stroke-width:0.79374999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
d="m 106.02828,147.47172 -2.05656,2.05656"
id="path817-3"
inkscape:connector-curvature="0" />
</g>
</g>
<path
style="fill:none;stroke:#000000;stroke-width:0.79374999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1;marker-mid:url(#Arrow1Mstart);marker-end:url(#marker1344)"
d="m 79.169044,148.5 h 18.789241 20.552955 20.55295"
id="path844"
inkscape:connector-curvature="0"
sodipodi:nodetypes="cccc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.79374999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1;marker-mid:url(#marker1286);marker-end:url(#marker1286)"
d="m 84.350997,122.80051 h 18.237733 18.23773 18.23773"
id="path844-7"
inkscape:connector-curvature="0"
sodipodi:nodetypes="cccc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.79374999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
d="m 89.294491,129.41736 11.310069,-6.61685"
id="path890"
inkscape:connector-curvature="0"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:1.05833328;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1;filter:url(#filter986)"
d="m 84.350997,122.80051 4.955092,6.63659"
id="path892"
inkscape:connector-curvature="0" />
<path
style="fill:none;stroke:#000000;stroke-width:0.79374999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
d="M 94.41159,147.12593 H 79.169045 v 2.74815 H 94.41159"
id="path1864"
inkscape:connector-curvature="0" />
<text
xml:space="preserve"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:4.23333311px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.26458332"
x="96.537186"
y="155.70245"
id="text1881"><tspan
sodipodi:role="line"
id="tspan1879"
x="96.537186"
y="155.70245"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.26458332">Syrène</tspan></text>
<text
xml:space="preserve"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:4.23333311px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.26458332"
x="95.569389"
y="132.23354"
id="text1885"><tspan
sodipodi:role="line"
id="tspan1883"
x="95.569389"
y="132.23354"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.26458332">Alexandrie</tspan></text>
<path
style="fill:none;stroke:#000000;stroke-width:0.5291667;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
d="M 89.294424,129.41725 56.85238,148.5 H 94.6016"
id="path1900"
inkscape:connector-curvature="0" />
</g>
<g
id="g1989">
<flowRoot
xml:space="preserve"
id="flowRoot1919"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:13.33333397px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;text-align:justify;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none"
transform="matrix(0.26458333,0,0,0.26458333,0,155.27276)"><flowRegion
id="flowRegion1921"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:13.33333397px;font-family:sans-serif;-inkscape-font-specification:sans-serif;text-align:justify;text-anchor:start"><rect
id="rect1923"
width="251.69719"
height="494.91534"
x="42.676441"
y="52.425682"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:13.33333397px;font-family:sans-serif;-inkscape-font-specification:sans-serif;text-align:justify;text-anchor:start" /></flowRegion><flowPara
id="flowPara1925"> Vers l'an 200 avant Jésus- Christ, des voyageurs dirent à Eratosthène, géomètre de l'école d'Alexandrie, que le premier jour de l'été, à Syène ( Prés de l'actuel Assouan, en haute Égypte ), rayons du soleil à midi étaient verticaux : Ils pouvaient éclairer le fond d'un puits. Or ce même jour, le soleil n'était pas au Zénith à Alexandrie puisqu'un piquet de 1m de haut, planté verticalement avait une ombre de 12,3 cm.</flowPara><flowPara
id="flowPara1927" /><flowPara
id="flowPara1929">Eratosthène savait également que les caravanes des chameaux partant de Syène, en parcourant 100 stades par jour ( le stade équivaut à 160m ), mettaient 50 jours pour arriver à Alexandrie ( Ville située au nord de Syène ).Enfin, il supposa que le soleil était assez éloigné pour que ses rayons lumineux frappent la surface terrestre en faisceaux parallèles.A partir de toutes ces informations, Eratosthène réussit à déterminer la valeur du rayon de la Terre.</flowPara><flowPara
id="flowPara1931" /><flowPara
id="flowPara1933" /><flowPara
id="flowPara1935" /><flowPara
id="flowPara1937" /></flowRoot> <flowRoot
xml:space="preserve"
id="flowRoot1951"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:16px;line-height:1.25;font-family:Consolas, 'Liberation Mono', Menlo, Courier, monospace;-inkscape-font-specification:'Consolas, Liberation Mono, Menlo, Courier, monospace';text-align:justify;letter-spacing:0px;word-spacing:0px;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none"
transform="matrix(0.26458333,0,0,0.26458333,3.3872696,156.98428)"><flowRegion
id="flowRegion1953"
style="text-align:justify;text-anchor:start"><rect
id="rect1955"
width="384.98282"
height="147.2262"
x="343.83264"
y="341.73132"
style="text-align:justify;text-anchor:start" /></flowRegion><flowPara
id="flowPara1957"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:13.33333397px;font-family:sans-serif;-inkscape-font-specification:sans-serif;text-align:justify;text-anchor:start">1) Reporter les informations du texte sur le schéma.</flowPara><flowPara
id="flowPara1959"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:13.33333397px;font-family:sans-serif;-inkscape-font-specification:sans-serif;text-align:justify;text-anchor:start">2) Calculer l'angle que fait les rayons du soleil avec le piquet planté à Alexandrie.</flowPara><flowPara
id="flowPara1961"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:13.33333397px;font-family:sans-serif;-inkscape-font-specification:sans-serif;text-align:justify;text-anchor:start">3) Quel angle y a-t-il entre Alexandrie, le centre de la terre et Syrène?</flowPara><flowPara
id="flowPara1963"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:13.33333397px;font-family:sans-serif;-inkscape-font-specification:sans-serif;text-align:justify;text-anchor:start">4) Calculer la circonférence de la terre.</flowPara><flowPara
id="flowPara1965"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:13.33333397px;font-family:sans-serif;-inkscape-font-specification:sans-serif;text-align:justify;text-anchor:start">5) En déduire le rayon de la terre.</flowPara></flowRoot> </g>
</g>
<text
xml:space="preserve"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:4.23333311px;line-height:1.25;font-family:sans-serif;-inkscape-font-specification:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.26458332"
x="75.414207"
y="161.02531"
id="text1969"><tspan
sodipodi:role="line"
id="tspan1967"
x="75.414207"
y="161.02531"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:sans-serif;stroke-width:0.26458332">Calculer la rayon de la terre</tspan></text>
</g>
</svg>