File: simsonsteiner.html

package info (click to toggle)
jsxgraph 1.10.1%2Bdfsg1-1
  • links: PTS, VCS
  • area: main
  • in suites: trixie
  • size: 24,804 kB
  • sloc: javascript: 82,299; xml: 5,869; java: 1,072; php: 281; makefile: 184; python: 174; cpp: 76; sh: 12
file content (143 lines) | stat: -rw-r--r-- 22,371 bytes parent folder | download | duplicates (3) 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
 
<html>
<head>
   <title>Simson-Steiner-Theorem | JSXGraph | Beispiel f&uuml;r einen geometrischen Ort</title>
   <link rel="stylesheet" type="text/css" href="../../distrib/jsxgraph.css" />
   <script type="text/javascript" src="../../distrib/jsxgraphcore.js"></script>
   <script type="text/javascript" src="../src/Triangle.js"></script>
</head>
<body>
<h2>/ <a href="index.html">root</a> / <a href="loci.html">Beispiele f&uuml;r geometrische Orte</a> / Simson-Steiner-Theorem</h2>
<div style="text-align: center">
  <div id="jxgbox" class="jxgbox" style="width:600px; height:500px; text-align: left; margin: auto;"></div>
</div>
   <script type="text/javascript">
    /* <![CDATA[ */

  board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-4, 6, 8, -4], axis: true, grid: false,
                                 keepaspectratio: true, showcopyright: false});
  p1 = board.createElement('point', [0, 0]);
  p2 = board.createElement('point', [6, 0]);
  p3 = board.createElement('point', [4, 4]);

  t1 = board.createElement('triangle', [p1, p2, p3], {strokeWidth: '1px'});

  m1 = board.createElement('point', [4, 1.5], {style:2,name:"X"});

  l1 = board.createElement('perpendicularpoint', [m1, t1.c]);
  l2 = board.createElement('perpendicularpoint', [m1, t1.a]);
  l3 = board.createElement('perpendicularpoint', [m1, t1.b]);

  t2 = board.createElement('triangle', [l1, l2, l3], {strokeWidth: '1px'});

  // Get area of triangle given by the three points A, B, C
  getTriangleArea = function(A, B, C, square) {
    var a = B.coords.distance(JXG.COORDS_BY_USER, C.coords),
        b = A.coords.distance(JXG.COORDS_BY_USER, C.coords),
        c = B.coords.distance(JXG.COORDS_BY_USER, A.coords),
        s = (typeof square == 'undefined' ? true : square);

    if (s)
      return (4*a*a*c*c-(a*a+c*c-b*b)*(a*a+c*c-b*b));
    else
      return Math.sqrt((4*a*a*c*c-(a*a+c*c-b*b)*(a*a+c*c-b*b))/16.);
  };

  te = board.createElement('text', [-3.8, 5.5, function () { return ("Fl&auml;che des Dreiecks EDF: " + getTriangleArea(l1, l2, l3, false)); }]);

  // dependency and polynomial generation hacking
  m1.ancestors[l1.id] = l1;
  m1.ancestors[l2.id] = l2;
  m1.ancestors[l3.id] = l3;
  m1.ancestors[p1.id] = p1;
  m1.ancestors[p2.id] = p2;
  m1.ancestors[p3.id] = p3;

  m1.generatePolynomial = function () {
    var as16 = getTriangleArea(l1, l2, l3),
        as = '((('+l2.symbolic.x+')-('+l3.symbolic.x+'))^2+(('+l2.symbolic.y+')-('+l3.symbolic.y+'))^2)',
        bs = '((('+l1.symbolic.x+')-('+l3.symbolic.x+'))^2+(('+l1.symbolic.y+')-('+l3.symbolic.y+'))^2)',
        cs = '((('+l2.symbolic.x+')-('+l1.symbolic.x+'))^2+(('+l2.symbolic.y+')-('+l1.symbolic.y+'))^2)',
        poly = '4*'+as+'*'+cs+'-('+as+'+'+cs+'-'+bs+')*('+as+'+'+cs+'-'+bs+')-('+as16+')';

    return ['4*'+as+'*'+cs+'-('+as+'+'+cs+'-'+bs+')*('+as+'+'+cs+'-'+bs+')-('+as16+')'];
  };

  loc = board.createElement('locus', [m1], {strokeColor: 'red', strokeWidth: '1px'});

  createControlElements = function () {
    glider = board.createElement('glider', [0, 5, loc]);
    lg1 = board.createElement('perpendicularpoint', [glider, t1.a]);
    lg2 = board.createElement('perpendicularpoint', [glider, t1.b]);
    lg3 = board.createElement('perpendicularpoint', [glider, t1.c]);

    tecontrol = board.createElement('text', [-3.8, 5, function () { return ("Fl&auml;che des Dreiecks HIJ: " + getTriangleArea(lg1, lg2, lg3, false)); }]);
  }

  /* ]]> */
  </script>
<a href="#" onclick="createControlElements();">Control the results</a><br />
<br/><br/>
<div id="src_disp" style="display:block;">
<h2><a href="#" name="src"></a>Quelltext der Konstruktion</h2>
<pre style="border: black solid 1px; padding: 4px"><tt>  board <font color="#990000">=</font> JXG<font color="#990000">.</font>JSXGraph<font color="#990000">.</font><b><font color="#000000">initBoard</font></b><font color="#990000">(</font><font color="#FF0000">'jxgbox'</font><font color="#990000">,</font> <font color="#FF0000">{</font>boundingbox<font color="#990000">:[-</font><font color="#993399">4</font><font color="#990000">,</font> <font color="#993399">6</font><font color="#990000">,</font> <font color="#993399">8</font><font color="#990000">,</font> <font color="#990000">-</font><font color="#993399">4</font><font color="#990000">],</font> axis<font color="#990000">:</font> <b><font color="#0000FF">true</font></b><font color="#990000">,</font> grid<font color="#990000">:</font> <b><font color="#0000FF">false</font></b><font color="#990000">,</font>
                                 keepaspectratio<font color="#990000">:</font> <b><font color="#0000FF">true</font></b><font color="#990000">,</font> showcopyright<font color="#990000">:</font> <b><font color="#0000FF">false</font></b><font color="#FF0000">}</font><font color="#990000">);</font>
  p1 <font color="#990000">=</font> board<font color="#990000">.</font><b><font color="#000000">createElement</font></b><font color="#990000">(</font><font color="#FF0000">'point'</font><font color="#990000">,</font> <font color="#990000">[</font><font color="#993399">0</font><font color="#990000">,</font> <font color="#993399">0</font><font color="#990000">]);</font>
  p2 <font color="#990000">=</font> board<font color="#990000">.</font><b><font color="#000000">createElement</font></b><font color="#990000">(</font><font color="#FF0000">'point'</font><font color="#990000">,</font> <font color="#990000">[</font><font color="#993399">6</font><font color="#990000">,</font> <font color="#993399">0</font><font color="#990000">]);</font>
  p3 <font color="#990000">=</font> board<font color="#990000">.</font><b><font color="#000000">createElement</font></b><font color="#990000">(</font><font color="#FF0000">'point'</font><font color="#990000">,</font> <font color="#990000">[</font><font color="#993399">4</font><font color="#990000">,</font> <font color="#993399">4</font><font color="#990000">]);</font>

  t1 <font color="#990000">=</font> board<font color="#990000">.</font><b><font color="#000000">createElement</font></b><font color="#990000">(</font><font color="#FF0000">'triangle'</font><font color="#990000">,</font> <font color="#990000">[</font>p1<font color="#990000">,</font> p2<font color="#990000">,</font> p3<font color="#990000">],</font> <font color="#FF0000">{</font>strokeWidth<font color="#990000">:</font> <font color="#FF0000">'1px'</font><font color="#FF0000">}</font><font color="#990000">);</font>

  m1 <font color="#990000">=</font> board<font color="#990000">.</font><b><font color="#000000">createElement</font></b><font color="#990000">(</font><font color="#FF0000">'point'</font><font color="#990000">,</font> <font color="#990000">[</font><font color="#993399">4</font><font color="#990000">,</font> <font color="#993399">1.5</font><font color="#990000">],</font> <font color="#FF0000">{</font>style<font color="#990000">:</font><font color="#993399">2</font><font color="#990000">,</font>name<font color="#990000">:</font><font color="#FF0000">"X"</font><font color="#FF0000">}</font><font color="#990000">);</font>

  l1 <font color="#990000">=</font> board<font color="#990000">.</font><b><font color="#000000">createElement</font></b><font color="#990000">(</font><font color="#FF0000">'perpendicularpoint'</font><font color="#990000">,</font> <font color="#990000">[</font>m1<font color="#990000">,</font> t1<font color="#990000">.</font>c<font color="#990000">]);</font>
  l2 <font color="#990000">=</font> board<font color="#990000">.</font><b><font color="#000000">createElement</font></b><font color="#990000">(</font><font color="#FF0000">'perpendicularpoint'</font><font color="#990000">,</font> <font color="#990000">[</font>m1<font color="#990000">,</font> t1<font color="#990000">.</font>a<font color="#990000">]);</font>
  l3 <font color="#990000">=</font> board<font color="#990000">.</font><b><font color="#000000">createElement</font></b><font color="#990000">(</font><font color="#FF0000">'perpendicularpoint'</font><font color="#990000">,</font> <font color="#990000">[</font>m1<font color="#990000">,</font> t1<font color="#990000">.</font>b<font color="#990000">]);</font>

  t2 <font color="#990000">=</font> board<font color="#990000">.</font><b><font color="#000000">createElement</font></b><font color="#990000">(</font><font color="#FF0000">'triangle'</font><font color="#990000">,</font> <font color="#990000">[</font>l1<font color="#990000">,</font> l2<font color="#990000">,</font> l3<font color="#990000">],</font> <font color="#FF0000">{</font>strokeWidth<font color="#990000">:</font> <font color="#FF0000">'1px'</font><font color="#FF0000">}</font><font color="#990000">);</font>

  <i><font color="#9A1900">// Get area of triangle given by the three points A, B, C</font></i>
  getTriangleArea <font color="#990000">=</font> <b><font color="#0000FF">function</font></b><font color="#990000">(</font>A<font color="#990000">,</font> B<font color="#990000">,</font> C<font color="#990000">,</font> square<font color="#990000">)</font> <font color="#FF0000">{</font>
    <b><font color="#0000FF">var</font></b> a <font color="#990000">=</font> B<font color="#990000">.</font>coords<font color="#990000">.</font><b><font color="#000000">distance</font></b><font color="#990000">(</font>JXG<font color="#990000">.</font>COORDS_BY_USER<font color="#990000">,</font> C<font color="#990000">.</font>coords<font color="#990000">),</font>
        b <font color="#990000">=</font> A<font color="#990000">.</font>coords<font color="#990000">.</font><b><font color="#000000">distance</font></b><font color="#990000">(</font>JXG<font color="#990000">.</font>COORDS_BY_USER<font color="#990000">,</font> C<font color="#990000">.</font>coords<font color="#990000">),</font>
        c <font color="#990000">=</font> B<font color="#990000">.</font>coords<font color="#990000">.</font><b><font color="#000000">distance</font></b><font color="#990000">(</font>JXG<font color="#990000">.</font>COORDS_BY_USER<font color="#990000">,</font> A<font color="#990000">.</font>coords<font color="#990000">),</font>
        s <font color="#990000">=</font> <font color="#990000">(</font><b><font color="#0000FF">typeof</font></b> square <font color="#990000">==</font> <font color="#FF0000">'undefined'</font> <font color="#990000">?</font> <b><font color="#0000FF">true</font></b> <font color="#990000">:</font> square<font color="#990000">);</font>

    <b><font color="#0000FF">if</font></b> <font color="#990000">(</font>s<font color="#990000">)</font>
      <b><font color="#0000FF">return</font></b> <font color="#990000">(</font><font color="#993399">4</font><font color="#990000">*</font>a<font color="#990000">*</font>a<font color="#990000">*</font>c<font color="#990000">*</font>c<font color="#990000">-(</font>a<font color="#990000">*</font>a<font color="#990000">+</font>c<font color="#990000">*</font>c<font color="#990000">-</font>b<font color="#990000">*</font>b<font color="#990000">)*(</font>a<font color="#990000">*</font>a<font color="#990000">+</font>c<font color="#990000">*</font>c<font color="#990000">-</font>b<font color="#990000">*</font>b<font color="#990000">));</font>
    <b><font color="#0000FF">else</font></b>
      <b><font color="#0000FF">return</font></b> Math<font color="#990000">.</font><b><font color="#000000">sqrt</font></b><font color="#990000">((</font><font color="#993399">4</font><font color="#990000">*</font>a<font color="#990000">*</font>a<font color="#990000">*</font>c<font color="#990000">*</font>c<font color="#990000">-(</font>a<font color="#990000">*</font>a<font color="#990000">+</font>c<font color="#990000">*</font>c<font color="#990000">-</font>b<font color="#990000">*</font>b<font color="#990000">)*(</font>a<font color="#990000">*</font>a<font color="#990000">+</font>c<font color="#990000">*</font>c<font color="#990000">-</font>b<font color="#990000">*</font>b<font color="#990000">))/</font><font color="#993399">16</font><font color="#990000">.);</font>
  <font color="#FF0000">}</font><font color="#990000">;</font>

  te <font color="#990000">=</font> board<font color="#990000">.</font><b><font color="#000000">createElement</font></b><font color="#990000">(</font><font color="#FF0000">'text'</font><font color="#990000">,</font> <font color="#990000">[-</font><font color="#993399">3.8</font><font color="#990000">,</font> <font color="#993399">5.5</font><font color="#990000">,</font> <b><font color="#0000FF">function</font></b> <font color="#990000">()</font> <font color="#FF0000">{</font> <b><font color="#0000FF">return</font></b> <font color="#990000">(</font><font color="#FF0000">"Fl&amp;auml;che des Dreiecks EDF: "</font> <font color="#990000">+</font> <b><font color="#000000">getTriangleArea</font></b><font color="#990000">(</font>l1<font color="#990000">,</font> l2<font color="#990000">,</font> l3<font color="#990000">,</font> <b><font color="#0000FF">false</font></b><font color="#990000">));</font> <font color="#FF0000">}</font><font color="#990000">]);</font>

  <i><font color="#9A1900">// dependency and polynomial generation hacking</font></i>
  m1<font color="#990000">.</font>ancestors<font color="#990000">[</font>l1<font color="#990000">.</font>id<font color="#990000">]</font> <font color="#990000">=</font> l1<font color="#990000">;</font>
  m1<font color="#990000">.</font>ancestors<font color="#990000">[</font>l2<font color="#990000">.</font>id<font color="#990000">]</font> <font color="#990000">=</font> l2<font color="#990000">;</font>
  m1<font color="#990000">.</font>ancestors<font color="#990000">[</font>l3<font color="#990000">.</font>id<font color="#990000">]</font> <font color="#990000">=</font> l3<font color="#990000">;</font>
  m1<font color="#990000">.</font>ancestors<font color="#990000">[</font>p1<font color="#990000">.</font>id<font color="#990000">]</font> <font color="#990000">=</font> p1<font color="#990000">;</font>
  m1<font color="#990000">.</font>ancestors<font color="#990000">[</font>p2<font color="#990000">.</font>id<font color="#990000">]</font> <font color="#990000">=</font> p2<font color="#990000">;</font>
  m1<font color="#990000">.</font>ancestors<font color="#990000">[</font>p3<font color="#990000">.</font>id<font color="#990000">]</font> <font color="#990000">=</font> p3<font color="#990000">;</font>

  m1<font color="#990000">.</font>generatePolynomial <font color="#990000">=</font> <b><font color="#0000FF">function</font></b> <font color="#990000">()</font> <font color="#FF0000">{</font>
    <b><font color="#0000FF">var</font></b> as16 <font color="#990000">=</font> <b><font color="#000000">getTriangleArea</font></b><font color="#990000">(</font>l1<font color="#990000">,</font> l2<font color="#990000">,</font> l3<font color="#990000">),</font>
        as <font color="#990000">=</font> <font color="#FF0000">'((('</font><font color="#990000">+</font>l2<font color="#990000">.</font>symbolic<font color="#990000">.</font>x<font color="#990000">+</font><font color="#FF0000">')-('</font><font color="#990000">+</font>l3<font color="#990000">.</font>symbolic<font color="#990000">.</font>x<font color="#990000">+</font><font color="#FF0000">'))^2+(('</font><font color="#990000">+</font>l2<font color="#990000">.</font>symbolic<font color="#990000">.</font>y<font color="#990000">+</font><font color="#FF0000">')-('</font><font color="#990000">+</font>l3<font color="#990000">.</font>symbolic<font color="#990000">.</font>y<font color="#990000">+</font><font color="#FF0000">'))^2)'</font><font color="#990000">,</font>
        bs <font color="#990000">=</font> <font color="#FF0000">'((('</font><font color="#990000">+</font>l1<font color="#990000">.</font>symbolic<font color="#990000">.</font>x<font color="#990000">+</font><font color="#FF0000">')-('</font><font color="#990000">+</font>l3<font color="#990000">.</font>symbolic<font color="#990000">.</font>x<font color="#990000">+</font><font color="#FF0000">'))^2+(('</font><font color="#990000">+</font>l1<font color="#990000">.</font>symbolic<font color="#990000">.</font>y<font color="#990000">+</font><font color="#FF0000">')-('</font><font color="#990000">+</font>l3<font color="#990000">.</font>symbolic<font color="#990000">.</font>y<font color="#990000">+</font><font color="#FF0000">'))^2)'</font><font color="#990000">,</font>
        cs <font color="#990000">=</font> <font color="#FF0000">'((('</font><font color="#990000">+</font>l2<font color="#990000">.</font>symbolic<font color="#990000">.</font>x<font color="#990000">+</font><font color="#FF0000">')-('</font><font color="#990000">+</font>l1<font color="#990000">.</font>symbolic<font color="#990000">.</font>x<font color="#990000">+</font><font color="#FF0000">'))^2+(('</font><font color="#990000">+</font>l2<font color="#990000">.</font>symbolic<font color="#990000">.</font>y<font color="#990000">+</font><font color="#FF0000">')-('</font><font color="#990000">+</font>l1<font color="#990000">.</font>symbolic<font color="#990000">.</font>y<font color="#990000">+</font><font color="#FF0000">'))^2)'</font><font color="#990000">,</font>
        poly <font color="#990000">=</font> <font color="#FF0000">'4*'</font><font color="#990000">+</font>as<font color="#990000">+</font><font color="#FF0000">'*'</font><font color="#990000">+</font>cs<font color="#990000">+</font><font color="#FF0000">'-('</font><font color="#990000">+</font>as<font color="#990000">+</font><font color="#FF0000">'+'</font><font color="#990000">+</font>cs<font color="#990000">+</font><font color="#FF0000">'-'</font><font color="#990000">+</font>bs<font color="#990000">+</font><font color="#FF0000">')*('</font><font color="#990000">+</font>as<font color="#990000">+</font><font color="#FF0000">'+'</font><font color="#990000">+</font>cs<font color="#990000">+</font><font color="#FF0000">'-'</font><font color="#990000">+</font>bs<font color="#990000">+</font><font color="#FF0000">')-('</font><font color="#990000">+</font>as16<font color="#990000">+</font><font color="#FF0000">')'</font><font color="#990000">;</font>

    <b><font color="#0000FF">return</font></b> <font color="#990000">[</font><font color="#FF0000">'4*'</font><font color="#990000">+</font>as<font color="#990000">+</font><font color="#FF0000">'*'</font><font color="#990000">+</font>cs<font color="#990000">+</font><font color="#FF0000">'-('</font><font color="#990000">+</font>as<font color="#990000">+</font><font color="#FF0000">'+'</font><font color="#990000">+</font>cs<font color="#990000">+</font><font color="#FF0000">'-'</font><font color="#990000">+</font>bs<font color="#990000">+</font><font color="#FF0000">')*('</font><font color="#990000">+</font>as<font color="#990000">+</font><font color="#FF0000">'+'</font><font color="#990000">+</font>cs<font color="#990000">+</font><font color="#FF0000">'-'</font><font color="#990000">+</font>bs<font color="#990000">+</font><font color="#FF0000">')-('</font><font color="#990000">+</font>as16<font color="#990000">+</font><font color="#FF0000">')'</font><font color="#990000">];</font>
  <font color="#FF0000">}</font><font color="#990000">;</font>

  loc <font color="#990000">=</font> board<font color="#990000">.</font><b><font color="#000000">createElement</font></b><font color="#990000">(</font><font color="#FF0000">'locus'</font><font color="#990000">,</font> <font color="#990000">[</font>m1<font color="#990000">],</font> <font color="#FF0000">{</font>strokeColor<font color="#990000">:</font> <font color="#FF0000">'red'</font><font color="#990000">,</font> strokeWidth<font color="#990000">:</font> <font color="#FF0000">'1px'</font><font color="#FF0000">}</font><font color="#990000">);</font>

  createControlElements <font color="#990000">=</font> <b><font color="#0000FF">function</font></b> <font color="#990000">()</font> <font color="#FF0000">{</font>
    glider <font color="#990000">=</font> board<font color="#990000">.</font><b><font color="#000000">createElement</font></b><font color="#990000">(</font><font color="#FF0000">'glider'</font><font color="#990000">,</font> <font color="#990000">[</font><font color="#993399">0</font><font color="#990000">,</font> <font color="#993399">5</font><font color="#990000">,</font> loc<font color="#990000">]);</font>
    lg1 <font color="#990000">=</font> board<font color="#990000">.</font><b><font color="#000000">createElement</font></b><font color="#990000">(</font><font color="#FF0000">'perpendicularpoint'</font><font color="#990000">,</font> <font color="#990000">[</font>glider<font color="#990000">,</font> t1<font color="#990000">.</font>a<font color="#990000">]);</font>
    lg2 <font color="#990000">=</font> board<font color="#990000">.</font><b><font color="#000000">createElement</font></b><font color="#990000">(</font><font color="#FF0000">'perpendicularpoint'</font><font color="#990000">,</font> <font color="#990000">[</font>glider<font color="#990000">,</font> t1<font color="#990000">.</font>b<font color="#990000">]);</font>
    lg3 <font color="#990000">=</font> board<font color="#990000">.</font><b><font color="#000000">createElement</font></b><font color="#990000">(</font><font color="#FF0000">'perpendicularpoint'</font><font color="#990000">,</font> <font color="#990000">[</font>glider<font color="#990000">,</font> t1<font color="#990000">.</font>c<font color="#990000">]);</font>

    tecontrol <font color="#990000">=</font> board<font color="#990000">.</font><b><font color="#000000">createElement</font></b><font color="#990000">(</font><font color="#FF0000">'text'</font><font color="#990000">,</font> <font color="#990000">[-</font><font color="#993399">3.8</font><font color="#990000">,</font> <font color="#993399">5</font><font color="#990000">,</font> <b><font color="#0000FF">function</font></b> <font color="#990000">()</font> <font color="#FF0000">{</font> <b><font color="#0000FF">return</font></b> <font color="#990000">(</font><font color="#FF0000">"Fl&amp;auml;che des Dreiecks HIJ: "</font> <font color="#990000">+</font> <b><font color="#000000">getTriangleArea</font></b><font color="#990000">(</font>lg1<font color="#990000">,</font> lg2<font color="#990000">,</font> lg3<font color="#990000">,</font> <b><font color="#0000FF">false</font></b><font color="#990000">));</font> <font color="#FF0000">}</font><font color="#990000">]);</font>
  <font color="#FF0000">}</font>
</tt></pre>
</div></body>
</html>