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La Clotoide Grupo 39 - Historial de revisiones
2026-04-30T18:07:11Z
Historial de revisiones para esta página en el wiki
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https://mat.caminos.upm.es/w/index.php?title=La_Clotoide_Grupo_39&diff=103814&oldid=prev
Luis García García: /* Circunferencia osculatriz */
2025-12-08T10:37:44Z
<p><span dir="auto"><span class="autocomment">Circunferencia osculatriz</span></span></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Revisión del 10:37 8 dic 2025</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l330" >Línea 330:</td>
<td colspan="2" class="diff-lineno">Línea 330:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><center><math>R(1.5)=\frac{1}{1.5}</math> </center><br/><br/></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><center><math>R(1.5)=\frac{1}{1.5}</math> </center><br/><br/></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><center><math>Q(1.5) = \left\{\begin{matrix}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><center><math>Q(1.5) = \left\{\begin{matrix}</div></td></tr>
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<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Q_x(1.5)=\int_{0}^{1.5}cos(\frac{<del class="diffchange diffchange-inline">t</del>^2}{<del class="diffchange diffchange-inline">s</del>})ds - sin(\frac{1}{2})\\\\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Q_x(1.5)=\int_{0}^{1.5}<ins class="diffchange diffchange-inline">\</ins>cos<ins class="diffchange diffchange-inline">\left</ins>(\frac{<ins class="diffchange diffchange-inline">s</ins>^2}{<ins class="diffchange diffchange-inline">2</ins>}<ins class="diffchange diffchange-inline">\right</ins>)<ins class="diffchange diffchange-inline">\,</ins>ds-<ins class="diffchange diffchange-inline">\frac{1}{1.5}\</ins>sin<ins class="diffchange diffchange-inline">\left</ins>(\frac{<ins class="diffchange diffchange-inline">(</ins>1<ins class="diffchange diffchange-inline">.5)^2</ins>}{2}<ins class="diffchange diffchange-inline">\right</ins>)\\\\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline"> </del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Q_y(1.5)=\int_{0}^{1.5}<ins class="diffchange diffchange-inline">\</ins>sin<ins class="diffchange diffchange-inline">\left</ins>(\frac{<ins class="diffchange diffchange-inline">s</ins>^2}{2}<ins class="diffchange diffchange-inline">\right</ins>)<ins class="diffchange diffchange-inline">\,</ins>ds+<ins class="diffchange diffchange-inline">\frac{1}{1.5}\</ins>cos<ins class="diffchange diffchange-inline">\left</ins>(\frac{<ins class="diffchange diffchange-inline">(</ins>1<ins class="diffchange diffchange-inline">.5)^2</ins>}{2}<ins class="diffchange diffchange-inline">\right</ins>)</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Q_y(1.5)=\int_{0}^{1.5}sin(\frac{<del class="diffchange diffchange-inline">t</del>^2}{2})ds+cos(\frac{1}{2})</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\end{matrix}\right.</math></center></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\end{matrix}\right.</math></center></div></td></tr>
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Luis García García
https://mat.caminos.upm.es/w/index.php?title=La_Clotoide_Grupo_39&diff=99135&oldid=prev
David: /* Poster */
2025-12-04T15:47:16Z
<p><span dir="auto"><span class="autocomment">Poster</span></span></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Revisión del 15:47 4 dic 2025</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l595" >Línea 595:</td>
<td colspan="2" class="diff-lineno">Línea 595:</td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>=Poster=</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>=Poster=</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[File:<del class="diffchange diffchange-inline">la clotoide poster</del>.jpg|650px|miniaturadeimagen|right|<del class="diffchange diffchange-inline">'''Dibujo de la curva''' </del><br />]]</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[File:<ins class="diffchange diffchange-inline">LaClotoideposter33</ins>.jpg|650px|miniaturadeimagen|right| <br />]]</div></td></tr>
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David
https://mat.caminos.upm.es/w/index.php?title=La_Clotoide_Grupo_39&diff=99109&oldid=prev
David en 15:40 4 dic 2025
2025-12-04T15:40:20Z
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revisión del 15:40 4 dic 2025</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l595" >Línea 595:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>=Poster=</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>=Poster=</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[File:la clotoide poster.jpg|650px|miniaturadeimagen|right|'''Dibujo de la curva''' <br />]]</ins></div></td></tr>
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David
https://mat.caminos.upm.es/w/index.php?title=La_Clotoide_Grupo_39&diff=99070&oldid=prev
David en 15:28 4 dic 2025
2025-12-04T15:28:56Z
<p></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revisión del 15:28 4 dic 2025</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l594" >Línea 594:</td>
<td colspan="2" class="diff-lineno">Línea 594:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>fprintf('Masa aproximada de la superficie: %.4f\n', M_total);</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>fprintf('Masa aproximada de la superficie: %.4f\n', M_total);</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">=Poster=</ins></div></td></tr>
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David
https://mat.caminos.upm.es/w/index.php?title=La_Clotoide_Grupo_39&diff=99013&oldid=prev
Luis García García: /* Masa de la superficie reglada */
2025-12-04T15:10:05Z
<p><span dir="auto"><span class="autocomment">Masa de la superficie reglada</span></span></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revisión del 15:10 4 dic 2025</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l555" >Línea 555:</td>
<td colspan="2" class="diff-lineno">Línea 555:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Utilizando la siguiente expresión y resolviendo la integral mediante el método del rectángulo obtenemos que la masa es 2406. Este resultando es el mismo que obtenemos si realizamos el mismo procedimiento con Matlab.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Utilizando la siguiente expresión y resolviendo la integral mediante el método del rectángulo obtenemos que la masa es 2406. Este resultando es el mismo que obtenemos si realizamos el mismo procedimiento con Matlab.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><br/></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><br/></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"><center></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\text{MASA} = \int_{2\pi}^{6\pi} \int_{0}^{1} \frac{(u+v)^2}{v} \, \sqrt{1+(u+v)^2} \, du \, dv= 2406</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\text{MASA} = \int_{2\pi}^{6\pi} \int_{0}^{1} \frac{(u+v)^2}{v} \, \sqrt{1+(u+v)^2} \, du \, dv= 2406</div></td></tr>
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Luis García García
https://mat.caminos.upm.es/w/index.php?title=La_Clotoide_Grupo_39&diff=99003&oldid=prev
Luis García García: /* Masa de la superficie reglada */
2025-12-04T15:07:15Z
<p><span dir="auto"><span class="autocomment">Masa de la superficie reglada</span></span></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Revisión del 15:07 4 dic 2025</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l550" >Línea 550:</td>
<td colspan="2" class="diff-lineno">Línea 550:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>La función evaluada según el vector <math>\vec{{r}}(u,v)</math> nos da  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>La función evaluada según el vector <math>\vec{{r}}(u,v)</math> nos da  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><center></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><center></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math>\displaystyle f\big(\vec{r}(u,v)\big)=\frac{\big(\cos v(u+v)\big)^{2}+\big(\sin v(u+v)\big)^{2}}{v}<del class="diffchange diffchange-inline">=\displaystyle f\big(\vec{r}(u,v)\big)</del>=\frac{(u+v)^{2}}{v}</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><math>\displaystyle f\big(\vec{r}(u,v)\big)=\frac{\big(\cos v(u+v)\big)^{2}+\big(\sin v(u+v)\big)^{2}}{v}=\frac{(u+v)^{2}}{v}</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><br/></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><br/></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><br/></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><br/></div></td></tr>
</table>
Luis García García
https://mat.caminos.upm.es/w/index.php?title=La_Clotoide_Grupo_39&diff=98999&oldid=prev
Luis García García: /* Masa de la superficie reglada */
2025-12-04T15:06:13Z
<p><span dir="auto"><span class="autocomment">Masa de la superficie reglada</span></span></p>
<table class='diff diff-contentalign-left'>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Revisión del 15:06 4 dic 2025</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l550" >Línea 550:</td>
<td colspan="2" class="diff-lineno">Línea 550:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>La función evaluada según el vector <math>\vec{{r}}(u,v)</math> nos da  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>La función evaluada según el vector <math>\vec{{r}}(u,v)</math> nos da  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><center></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><center></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math>\displaystyle f\big(\vec{r}(u,v)\big)=\frac{\big(\cos v<del class="diffchange diffchange-inline">,</del>(u+v)\big)^{2}+\big(\sin v<del class="diffchange diffchange-inline">,</del>(u+v)\big)^{2}}{v}=\displaystyle f\big(\vec{r}(u,v)\big)=\frac{(u+v)^{2}}{v}</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><math>\displaystyle f\big(\vec{r}(u,v)\big)=\frac{\big(\cos v(u+v)\big)^{2}+\big(\sin v(u+v)\big)^{2}}{v}=\displaystyle f\big(\vec{r}(u,v)\big)=\frac{(u+v)^{2}}{v}</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><br/></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><br/></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><br/></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><br/></div></td></tr>
</table>
Luis García García
https://mat.caminos.upm.es/w/index.php?title=La_Clotoide_Grupo_39&diff=98997&oldid=prev
Luis García García: /* Masa de la superficie reglada */
2025-12-04T15:05:30Z
<p><span dir="auto"><span class="autocomment">Masa de la superficie reglada</span></span></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Revisión del 15:05 4 dic 2025</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l550" >Línea 550:</td>
<td colspan="2" class="diff-lineno">Línea 550:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>La función evaluada según el vector <math>\vec{{r}}(u,v)</math> nos da  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>La función evaluada según el vector <math>\vec{{r}}(u,v)</math> nos da  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><center></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><center></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math>f(\vec{r}(u,v))=<del class="diffchange diffchange-inline">100-</del>(<del class="diffchange diffchange-inline">v</del>\<del class="diffchange diffchange-inline">cdot cosv+</del>u\<del class="diffchange diffchange-inline">cdot cosv</del>)^{2}<del class="diffchange diffchange-inline">-</del>(<del class="diffchange diffchange-inline">v</del>\<del class="diffchange diffchange-inline">cdot sinv+</del>u\<del class="diffchange diffchange-inline">cdot sinv</del>)^{2}<del class="diffchange diffchange-inline">=100-</del>v<del class="diffchange diffchange-inline">^</del>{<del class="diffchange diffchange-inline">2</del>}<del class="diffchange diffchange-inline">-</del>u^{2}<del class="diffchange diffchange-inline">-2uv</del></math<del class="diffchange diffchange-inline">></center</del>></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><math><ins class="diffchange diffchange-inline">\displaystyle </ins>f<ins class="diffchange diffchange-inline">\big</ins>(\vec{r}(u,v)<ins class="diffchange diffchange-inline">\big</ins>)=<ins class="diffchange diffchange-inline">\frac{\big</ins>(\<ins class="diffchange diffchange-inline">cos v,(</ins>u<ins class="diffchange diffchange-inline">+v)</ins>\<ins class="diffchange diffchange-inline">big</ins>)^{2}<ins class="diffchange diffchange-inline">+\big</ins>(\<ins class="diffchange diffchange-inline">sin v,(</ins>u<ins class="diffchange diffchange-inline">+v)</ins>\<ins class="diffchange diffchange-inline">big</ins>)^{2}<ins class="diffchange diffchange-inline">}{</ins>v<ins class="diffchange diffchange-inline">}=\displaystyle f\big(\vec</ins>{<ins class="diffchange diffchange-inline">r</ins>}<ins class="diffchange diffchange-inline">(</ins>u<ins class="diffchange diffchange-inline">,v)\big)=\frac{(u+v)</ins>^{2}<ins class="diffchange diffchange-inline">}{v}</ins></math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><br/></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><br/></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><br/></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><br/></div></td></tr>
</table>
Luis García García
https://mat.caminos.upm.es/w/index.php?title=La_Clotoide_Grupo_39&diff=97449&oldid=prev
Laura ortiz en 18:23 3 dic 2025
2025-12-03T18:23:50Z
<p></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Revisión del 18:23 3 dic 2025</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l595" >Línea 595:</td>
<td colspan="2" class="diff-lineno">Línea 595:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>fprintf('Masa aproximada de la superficie: %.4f\n', M_total);</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>fprintf('Masa aproximada de la superficie: %.4f\n', M_total);</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">[[Categoría:Teoría de Campos]]</del></div></td><td colspan="2"> </td></tr>
</table>
Laura ortiz
https://mat.caminos.upm.es/w/index.php?title=La_Clotoide_Grupo_39&diff=97445&oldid=prev
Laura ortiz: /* Masa de la superficie reglada */
2025-12-03T18:22:46Z
<p><span dir="auto"><span class="autocomment">Masa de la superficie reglada</span></span></p>
<table class='diff diff-contentalign-left'>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Revisión del 18:22 3 dic 2025</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l596" >Línea 596:</td>
<td colspan="2" class="diff-lineno">Línea 596:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Categoría:Teoría de Campos]]</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Categoría:Teoría de Campos]]</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">[[Categoría:TC24/25]]</del></div></td><td colspan="2"> </td></tr>
</table>
Laura ortiz