Difference between revisions of "A 5-circle incidence theorem"

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This is a visualization of ''A 5-Circle Incidence Theorem'' by J. Chris Fisher, Larry Hoehn and Eberhard. M. Schröder,
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[https://www.tandfonline.com/doi/abs/10.4169/math.mag.87.1.44?journalCode=umma20 Mathematics Magazine, Volume 87, 2014 - Issue 1].
 
<jsxgraph width="600" height="600">
 
<jsxgraph width="600" height="600">
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,5,5,-5]});
+
var board = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,5,5,-5]});
var A = [], s = [], B = [], k;
+
var A = [], s = [], B = [], c = [], r = [], k;
  
var attA = {name:'',strokeColor:'#7355ff',fillColor:'#7355ff'};
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var attA = {name:'',strokeColor: '#7355ff', fillColor: '#7355ff'};
attA.name = "0";
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A[0] = board.create('point', [2.5, -3], attA);
A[0] = brd.create('point', [2.5, -3], attA);
+
A[1] = board.create('point', [2, 4], attA);
attA.name = "1";
+
A[2] = board.create('point', [-2.5, 3], attA);
A[1] = brd.create('point', [0, 4], attA);
+
A[3] = board.create('point', [-4, -2], attA);
attA.name = "2";
+
A[4] = board.create('point', [0, -4], attA);
  
A[2] = brd.create('point', [-2.5, 3], attA);
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for (k = 0; k < 5; k++) {
attA.name = "";
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  s[k] = board.create('segment',[A[k], A[(k + 2) % 5]],{strokeColor:'blue',strokeWidth:1});
A[3] = brd.create('point', [-4, -2], attA);
+
}
A[4] = brd.create('point', [0, -2], attA);
+
 
 +
var attB = {name: '', strokeColor: '#EA0000', fillColor: '#EA0000'};
 +
for (k = 0; k < 5; k++) {
 +
  B[k] = board.create('intersection', [s[k], s[(k-1+5)%5], 0], attB);
 +
}
  
 +
var attC = {strokeColor: '#aaaaaa', strokeWidth: 1};
 
for (k = 0; k < 5; k++) {
 
for (k = 0; k < 5; k++) {
   s[k] = brd.create('segment',[A[k], A[(k + 2) % 5]],{strokeColor:'blue',strokeWidth:1});
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   c[k] = board.create('circle', [A[k], B[k], A[(k+1)%5]], attC);
 
}
 
}
  
 +
var attR = {strokeColor: '#ff0000', strokeWidth: 2};
 +
for (k = 0; k < 5; k++) {
 +
  r[k] = board.create('radicalaxis', [c[k], c[(k-1+5)%5]], attR);
 +
}
 
</jsxgraph>
 
</jsxgraph>
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 +
===The underlying JavaScript code===
 +
 +
<source lang="javascript">
 +
var board = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,5,5,-5]});
 +
var A = [], s = [], B = [], c = [], r = [], k;
 +
 +
var attA = {name:'',strokeColor: '#7355ff', fillColor: '#7355ff'};
 +
A[0] = board.create('point', [2.5, -3], attA);
 +
A[1] = board.create('point', [2, 4], attA);
 +
A[2] = board.create('point', [-2.5, 3], attA);
 +
A[3] = board.create('point', [-4, -2], attA);
 +
A[4] = board.create('point', [0, -4], attA);
 +
 +
for (k = 0; k < 5; k++) {
 +
  s[k] = board.create('segment',[A[k], A[(k + 2) % 5]],{strokeColor:'blue',strokeWidth:1});
 +
}
 +
 +
var attB = {name: '', strokeColor: '#EA0000', fillColor: '#EA0000'};
 +
for (k = 0; k < 5; k++) {
 +
  B[k] = board.create('intersection', [s[k], s[(k-1+5)%5], 0], attB);
 +
}
 +
 +
var attC = {strokeColor: '#aaaaaa', strokeWidth: 1};
 +
for (k = 0; k < 5; k++) {
 +
  c[k] = board.create('circle', [A[k], B[k], A[(k+1)%5]], attC);
 +
}
 +
 +
var attR = {strokeColor: '#ff0000', strokeWidth: 2};
 +
for (k = 0; k < 5; k++) {
 +
  r[k] = board.create('radicalaxis', [c[k], c[(k-1+5)%5]], attR);
 +
}
 +
</source>
 +
 +
[[Category:Examples]]
 +
[[Category:Geometry]]

Latest revision as of 13:30, 13 August 2019

This is a visualization of A 5-Circle Incidence Theorem by J. Chris Fisher, Larry Hoehn and Eberhard. M. Schröder, Mathematics Magazine, Volume 87, 2014 - Issue 1.

The underlying JavaScript code

var board = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,5,5,-5]});
var A = [], s = [], B = [], c = [], r = [], k;

var attA = {name:'',strokeColor: '#7355ff', fillColor: '#7355ff'};
A[0] = board.create('point', [2.5, -3], attA);
A[1] = board.create('point', [2, 4], attA);
A[2] = board.create('point', [-2.5, 3], attA);
A[3] = board.create('point', [-4, -2], attA);
A[4] = board.create('point', [0, -4], attA);

for (k = 0; k < 5; k++) {
   s[k] = board.create('segment',[A[k], A[(k + 2) % 5]],{strokeColor:'blue',strokeWidth:1});
}

var attB = {name: '', strokeColor: '#EA0000', fillColor: '#EA0000'};
for (k = 0; k < 5; k++) {
   B[k] = board.create('intersection', [s[k], s[(k-1+5)%5], 0], attB);
}

var attC = {strokeColor: '#aaaaaa', strokeWidth: 1};
for (k = 0; k < 5; k++) {
   c[k] = board.create('circle', [A[k], B[k], A[(k+1)%5]], attC);
}

var attR = {strokeColor: '#ff0000', strokeWidth: 2};
for (k = 0; k < 5; k++) {
   r[k] = board.create('radicalaxis', [c[k], c[(k-1+5)%5]], attR);
}