http://www.multimediaexpo.cz/mmecz/index.php?feed=atom&target=Br%C3%A1na_%28rozcestn%C3%ADk%29&title=Speci%C3%A1ln%C3%AD%3ASouvisej%C3%ADc%C3%AD_zm%C4%9Bny%2FBr%C3%A1na_%28rozcestn%C3%ADk%29
Multimediaexpo.cz - Související změny pro stránku "Brána (rozcestník)" [cs]
2026-07-11T23:37:58Z
Související změny
MediaWiki 1.16.5
http://www.multimediaexpo.cz/mmecz/index.php?title=Plocha&diff=3068341&oldid=prev
Plocha
2026-07-09T11:37:00Z
<p><span class="autocomment">Vlastnosti: </span> Partial</p>
<table style="background-color: white; color:black;">
<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;">← Starší verze</td>
<td colspan='2' style="background-color: white; color:black;">Verze z 9. 7. 2026, 11:37</td>
</tr><tr><td colspan='4' align='center' class='diff-multi'>(Není zobrazena jedna mezilehlá verze.)</td></tr><tr><td colspan="2" class="diff-lineno">Řádka 39:</td>
<td colspan="2" class="diff-lineno">Řádka 39:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=== Weingartenovy rovnice plochy ===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=== Weingartenovy rovnice plochy ===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>'''Weingartenovy rovnice plochy''' určují vztahy mezi [[derivace]]mi [[vektor]]ů <big>\(\mathbf{n}\)</big> a <big>\(\mathbf{r}\)</big>.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>'''Weingartenovy rovnice plochy''' určují vztahy mezi [[derivace]]mi [[vektor]]ů <big>\(\mathbf{n}\)</big> a <big>\(\mathbf{r}\)</big>.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:<big>\(\frac{\<del class="diffchange diffchange-inline">part</del>\mathbf{n}}{\<del class="diffchange diffchange-inline">part </del>u} = \frac{FM-GL}{EG-F^2}\frac{\<del class="diffchange diffchange-inline">part</del>\mathbf{r}}{\<del class="diffchange diffchange-inline">part </del>u} + \frac{FL-EM}{EG-F^2}\frac{\<del class="diffchange diffchange-inline">part</del>\mathbf{r}}{\<del class="diffchange diffchange-inline">part </del>v}\)</big></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:<big>\(\frac{\<ins class="diffchange diffchange-inline">partial</ins>\mathbf{n}}{\<ins class="diffchange diffchange-inline">partial </ins>u} = \frac{FM-GL}{EG-F^2}\frac{\<ins class="diffchange diffchange-inline">partial</ins>\mathbf{r}}{\<ins class="diffchange diffchange-inline">partial </ins>u} + \frac{FL-EM}{EG-F^2}\frac{\<ins class="diffchange diffchange-inline">partial</ins>\mathbf{r}}{\<ins class="diffchange diffchange-inline">partial </ins>v}\)</big></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:<big>\(\frac{\<del class="diffchange diffchange-inline">part</del>\mathbf{n}}{\<del class="diffchange diffchange-inline">part </del>v} = \frac{FN-GM}{EG-F^2}\frac{\<del class="diffchange diffchange-inline">part</del>\mathbf{r}}{\<del class="diffchange diffchange-inline">part </del>u} + \frac{FM-EN}{EG-F^2}\frac{\<del class="diffchange diffchange-inline">part</del>\mathbf{r}}{\<del class="diffchange diffchange-inline">part </del>v}\)</big></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:<big>\(\frac{\<ins class="diffchange diffchange-inline">partial</ins>\mathbf{n}}{\<ins class="diffchange diffchange-inline">partial </ins>v} = \frac{FN-GM}{EG-F^2}\frac{\<ins class="diffchange diffchange-inline">partial</ins>\mathbf{r}}{\<ins class="diffchange diffchange-inline">partial </ins>u} + \frac{FM-EN}{EG-F^2}\frac{\<ins class="diffchange diffchange-inline">partial</ins>\mathbf{r}}{\<ins class="diffchange diffchange-inline">partial </ins>v}\)</big></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:</div></td><td class='diff-marker'> </td><td style="background: #eee; 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>:<big>\(\frac{\<del class="diffchange diffchange-inline">part</del>\mathbf{r}}{\<del class="diffchange diffchange-inline">part </del>u} = \frac{MF-NE}{LN-M^2}\frac{\<del class="diffchange diffchange-inline">part</del>\mathbf{n}}{\<del class="diffchange diffchange-inline">part </del>u} + \frac{ME-LF}{LN-M^2}\frac{\<del class="diffchange diffchange-inline">part</del>\mathbf{n}}{\<del class="diffchange diffchange-inline">part </del>v}\)</big></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:<big>\(\frac{\<ins class="diffchange diffchange-inline">partial</ins>\mathbf{r}}{\<ins class="diffchange diffchange-inline">partial </ins>u} = \frac{MF-NE}{LN-M^2}\frac{\<ins class="diffchange diffchange-inline">partial</ins>\mathbf{n}}{\<ins class="diffchange diffchange-inline">partial </ins>u} + \frac{ME-LF}{LN-M^2}\frac{\<ins class="diffchange diffchange-inline">partial</ins>\mathbf{n}}{\<ins class="diffchange diffchange-inline">partial </ins>v}\)</big></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:<big>\(\frac{\<del class="diffchange diffchange-inline">part</del>\mathbf{r}}{\<del class="diffchange diffchange-inline">part </del>v} = \frac{MG-NF}{LN-M^2}\frac{\<del class="diffchange diffchange-inline">part</del>\mathbf{n}}{\<del class="diffchange diffchange-inline">part </del>u} + \frac{MF-LG}{LN-M^2}\frac{\<del class="diffchange diffchange-inline">part</del>\mathbf{n}}{\<del class="diffchange diffchange-inline">part </del>v}\)</big></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:<big>\(\frac{\<ins class="diffchange diffchange-inline">partial</ins>\mathbf{r}}{\<ins class="diffchange diffchange-inline">partial </ins>v} = \frac{MG-NF}{LN-M^2}\frac{\<ins class="diffchange diffchange-inline">partial</ins>\mathbf{n}}{\<ins class="diffchange diffchange-inline">partial </ins>u} + \frac{MF-LG}{LN-M^2}\frac{\<ins class="diffchange diffchange-inline">partial</ins>\mathbf{n}}{\<ins class="diffchange diffchange-inline">partial </ins>v}\)</big></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>kde <big>\(E, F, G\)</big> jsou [[základní veličina plochy|základní veličiny plochy prvního řádu]] a <big>\(L, M, N\)</big> jsou [[základní veličina plochy|základní veličiny plochy druhého řádu]].</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>kde <big>\(E, F, G\)</big> jsou [[základní veličina plochy|základní veličiny plochy prvního řádu]] a <big>\(L, M, N\)</big> jsou [[základní veličina plochy|základní veličiny plochy druhého řádu]].</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 colspan="2" class="diff-lineno">Řádka 60:</td>
<td colspan="2" class="diff-lineno">Řádka 60:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Vlastnosti ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Vlastnosti ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* Zavedeme [[matice|matici]] </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>* Zavedeme [[matice|matici]] </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:<big>\(\begin{pmatrix} \frac{\<del class="diffchange diffchange-inline">part </del>x}{\<del class="diffchange diffchange-inline">part </del>u} & \frac{\<del class="diffchange diffchange-inline">part </del>y}{\<del class="diffchange diffchange-inline">part </del>u} & \frac{\<del class="diffchange diffchange-inline">part </del>z}{\<del class="diffchange diffchange-inline">part </del>u} \\ \frac{\<del class="diffchange diffchange-inline">part </del>x}{\<del class="diffchange diffchange-inline">part </del>v} & \frac{\<del class="diffchange diffchange-inline">part </del>y}{\<del class="diffchange diffchange-inline">part </del>v} & \frac{\<del class="diffchange diffchange-inline">part </del>z}{\<del class="diffchange diffchange-inline">part </del>v} \end{pmatrix}\)</big></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:<big>\(\begin{pmatrix} \frac{\<ins class="diffchange diffchange-inline">partial </ins>x}{\<ins class="diffchange diffchange-inline">partial </ins>u} & \frac{\<ins class="diffchange diffchange-inline">partial </ins>y}{\<ins class="diffchange diffchange-inline">partial </ins>u} & \frac{\<ins class="diffchange diffchange-inline">partial </ins>z}{\<ins class="diffchange diffchange-inline">partial </ins>u} \\ \frac{\<ins class="diffchange diffchange-inline">partial </ins>x}{\<ins class="diffchange diffchange-inline">partial </ins>v} & \frac{\<ins class="diffchange diffchange-inline">partial </ins>y}{\<ins class="diffchange diffchange-inline">partial </ins>v} & \frac{\<ins class="diffchange diffchange-inline">partial </ins>z}{\<ins class="diffchange diffchange-inline">partial </ins>v} \end{pmatrix}\)</big></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Body plochy, v nichž má tato matice [[hodnost matice|hodnost]] <big>\(h=2\)</big> jsou regulárními body. Je-li hodnost matice <big>\(h<2\)</big>, pak jde o singulární body.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Body plochy, v nichž má tato matice [[hodnost matice|hodnost]] <big>\(h=2\)</big> jsou regulárními body. Je-li hodnost matice <big>\(h<2\)</big>, pak jde o singulární body.</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>
Sysop