El llibre de miralls

Mou el mirall, observa com canvien les repeticions en funció del angle.

L’aparell consta de dos miralls verticals, un d’ells mòbil. Variant l’angle del diedre que formen els miralls es visualitzen, amb els segments dibuixats a la base, el triangle equilàter, el quadrat, el pentàgon i els successius polígons regulars.

  • Ubicació: Sala Emma Castelnuovo
  • Edat mínima: a partir de 6 anys.
  • Temps requerit: 5 minuts.
  • Nombre de participants: Una o més persones
  • Paraules clau: simetria angle polígons
  • Taxonomia: GEOMETRIA
modul_llibre_miralls

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GeoGebra - Passos de la construcci󼯴itle> <meta http-equiv="content-type" content="text/html; charset=utf-8"></head> <body data-rsssl=1> <h1>Llibre mirall</h1> <h3>Bernat Ancochea i Isabel Sorigué</h3> <table border="1"> <tr> <th>Nom</th> <th>Definició</th> <th>Valor</th> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#00679A">Punt A</span></td> <td><span style="color:#00679A">Intersecció(EixX, EixY)</span></td> <td><span style="color:#00679A">A = (0, 0)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#2828AA">Punt B</span></td> <td><span style="color:#2828AA">Punt(EixY)</span></td> <td><span style="color:#2828AA">B = (0, -4)</span></td> </tr> <tr style='vertical-align:baseline;'> <td>Recta a</td> <td>Recta(A, B)</td> <td>a: x = 0</td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#006400">Angle ±</span></td> <td> </td> <td><span style="color:#006400">± = 87°</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#00679A"><html>Punt B'<sub><font size="-1">1</font></sub></html></span></td> <td><span style="color:#00679A">Rotació(B, α / 2, A)</span></td> <td><span style="color:#00679A">B'<sub><font size="-1">1</font></sub> = (2.75, -2.9)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#00679A"><html>Punt B'<sub><font size="-1">2</font></sub></html></span></td> <td><span style="color:#00679A">Rotació(B, -(α / 2), A)</span></td> <td><span style="color:#00679A">B'<sub><font size="-1">2</font></sub> = (-2.75, -2.9)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#00679A">Segment b</span></td> <td><span style="color:#00679A">Segment(A, B'<sub><font size="-1">2</font></sub>)</span></td> <td><span style="color:#00679A">b = 4</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#00679A">Segment c</span></td> <td><span style="color:#00679A">Segment(A, B'<sub><font size="-1">1</font></sub>)</span></td> <td><span style="color:#00679A">c = 4</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#00679A"><html>Punt A'<sub><font size="-1">1</font></sub></html></span></td> <td><span style="color:#00679A">Simetria(A, c)</span></td> <td><span style="color:#00679A">A'<sub><font size="-1">1</font></sub> = (0, 0)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#828200"><html>Punt B''<sub><font size="-1">1</font></sub></html></span></td> <td><span style="color:#828200">Simetria(B'<sub><font size="-1">2</font></sub>, c)</span></td> <td><span style="color:#828200">B''<sub><font size="-1">1</font></sub> = (3.04, 2.6)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#828200"><html>Segment b'<sub><font size="-1">1</font></sub></html></span></td> <td><span style="color:#828200">Segment(A'<sub><font size="-1">1</font></sub>, B''<sub><font size="-1">1</font></sub>)</span></td> <td><span style="color:#828200">b'<sub><font size="-1">1</font></sub> = 4</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#00679A"><html>Punt A'<sub><font size="-1">2</font></sub></html></span></td> <td><span style="color:#00679A">Simetria(A, b)</span></td> <td><span style="color:#00679A">A'<sub><font size="-1">2</font></sub> = (0, 0)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#828200">Punt C</span></td> <td><span style="color:#828200">Simetria(B'<sub><font size="-1">1</font></sub>, b)</span></td> <td><span style="color:#828200">C = (-3.04, 2.6)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#828200"><html>Segment c'<sub><font size="-1">1</font></sub></html></span></td> <td><span style="color:#828200">Segment(A'<sub><font size="-1">2</font></sub>, C)</span></td> <td><span style="color:#828200">c'<sub><font size="-1">1</font></sub> = 4</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#00679A"><html>Punt A'<sub><font size="-1">3</font></sub></html></span></td> <td><span style="color:#00679A">Simetria(A, c'<sub><font size="-1">1</font></sub>)</span></td> <td><span style="color:#00679A">A'<sub><font size="-1">3</font></sub> = (0, 0)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#828200">Punt B''</span></td> <td><span style="color:#828200">Simetria(B'<sub><font size="-1">2</font></sub>, c'<sub><font size="-1">1</font></sub>)</span></td> <td><span style="color:#828200">B'' = (2.44, 3.17)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#828200">Segment b'</span></td> <td><span style="color:#828200">Segment(A'<sub><font size="-1">3</font></sub>, B'')</span></td> <td><span style="color:#828200">b' = 4</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#00679A">Punt A'</span></td> <td><span style="color:#00679A">Simetria(A, b'<sub><font size="-1">1</font></sub>)</span></td> <td><span style="color:#00679A">A' = (0, 0)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#828200">Punt E</span></td> <td><span style="color:#828200">Simetria(B'<sub><font size="-1">1</font></sub>, b'<sub><font size="-1">1</font></sub>)</span></td> <td><span style="color:#828200">E = (-2.44, 3.17)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#828200">Segment c'</span></td> <td><span style="color:#828200">Segment(A', E)</span></td> <td><span style="color:#828200">c' = 4</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#2828AA">Punt B'</span></td> <td><span style="color:#2828AA">Simetria(B, A')</span></td> <td><span style="color:#2828AA">B' = (0, 4)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#818100">Semirecta d</span></td> <td><span style="color:#818100">Semirecta(A', B')</span></td> <td><span style="color:#818100">d: x = 0</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#00679A">Punt D</span></td> <td><span style="color:#00679A">Simetria(A'<sub><font size="-1">2</font></sub>, b')</span></td> <td><span style="color:#00679A">D = (0, 0)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#828200">Punt C'</span></td> <td><span style="color:#828200">Simetria(C, b')</span></td> <td><span style="color:#828200">C' = (3.3, -2.27)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#828200">Segment e</span></td> <td><span style="color:#828200">Segment(D, C')</span></td> <td><span style="color:#828200">e = 4</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#00679A">Punt F</span></td> <td><span style="color:#00679A">Simetria(A'<sub><font size="-1">1</font></sub>, c')</span></td> <td><span style="color:#00679A">F = (0, 0)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#828200">Punt G</span></td> <td><span style="color:#828200">Simetria(B''<sub><font size="-1">1</font></sub>, c')</span></td> <td><span style="color:#828200">G = (-3.3, -2.27)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#828200">Segment f</span></td> <td><span style="color:#828200">Segment(F, G)</span></td> <td><span style="color:#828200">f = 4</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#00679A">Punt H</span></td> <td><span style="color:#00679A">Simetria(A'<sub><font size="-1">3</font></sub>, e)</span></td> <td><span style="color:#00679A">H = (0, 0)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#828200">Punt B'''</span></td> <td><span style="color:#828200">Simetria(B'', e)</span></td> <td><span style="color:#828200">B''' = (-2.09, -3.41)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#828200">Segment b''</span></td> <td><span style="color:#828200">Segment(H, B''')</span></td> <td><span style="color:#828200">b'' = 4</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#00679A">Punt A''</span></td> <td><span style="color:#00679A">Simetria(A', f)</span></td> <td><span style="color:#00679A">A'' = (0, 0)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#828200">Punt E'</span></td> <td><span style="color:#828200">Simetria(E, f)</span></td> <td><span style="color:#828200">E' = (2.09, -3.41)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#828200">Segment c''</span></td> <td><span style="color:#828200">Segment(A'', E')</span></td> <td><span style="color:#828200">c'' = 4</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#CC0033">Punt I</span></td> <td> </td> <td><span style="color:#CC0033">I = (-0.42, -2.21)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#CC0033">Punt J</span></td> <td> </td> <td><span style="color:#CC0033">J = (0.58, -2.21)</span></td> </tr> <tr style='vertical-align:baseline;'> <td>Segment j</td> <td>Segment(B'<sub><font size="-1">2</font></sub>, B'<sub><font size="-1">1</font></sub>)</td> <td>j = 5.51</td> </tr> <tr style='vertical-align:baseline;'> <td>Nombre ref1</td> <td>j / 2 / tan(α / 2)</td> <td>ref1 = 2.9</td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#CC0000">Punt O</span></td> <td> </td> <td><span style="color:#CC0000">O = (0.09, -2.32)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#CC0000"><html>Punt O'<sub><font size="-1">1</font></sub></html></span></td> <td><span style="color:#CC0000">Simetria(O, b)</span></td> <td><span style="color:#CC0000">O'<sub><font size="-1">1</font></sub> = (-2.32, -0.03)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#CC0000"><html>Punt O''<sub><font size="-1">1</font></sub></html></span></td> <td><span style="color:#CC0000">Simetria(O'<sub><font size="-1">1</font></sub>, c'<sub><font size="-1">1</font></sub>)</span></td> <td><span style="color:#CC0000">O''<sub><font size="-1">1</font></sub> = (-0.34, 2.29)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#CC0000"><html>Punt O'''<sub><font size="-1">1</font></sub></html></span></td> <td><span style="color:#CC0000">Simetria(O''<sub><font size="-1">1</font></sub>, b')</span></td> <td><span style="color:#CC0000">O'''<sub><font size="-1">1</font></sub> = (2.3, 0.27)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#CC0000">Punt P</span></td> <td><span style="color:#CC0000">Simetria(O'''<sub><font size="-1">1</font></sub>, e)</span></td> <td><span style="color:#CC0000">P = (0.57, -2.25)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#CC0000">Punt O'</span></td> <td><span style="color:#CC0000">Simetria(O, c)</span></td> <td><span style="color:#CC0000">O' = (2.31, -0.22)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#CC0000">Punt O''</span></td> <td><span style="color:#CC0000">Simetria(O', b'<sub><font size="-1">1</font></sub>)</span></td> <td><span style="color:#CC0000">O'' = (0.15, 2.31)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#CC0000">Punt O'''</span></td> <td><span style="color:#CC0000">Simetria(O'', c')</span></td> <td><span style="color:#CC0000">O''' = (-2.27, 0.46)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#CC0000">Punt Q</span></td> <td><span style="color:#CC0000">Simetria(O''', f)</span></td> <td><span style="color:#CC0000">Q = (-0.39, -2.29)</span></td> </tr> <tr style='vertical-align:baseline;'> <td>Segment g</td> <td>Segment(A'', O)</td> <td>g = 2.32</td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#006400">Angle ²</span></td> <td><span style="color:#006400">Angle(B'<sub><font size="-1">2</font></sub>, A'', O)</span></td> <td><span style="color:#006400">² = 45.82°</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#CC0000">Punt P'</span></td> <td><span style="color:#CC0000">Simetria(P, b'')</span></td> <td><span style="color:#CC0000">P' = (-2.26, -0.51)</span></td> </tr> <tr style='vertical-align:baseline;'> <td><span style="color:#009900">Text text1</span></td> <td> </td> <td><span style="color:#009900">"Posa el punt entre els dos miralls!"</span></td> </tr> </table> Created with <a href="https://www.geogebra.org/" target="_blank" >GeoGebra</a> <!-- Base64 string so that this file can be opened in GeoGebra with File -> Open --> <applet width='1' height='1' code='' style="display:none"> <param name="ggbBase64" 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