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2024-03-29T08:42:30Z
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Mozo: /* Explicit megadású görbe, kisérő triéder */
2009-10-19T20:16:41Z
<p><span class="autocomment">Explicit megadású görbe, kisérő triéder</span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr valign='top'>
<td colspan='2' style="background-color: white; color:black;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black;">A lap 2009. október 19., 20:16-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">80. sor:</td>
<td colspan="2" class="diff-lineno">80. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Az érintő párhuzamosságának feltétele, hogy a sík normálvektorára '''r'''(t) deriváltja merőleges legyen  </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Az érintő párhuzamosságának feltétele, hogy a sík normálvektorára '''r'''(t) deriváltja merőleges legyen  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:<math>1\cdot 2t+1\cdot 2+4\cdot(-1)=0\,</math>, <math>t=<del class="diffchange diffchange-inline">0</del>\,</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:<math>1\cdot 2t+1\cdot 2+4\cdot(-1)=0\,</math>, <math>t=<ins class="diffchange diffchange-inline">1</ins>\,</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Ívhossz===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Ívhossz===</div></td></tr>
</table>
Mozo
http://wiki.math.bme.hu/index.php?title=Matematika_A3a_2009/1._gyakorlat&diff=5643&oldid=prev
Mozo: /* Explicit megadású görbe, kisérő triéder */
2009-10-19T20:16:09Z
<p><span class="autocomment">Explicit megadású görbe, kisérő triéder</span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr valign='top'>
<td colspan='2' style="background-color: white; color:black;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black;">A lap 2009. október 19., 20:16-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">80. sor:</td>
<td colspan="2" class="diff-lineno">80. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Az érintő párhuzamosságának feltétele, hogy a sík normálvektorára '''r'''(t) deriváltja merőleges legyen  </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Az érintő párhuzamosságának feltétele, hogy a sík normálvektorára '''r'''(t) deriváltja merőleges legyen  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:<math>1\cdot 2t+<del class="diffchange diffchange-inline">2</del>\cdot 2+4\cdot(-1)=0\,</math>, <math>t=0\,</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:<math>1\cdot 2t+<ins class="diffchange diffchange-inline">1</ins>\cdot 2+4\cdot(-1)=0\,</math>, <math>t=0\,</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Ívhossz===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Ívhossz===</div></td></tr>
</table>
Mozo
http://wiki.math.bme.hu/index.php?title=Matematika_A3a_2009/1._gyakorlat&diff=5642&oldid=prev
Mozo: /* Explicit megadású görbe, kisérő triéder */
2009-10-19T20:15:04Z
<p><span class="autocomment">Explicit megadású görbe, kisérő triéder</span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr valign='top'>
<td colspan='2' style="background-color: white; color:black;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black;">A lap 2009. október 19., 20:15-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">76. sor:</td>
<td colspan="2" class="diff-lineno">76. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>\dot{\mathbf{r}}(t)=\begin{bmatrix}2t\\1\\-1\end{bmatrix}</math>, <math>\ddot{\mathbf{r}}(t)=\begin{bmatrix}2\\0\\0\end{bmatrix}</math>, <math>\mathbf{b}=\begin{bmatrix}2t\\1\\-1\end{bmatrix}\times\begin{bmatrix}2\\0\\0\end{bmatrix}=\begin{bmatrix}0\\2\\2\end{bmatrix}</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>\dot{\mathbf{r}}(t)=\begin{bmatrix}2t\\1\\-1\end{bmatrix}</math>, <math>\ddot{\mathbf{r}}(t)=\begin{bmatrix}2\\0\\0\end{bmatrix}</math>, <math>\mathbf{b}=\begin{bmatrix}2t\\1\\-1\end{bmatrix}\times\begin{bmatrix}2\\0\\0\end{bmatrix}=\begin{bmatrix}0\\2\\2\end{bmatrix}</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>végül a főnormális:  </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>végül a főnormális:  </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:<math>\mathbf{n}=\begin{bmatrix}0\\2\\2\end{bmatrix}\times\begin{bmatrix}2t\\1\\-1\end{bmatrix}=\begin{bmatrix}4\\-4t\\<del class="diffchange diffchange-inline">-</del>4t\end{bmatrix}</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:<math>\mathbf{n}=\begin{bmatrix}0\\2\\2\end{bmatrix}\times\begin{bmatrix}2t\\1\\-1\end{bmatrix}=\begin{bmatrix}4\\-4t\\4t\end{bmatrix}</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:<math>2t+2<del class="diffchange diffchange-inline">-</del>4=0\,</math>, <math>t=<del class="diffchange diffchange-inline">1</del>\,</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">Az érintő párhuzamosságának feltétele, hogy a sík normálvektorára '''r'''(t) deriváltja merőleges legyen </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:<math><ins class="diffchange diffchange-inline">1\cdot </ins>2t+2<ins class="diffchange diffchange-inline">\cdot 2+</ins>4<ins class="diffchange diffchange-inline">\cdot(-1)</ins>=0\,</math>, <math>t=<ins class="diffchange diffchange-inline">0</ins>\,</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Ívhossz===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Ívhossz===</div></td></tr>
</table>
Mozo
http://wiki.math.bme.hu/index.php?title=Matematika_A3a_2009/1._gyakorlat&diff=5641&oldid=prev
Mozo: /* Explicit megadású görbe, kisérő triéder */
2009-10-19T20:09:56Z
<p><span class="autocomment">Explicit megadású görbe, kisérő triéder</span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr valign='top'>
<td colspan='2' style="background-color: white; color:black;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black;">A lap 2009. október 19., 20:09-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">76. sor:</td>
<td colspan="2" class="diff-lineno">76. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>\dot{\mathbf{r}}(t)=\begin{bmatrix}2t\\1\\-1\end{bmatrix}</math>, <math>\ddot{\mathbf{r}}(t)=\begin{bmatrix}2\\0\\0\end{bmatrix}</math>, <math>\mathbf{b}=\begin{bmatrix}2t\\1\\-1\end{bmatrix}\times\begin{bmatrix}2\\0\\0\end{bmatrix}=\begin{bmatrix}0\\2\\2\end{bmatrix}</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>\dot{\mathbf{r}}(t)=\begin{bmatrix}2t\\1\\-1\end{bmatrix}</math>, <math>\ddot{\mathbf{r}}(t)=\begin{bmatrix}2\\0\\0\end{bmatrix}</math>, <math>\mathbf{b}=\begin{bmatrix}2t\\1\\-1\end{bmatrix}\times\begin{bmatrix}2\\0\\0\end{bmatrix}=\begin{bmatrix}0\\2\\2\end{bmatrix}</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>végül a főnormális:  </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>végül a főnormális:  </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:<math>\mathbf{n}=\begin{bmatrix}0\\2\\2\end{bmatrix}\times\begin{bmatrix}2t\\1\\-1\end{bmatrix}=\begin{bmatrix}4\\<del class="diffchange diffchange-inline">2t</del>\\-4t\end{bmatrix}</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:<math>\mathbf{n}=\begin{bmatrix}0\\2\\2\end{bmatrix}\times\begin{bmatrix}2t\\1\\-1\end{bmatrix}=\begin{bmatrix}4\\<ins class="diffchange diffchange-inline">-4t</ins>\\-4t\end{bmatrix}</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>2t+2-4=0\,</math>, <math>t=1\,</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>2t+2-4=0\,</math>, <math>t=1\,</math></div></td></tr>
</table>
Mozo
http://wiki.math.bme.hu/index.php?title=Matematika_A3a_2009/1._gyakorlat&diff=5396&oldid=prev
Mozo: /* Házi feladatok */
2009-09-10T18:58:40Z
<p><span class="autocomment">Házi feladatok</span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr valign='top'>
<td colspan='2' style="background-color: white; color:black;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black;">A lap 2009. szeptember 10., 18:58-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">136. sor:</td>
<td colspan="2" class="diff-lineno">136. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>'''4.''' Határozzuk meg a  </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>'''4.''' Határozzuk meg a  </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:<math>\mathbf{r}(t)=e^t\cos t \mathbf{i}+e^t\sin t \mathbf{j}+e^t\mathbf{k}\,</math> <math>t\in[0,2]</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:<math>\mathbf{r}(t)=e^t\cos t \mathbf{i}+e^t\sin t \mathbf{j}+e^t\mathbf{k}\,</math><ins class="diffchange diffchange-inline">, </ins><math>t\in[0,2]</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>györbeszakasz ívhosszát!</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>györbeszakasz ívhosszát!</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
</table>
Mozo
http://wiki.math.bme.hu/index.php?title=Matematika_A3a_2009/1._gyakorlat&diff=5395&oldid=prev
Mozo: /* Felületek */
2009-09-10T15:04:14Z
<p><span class="autocomment">Felületek</span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr valign='top'>
<td colspan='2' style="background-color: white; color:black;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black;">A lap 2009. szeptember 10., 15:04-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">109. sor:</td>
<td colspan="2" class="diff-lineno">109. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>''Mo.''</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>''Mo.''</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:<math>\mathbf{r}(r,\varphi)=\begin{bmatrix}r\cdot \cos\varphi\\r\sin\varphi\\ r\end{bmatrix}</math>  </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:<math>\mathbf{r}(r,\varphi)=\begin{bmatrix}r\cdot \cos\varphi\\r\sin\varphi\\ r\end{bmatrix}</math><ins class="diffchange diffchange-inline">, </ins><math>\mathbf{r}(r,\varphi)=\begin{bmatrix}r\cdot \cos\varphi\\r\sin\varphi\\ r^2\end{bmatrix}</math><ins class="diffchange diffchange-inline">, </ins><math>\mathbf{r}(r,\varphi)=\begin{bmatrix}r\cdot \cos\varphi\\\frac{r}{2}\sin\varphi\\ r^2\end{bmatrix}</math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">:</del><math>\mathbf{r}(r,\varphi)=\begin{bmatrix}r\cdot \cos\varphi\\r\sin\varphi\\ r^2\end{bmatrix}</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">:</del><math>\mathbf{r}(r,\varphi)=\begin{bmatrix}r\cdot \cos\varphi\\\frac{r}{2}\sin\varphi\\ r^2\end{bmatrix}</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>'''7.''' Paraméterezzük a</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>'''7.''' Paraméterezzük a</div></td></tr>
</table>
Mozo
http://wiki.math.bme.hu/index.php?title=Matematika_A3a_2009/1._gyakorlat&diff=5394&oldid=prev
Mozo: /* Felületek */
2009-09-10T15:03:47Z
<p><span class="autocomment">Felületek</span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr valign='top'>
<td colspan='2' style="background-color: white; color:black;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black;">A lap 2009. szeptember 10., 15:03-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">103. sor:</td>
<td colspan="2" class="diff-lineno">103. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Felületek==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Felületek==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Paraméterezzük az alábbi implicit megadású felületeket:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">'''6.''' </ins>Paraméterezzük az alábbi implicit megadású felületeket:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>x^2+y^2=z^2\,</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>x^2+y^2=z^2\,</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>x^2+y^2=z\,</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>x^2+y^2=z\,</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>x^2+4y^2=z\,</math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:<math>x^2+4y^2=z\,</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Paraméterezzük a</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">''Mo.''</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:<math>\mathbf{r}(r,\varphi)=\begin{bmatrix}r\cdot \cos\varphi\\r\sin\varphi\\ r\end{bmatrix}</math> </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:<math>\mathbf{r}(r,\varphi)=\begin{bmatrix}r\cdot \cos\varphi\\r\sin\varphi\\ r^2\end{bmatrix}</math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:<math>\mathbf{r}(r,\varphi)=\begin{bmatrix}r\cdot \cos\varphi\\\frac{r}{2}\sin\varphi\\ r^2\end{bmatrix}</math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">'''7.''' </ins>Paraméterezzük a</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:<math>\mathbf{r}(t)=\begin{bmatrix}t\\t^2\\ t^3 \end{bmatrix}</math> </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">görbe érintői által kirajzolt felületet!</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">''Mo.'' </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:<math>\mathbf{r}_0(t)=\mathbf{r}(t)=\begin{bmatrix}t\\t^2\\ t^3 \end{bmatrix}</math>, <math>\mathbf{v}(t)=\dot\mathbf{r}(t)=\begin{bmatrix}1\\2t\\ 3t^2 \end{bmatrix}</math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:<math>\mathbf{r}(t,s)=\mathbf{r}_0(t)+s\mathbf{v}(t)=\begin{bmatrix}t+s\\t^2+2ts\\ t^3+3t^2s \end{bmatrix}</math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Házi feladatok==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Házi feladatok==</div></td></tr>
</table>
Mozo
http://wiki.math.bme.hu/index.php?title=Matematika_A3a_2009/1._gyakorlat&diff=5393&oldid=prev
Mozo: /* Felületek */
2009-09-10T14:53:12Z
<p><span class="autocomment">Felületek</span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr valign='top'>
<td colspan='2' style="background-color: white; color:black;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black;">A lap 2009. szeptember 10., 14:53-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">103. sor:</td>
<td colspan="2" class="diff-lineno">103. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Felületek==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Felületek==</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Paraméterezzük az alábbi implicit megadású felületeket:</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">:<math>x^2+y^2=z^2\,</math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">:<math>x^2+y^2=z\,</math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">:<math>x^2+4y^2=z\,</math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Paraméterezzük a</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Házi feladatok==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Házi feladatok==</div></td></tr>
</table>
Mozo
http://wiki.math.bme.hu/index.php?title=Matematika_A3a_2009/1._gyakorlat&diff=5392&oldid=prev
Mozo: /* Ívhossz */
2009-09-10T14:49:33Z
<p><span class="autocomment">Ívhossz</span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr valign='top'>
<td colspan='2' style="background-color: white; color:black;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black;">A lap 2009. szeptember 10., 14:49-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">98. sor:</td>
<td colspan="2" class="diff-lineno">98. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>(Szimmetriákkal) A '''<del class="diffchange diffchange-inline">d</del>''<del class="diffchange diffchange-inline">r </del>elemi érintővektor mindenhol 1 iránytangensű szögben hajlik az [xy] síkhoz, erre eső vetülete pedig mindig ugyanakkora. A ívhossz tehát egy derékszögű háromszög átfogója.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>(Szimmetriákkal) A <ins class="diffchange diffchange-inline">d</ins>'''<ins class="diffchange diffchange-inline">r'</ins>'' elemi érintővektor mindenhol 1 iránytangensű szögben hajlik az [xy] síkhoz, erre eső vetülete pedig mindig ugyanakkora. A ívhossz tehát egy derékszögű háromszög átfogója<ins class="diffchange diffchange-inline">.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">Ívhossz paraméterezésben a görbület az <math> |\mathbf{r}''(s)|</math> mennyiség. t:0->2&pi;, akkor s:0->10&pi;, azaz t=s/5</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Ívhossz paraméterezésben a görbület az |\mathbf{r}''(s)| mennyiség. t:0->2&pi;, akkor s:0->10&pi;, azaz t=s/5.</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Felületek==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Felületek==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
</table>
Mozo
http://wiki.math.bme.hu/index.php?title=Matematika_A3a_2009/1._gyakorlat&diff=5391&oldid=prev
Mozo: /* Ívhossz */
2009-09-10T14:48:45Z
<p><span class="autocomment">Ívhossz</span></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr valign='top'>
<td colspan='2' style="background-color: white; color:black;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black;">A lap 2009. szeptember 10., 14:48-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">101. sor:</td>
<td colspan="2" class="diff-lineno">101. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Ívhossz paraméterezésben a görbület az |\mathbf{r}''(s)| mennyiség. t:0->2&pi;, akkor s:0->10&pi;, azaz t=s/5.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Ívhossz paraméterezésben a görbület az |\mathbf{r}''(s)| mennyiség. t:0->2&pi;, akkor s:0->10&pi;, azaz t=s/5.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">==Felületek==</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Házi feladatok==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Házi feladatok==</div></td></tr>
</table>
Mozo