// Define the id of your board in BOARDID
const board = JXG.JSXGraph.initBoard(BOARDID, {
boundingbox: [-2, 2, 2, -2],
keepaspectratio: true
});
var b0, c0, c1, c2, c3,
a, p1,
solveQ2, thirdCircleX, thirdCircleY, thirdCircleRadius,
otherCirc;
solveQ2 = function(x1, x2, x3, off) {
var a, b, c, d;
a = 0.5;
b = -(x1 + x2 + x3);
c = x1 * x1 + x2 * x2 + x3 * x3 - 0.5 * (x1 + x2 + x3) * (x1 + x2 + x3) - off;
d = b * b - 4 * a * c;
if (Math.abs(d) < 0.00000001) d = 0.0;
return [(-b + Math.sqrt(d)) / (2.0 * a), (-b - Math.sqrt(d)) / (2.0 * a)];
}
a = board.create('segment', [
[0, 0],
[2, 0]
], {
visible: false
});
p1 = board.create('glider', [1.3, 0, a], {
name: 'Drag me'
});
b0 = -0.5;
c0 = board.create('circle', [
[0, 0], Math.abs(1.0 / b0)
], {
strokeWidth: 1
});
c1 = board.create('circle', [p1, function() {
return 2 - p1.X();
}], {
strokeWidth: 1
});
c2 = board.create('circle', [
[function() {
return p1.X() - 2;
}, 0],
function() {
return p1.X();
}
], {
strokeWidth: 1
});
// Constant curvature
c0.curvature = function() {
return b0;
};
c1.curvature = function() {
return 1 / (2 - p1.X());
};
c2.curvature = function() {
return 1 / (p1.X());
};
thirdCircleX = function() {
var b0, b1, b2, x0, x1, x2, b3, bx3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
x0 = c0.midpoint.X();
x1 = c1.midpoint.X();
x2 = c2.midpoint.X();
b3 = solveQ2(b0, b1, b2, 0);
bx3 = solveQ2(b0 * x0, b1 * x1, b2 * x2, 2);
return bx3[0] / b3[0];
}
thirdCircleY = function() {
var b0, b1, b2, y0, y1, y2, b3, by3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
y0 = c0.midpoint.Y();
y1 = c1.midpoint.Y();
y2 = c2.midpoint.Y();
b3 = solveQ2(b0, b1, b2, 0);
by3 = solveQ2(b0 * y0, b1 * y1, b2 * y2, 2);
return by3[0] / b3[0];
}
thirdCircleRadius = function() {
var b0, b1, b2, b3, bx3, by3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
b3 = solveQ2(b0, b1, b2, 0);
return 1.0 / b3[0];
}
c3 = board.create('circle', [
[thirdCircleX, thirdCircleY], thirdCircleRadius
], {
strokeWidth: 1
});
c3.curvature = function() {
return 1.0 / this.radius;
};
otherCirc = function(circs, level) {
var c, fx, fy, fr;
if (level <= 0) return;
fx = function() {
var b, x, i;
b = [];
x = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
x[i] = circs[i].midpoint.X();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
x[4] = (2 * (b[0] * x[0] + b[1] * x[1] + b[2] * x[2]) - b[3] * x[3]) / b[4];
return x[4];
}
fy = function() {
var b, y, i;
b = [];
y = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
y[i] = circs[i].midpoint.Y();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
y[4] = (2 * (b[0] * y[0] + b[1] * y[1] + b[2] * y[2]) - b[3] * y[3]) / b[4];
return y[4];
}
fr = function() {
var b, i;
b = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
if (isNaN(b[4])) {
return 1000.0;
} else {
return 1 / b[4];
}
}
c = board.create('circle', [
[fx, fy], fr
], {
strokeWidth: 1,
name: '',
fillColor: JXG.hsv2rgb(50 * level, 0.8, 0.8),
highlightFillColor: JXG.hsv2rgb(50 * level, 0.5, 0.8),
fillOpacity: 0.5,
highlightFillOpacity: 0.5
});
c.curvature = function() {
return 1 / this.radius;
};
// Recursion
otherCirc([circs[0], circs[1], c, circs[2]], level - 1);
otherCirc([circs[0], circs[2], c, circs[1]], level - 1);
otherCirc([circs[1], circs[2], c, circs[0]], level - 1);
return c;
}
//-------------------------------------------------------
var level = 4;
otherCirc([c0, c1, c2, c3], level);
otherCirc([c3, c1, c2, c0], level);
otherCirc([c0, c2, c3, c1], level);
otherCirc([c0, c1, c3, c2], level);
This example is licensed under a Creative Commons Attribution 4.0 International License.
Please note that you have to mention The Center of Mobile Learning with Digital Technology in the credits.
/*
This example is licensed under a
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
Please note that you have to mention
The Center of Mobile Learning with Digital Technology
in the credits.
*/
const BOARDID = 'your_div_id'; // Insert your id here!
const board = JXG.JSXGraph.initBoard(BOARDID, {
boundingbox: [-2, 2, 2, -2],
keepaspectratio: true
});
var b0, c0, c1, c2, c3,
a, p1,
solveQ2, thirdCircleX, thirdCircleY, thirdCircleRadius,
otherCirc;
solveQ2 = function(x1, x2, x3, off) {
var a, b, c, d;
a = 0.5;
b = -(x1 + x2 + x3);
c = x1 * x1 + x2 * x2 + x3 * x3 - 0.5 * (x1 + x2 + x3) * (x1 + x2 + x3) - off;
d = b * b - 4 * a * c;
if (Math.abs(d) < 0.00000001) d = 0.0;
return [(-b + Math.sqrt(d)) / (2.0 * a), (-b - Math.sqrt(d)) / (2.0 * a)];
}
a = board.create('segment', [
[0, 0],
[2, 0]
], {
visible: false
});
p1 = board.create('glider', [1.3, 0, a], {
name: 'Drag me'
});
b0 = -0.5;
c0 = board.create('circle', [
[0, 0], Math.abs(1.0 / b0)
], {
strokeWidth: 1
});
c1 = board.create('circle', [p1, function() {
return 2 - p1.X();
}], {
strokeWidth: 1
});
c2 = board.create('circle', [
[function() {
return p1.X() - 2;
}, 0],
function() {
return p1.X();
}
], {
strokeWidth: 1
});
// Constant curvature
c0.curvature = function() {
return b0;
};
c1.curvature = function() {
return 1 / (2 - p1.X());
};
c2.curvature = function() {
return 1 / (p1.X());
};
thirdCircleX = function() {
var b0, b1, b2, x0, x1, x2, b3, bx3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
x0 = c0.midpoint.X();
x1 = c1.midpoint.X();
x2 = c2.midpoint.X();
b3 = solveQ2(b0, b1, b2, 0);
bx3 = solveQ2(b0 * x0, b1 * x1, b2 * x2, 2);
return bx3[0] / b3[0];
}
thirdCircleY = function() {
var b0, b1, b2, y0, y1, y2, b3, by3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
y0 = c0.midpoint.Y();
y1 = c1.midpoint.Y();
y2 = c2.midpoint.Y();
b3 = solveQ2(b0, b1, b2, 0);
by3 = solveQ2(b0 * y0, b1 * y1, b2 * y2, 2);
return by3[0] / b3[0];
}
thirdCircleRadius = function() {
var b0, b1, b2, b3, bx3, by3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
b3 = solveQ2(b0, b1, b2, 0);
return 1.0 / b3[0];
}
c3 = board.create('circle', [
[thirdCircleX, thirdCircleY], thirdCircleRadius
], {
strokeWidth: 1
});
c3.curvature = function() {
return 1.0 / this.radius;
};
otherCirc = function(circs, level) {
var c, fx, fy, fr;
if (level <= 0) return;
fx = function() {
var b, x, i;
b = [];
x = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
x[i] = circs[i].midpoint.X();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
x[4] = (2 * (b[0] * x[0] + b[1] * x[1] + b[2] * x[2]) - b[3] * x[3]) / b[4];
return x[4];
}
fy = function() {
var b, y, i;
b = [];
y = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
y[i] = circs[i].midpoint.Y();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
y[4] = (2 * (b[0] * y[0] + b[1] * y[1] + b[2] * y[2]) - b[3] * y[3]) / b[4];
return y[4];
}
fr = function() {
var b, i;
b = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
if (isNaN(b[4])) {
return 1000.0;
} else {
return 1 / b[4];
}
}
c = board.create('circle', [
[fx, fy], fr
], {
strokeWidth: 1,
name: '',
fillColor: JXG.hsv2rgb(50 * level, 0.8, 0.8),
highlightFillColor: JXG.hsv2rgb(50 * level, 0.5, 0.8),
fillOpacity: 0.5,
highlightFillOpacity: 0.5
});
c.curvature = function() {
return 1 / this.radius;
};
// Recursion
otherCirc([circs[0], circs[1], c, circs[2]], level - 1);
otherCirc([circs[0], circs[2], c, circs[1]], level - 1);
otherCirc([circs[1], circs[2], c, circs[0]], level - 1);
return c;
}
//-------------------------------------------------------
var level = 4;
otherCirc([c0, c1, c2, c3], level);
otherCirc([c3, c1, c2, c0], level);
otherCirc([c0, c2, c3, c1], level);
otherCirc([c0, c1, c3, c2], level);
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
<div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>
<script type = "text/javascript">
/*
This example is licensed under a
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
Please note that you have to mention
The Center of Mobile Learning with Digital Technology
in the credits.
*/
const BOARDID = 'board-0';
const board = JXG.JSXGraph.initBoard(BOARDID, {
boundingbox: [-2, 2, 2, -2],
keepaspectratio: true
});
var b0, c0, c1, c2, c3,
a, p1,
solveQ2, thirdCircleX, thirdCircleY, thirdCircleRadius,
otherCirc;
solveQ2 = function(x1, x2, x3, off) {
var a, b, c, d;
a = 0.5;
b = -(x1 + x2 + x3);
c = x1 * x1 + x2 * x2 + x3 * x3 - 0.5 * (x1 + x2 + x3) * (x1 + x2 + x3) - off;
d = b * b - 4 * a * c;
if (Math.abs(d) < 0.00000001) d = 0.0;
return [(-b + Math.sqrt(d)) / (2.0 * a), (-b - Math.sqrt(d)) / (2.0 * a)];
}
a = board.create('segment', [
[0, 0],
[2, 0]
], {
visible: false
});
p1 = board.create('glider', [1.3, 0, a], {
name: 'Drag me'
});
b0 = -0.5;
c0 = board.create('circle', [
[0, 0], Math.abs(1.0 / b0)
], {
strokeWidth: 1
});
c1 = board.create('circle', [p1, function() {
return 2 - p1.X();
}], {
strokeWidth: 1
});
c2 = board.create('circle', [
[function() {
return p1.X() - 2;
}, 0],
function() {
return p1.X();
}
], {
strokeWidth: 1
});
// Constant curvature
c0.curvature = function() {
return b0;
};
c1.curvature = function() {
return 1 / (2 - p1.X());
};
c2.curvature = function() {
return 1 / (p1.X());
};
thirdCircleX = function() {
var b0, b1, b2, x0, x1, x2, b3, bx3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
x0 = c0.midpoint.X();
x1 = c1.midpoint.X();
x2 = c2.midpoint.X();
b3 = solveQ2(b0, b1, b2, 0);
bx3 = solveQ2(b0 * x0, b1 * x1, b2 * x2, 2);
return bx3[0] / b3[0];
}
thirdCircleY = function() {
var b0, b1, b2, y0, y1, y2, b3, by3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
y0 = c0.midpoint.Y();
y1 = c1.midpoint.Y();
y2 = c2.midpoint.Y();
b3 = solveQ2(b0, b1, b2, 0);
by3 = solveQ2(b0 * y0, b1 * y1, b2 * y2, 2);
return by3[0] / b3[0];
}
thirdCircleRadius = function() {
var b0, b1, b2, b3, bx3, by3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
b3 = solveQ2(b0, b1, b2, 0);
return 1.0 / b3[0];
}
c3 = board.create('circle', [
[thirdCircleX, thirdCircleY], thirdCircleRadius
], {
strokeWidth: 1
});
c3.curvature = function() {
return 1.0 / this.radius;
};
otherCirc = function(circs, level) {
var c, fx, fy, fr;
if (level <= 0) return;
fx = function() {
var b, x, i;
b = [];
x = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
x[i] = circs[i].midpoint.X();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
x[4] = (2 * (b[0] * x[0] + b[1] * x[1] + b[2] * x[2]) - b[3] * x[3]) / b[4];
return x[4];
}
fy = function() {
var b, y, i;
b = [];
y = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
y[i] = circs[i].midpoint.Y();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
y[4] = (2 * (b[0] * y[0] + b[1] * y[1] + b[2] * y[2]) - b[3] * y[3]) / b[4];
return y[4];
}
fr = function() {
var b, i;
b = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
if (isNaN(b[4])) {
return 1000.0;
} else {
return 1 / b[4];
}
}
c = board.create('circle', [
[fx, fy], fr
], {
strokeWidth: 1,
name: '',
fillColor: JXG.hsv2rgb(50 * level, 0.8, 0.8),
highlightFillColor: JXG.hsv2rgb(50 * level, 0.5, 0.8),
fillOpacity: 0.5,
highlightFillOpacity: 0.5
});
c.curvature = function() {
return 1 / this.radius;
};
// Recursion
otherCirc([circs[0], circs[1], c, circs[2]], level - 1);
otherCirc([circs[0], circs[2], c, circs[1]], level - 1);
otherCirc([circs[1], circs[2], c, circs[0]], level - 1);
return c;
}
//-------------------------------------------------------
var level = 4;
otherCirc([c0, c1, c2, c3], level);
otherCirc([c3, c1, c2, c0], level);
otherCirc([c0, c2, c3, c1], level);
otherCirc([c0, c1, c3, c2], level);
</script>
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Apollonian circle packing" description="This construction was copied from JSXGraph examples database: https://jsxgraph.org/share/" useGlobalJS="false">
/*
This example is licensed under a
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
Please note that you have to mention
The Center of Mobile Learning with Digital Technology
in the credits.
*/
const board = JXG.JSXGraph.initBoard(BOARDID, {
boundingbox: [-2, 2, 2, -2],
keepaspectratio: true
});
var b0, c0, c1, c2, c3,
a, p1,
solveQ2, thirdCircleX, thirdCircleY, thirdCircleRadius,
otherCirc;
solveQ2 = function(x1, x2, x3, off) {
var a, b, c, d;
a = 0.5;
b = -(x1 + x2 + x3);
c = x1 * x1 + x2 * x2 + x3 * x3 - 0.5 * (x1 + x2 + x3) * (x1 + x2 + x3) - off;
d = b * b - 4 * a * c;
if (Math.abs(d) < 0.00000001) d = 0.0;
return [(-b + Math.sqrt(d)) / (2.0 * a), (-b - Math.sqrt(d)) / (2.0 * a)];
}
a = board.create('segment', [
[0, 0],
[2, 0]
], {
visible: false
});
p1 = board.create('glider', [1.3, 0, a], {
name: 'Drag me'
});
b0 = -0.5;
c0 = board.create('circle', [
[0, 0], Math.abs(1.0 / b0)
], {
strokeWidth: 1
});
c1 = board.create('circle', [p1, function() {
return 2 - p1.X();
}], {
strokeWidth: 1
});
c2 = board.create('circle', [
[function() {
return p1.X() - 2;
}, 0],
function() {
return p1.X();
}
], {
strokeWidth: 1
});
// Constant curvature
c0.curvature = function() {
return b0;
};
c1.curvature = function() {
return 1 / (2 - p1.X());
};
c2.curvature = function() {
return 1 / (p1.X());
};
thirdCircleX = function() {
var b0, b1, b2, x0, x1, x2, b3, bx3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
x0 = c0.midpoint.X();
x1 = c1.midpoint.X();
x2 = c2.midpoint.X();
b3 = solveQ2(b0, b1, b2, 0);
bx3 = solveQ2(b0 * x0, b1 * x1, b2 * x2, 2);
return bx3[0] / b3[0];
}
thirdCircleY = function() {
var b0, b1, b2, y0, y1, y2, b3, by3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
y0 = c0.midpoint.Y();
y1 = c1.midpoint.Y();
y2 = c2.midpoint.Y();
b3 = solveQ2(b0, b1, b2, 0);
by3 = solveQ2(b0 * y0, b1 * y1, b2 * y2, 2);
return by3[0] / b3[0];
}
thirdCircleRadius = function() {
var b0, b1, b2, b3, bx3, by3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
b3 = solveQ2(b0, b1, b2, 0);
return 1.0 / b3[0];
}
c3 = board.create('circle', [
[thirdCircleX, thirdCircleY], thirdCircleRadius
], {
strokeWidth: 1
});
c3.curvature = function() {
return 1.0 / this.radius;
};
otherCirc = function(circs, level) {
var c, fx, fy, fr;
if (level <= 0) return;
fx = function() {
var b, x, i;
b = [];
x = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
x[i] = circs[i].midpoint.X();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
x[4] = (2 * (b[0] * x[0] + b[1] * x[1] + b[2] * x[2]) - b[3] * x[3]) / b[4];
return x[4];
}
fy = function() {
var b, y, i;
b = [];
y = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
y[i] = circs[i].midpoint.Y();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
y[4] = (2 * (b[0] * y[0] + b[1] * y[1] + b[2] * y[2]) - b[3] * y[3]) / b[4];
return y[4];
}
fr = function() {
var b, i;
b = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
if (isNaN(b[4])) {
return 1000.0;
} else {
return 1 / b[4];
}
}
c = board.create('circle', [
[fx, fy], fr
], {
strokeWidth: 1,
name: '',
fillColor: JXG.hsv2rgb(50 * level, 0.8, 0.8),
highlightFillColor: JXG.hsv2rgb(50 * level, 0.5, 0.8),
fillOpacity: 0.5,
highlightFillOpacity: 0.5
});
c.curvature = function() {
return 1 / this.radius;
};
// Recursion
otherCirc([circs[0], circs[1], c, circs[2]], level - 1);
otherCirc([circs[0], circs[2], c, circs[1]], level - 1);
otherCirc([circs[1], circs[2], c, circs[0]], level - 1);
return c;
}
//-------------------------------------------------------
var level = 4;
otherCirc([c0, c1, c2, c3], level);
otherCirc([c3, c1, c2, c0], level);
otherCirc([c0, c2, c3, c1], level);
otherCirc([c0, c1, c3, c2], level);
</jsxgraph>
/*
This example is licensed under a
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
Please note that you have to mention
The Center of Mobile Learning with Digital Technology
in the credits.
*/
const BOARDID = 'your_div_id'; // Insert your id here!
const board = JXG.JSXGraph.initBoard(BOARDID, {
boundingbox: [-2, 2, 2, -2],
keepaspectratio: true
});
var b0, c0, c1, c2, c3,
a, p1,
solveQ2, thirdCircleX, thirdCircleY, thirdCircleRadius,
otherCirc;
solveQ2 = function(x1, x2, x3, off) {
var a, b, c, d;
a = 0.5;
b = -(x1 + x2 + x3);
c = x1 * x1 + x2 * x2 + x3 * x3 - 0.5 * (x1 + x2 + x3) * (x1 + x2 + x3) - off;
d = b * b - 4 * a * c;
if (Math.abs(d) < 0.00000001) d = 0.0;
return [(-b + Math.sqrt(d)) / (2.0 * a), (-b - Math.sqrt(d)) / (2.0 * a)];
}
a = board.create('segment', [
[0, 0],
[2, 0]
], {
visible: false
});
p1 = board.create('glider', [1.3, 0, a], {
name: 'Drag me'
});
b0 = -0.5;
c0 = board.create('circle', [
[0, 0], Math.abs(1.0 / b0)
], {
strokeWidth: 1
});
c1 = board.create('circle', [p1, function() {
return 2 - p1.X();
}], {
strokeWidth: 1
});
c2 = board.create('circle', [
[function() {
return p1.X() - 2;
}, 0],
function() {
return p1.X();
}
], {
strokeWidth: 1
});
// Constant curvature
c0.curvature = function() {
return b0;
};
c1.curvature = function() {
return 1 / (2 - p1.X());
};
c2.curvature = function() {
return 1 / (p1.X());
};
thirdCircleX = function() {
var b0, b1, b2, x0, x1, x2, b3, bx3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
x0 = c0.midpoint.X();
x1 = c1.midpoint.X();
x2 = c2.midpoint.X();
b3 = solveQ2(b0, b1, b2, 0);
bx3 = solveQ2(b0 * x0, b1 * x1, b2 * x2, 2);
return bx3[0] / b3[0];
}
thirdCircleY = function() {
var b0, b1, b2, y0, y1, y2, b3, by3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
y0 = c0.midpoint.Y();
y1 = c1.midpoint.Y();
y2 = c2.midpoint.Y();
b3 = solveQ2(b0, b1, b2, 0);
by3 = solveQ2(b0 * y0, b1 * y1, b2 * y2, 2);
return by3[0] / b3[0];
}
thirdCircleRadius = function() {
var b0, b1, b2, b3, bx3, by3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
b3 = solveQ2(b0, b1, b2, 0);
return 1.0 / b3[0];
}
c3 = board.create('circle', [
[thirdCircleX, thirdCircleY], thirdCircleRadius
], {
strokeWidth: 1
});
c3.curvature = function() {
return 1.0 / this.radius;
};
otherCirc = function(circs, level) {
var c, fx, fy, fr;
if (level <= 0) return;
fx = function() {
var b, x, i;
b = [];
x = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
x[i] = circs[i].midpoint.X();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
x[4] = (2 * (b[0] * x[0] + b[1] * x[1] + b[2] * x[2]) - b[3] * x[3]) / b[4];
return x[4];
}
fy = function() {
var b, y, i;
b = [];
y = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
y[i] = circs[i].midpoint.Y();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
y[4] = (2 * (b[0] * y[0] + b[1] * y[1] + b[2] * y[2]) - b[3] * y[3]) / b[4];
return y[4];
}
fr = function() {
var b, i;
b = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
if (isNaN(b[4])) {
return 1000.0;
} else {
return 1 / b[4];
}
}
c = board.create('circle', [
[fx, fy], fr
], {
strokeWidth: 1,
name: '',
fillColor: JXG.hsv2rgb(50 * level, 0.8, 0.8),
highlightFillColor: JXG.hsv2rgb(50 * level, 0.5, 0.8),
fillOpacity: 0.5,
highlightFillOpacity: 0.5
});
c.curvature = function() {
return 1 / this.radius;
};
// Recursion
otherCirc([circs[0], circs[1], c, circs[2]], level - 1);
otherCirc([circs[0], circs[2], c, circs[1]], level - 1);
otherCirc([circs[1], circs[2], c, circs[0]], level - 1);
return c;
}
//-------------------------------------------------------
var level = 4;
otherCirc([c0, c1, c2, c3], level);
otherCirc([c3, c1, c2, c0], level);
otherCirc([c0, c2, c3, c1], level);
otherCirc([c0, c1, c3, c2], level);
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
<div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>
<script type = "text/javascript">
/*
This example is licensed under a
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
Please note that you have to mention
The Center of Mobile Learning with Digital Technology
in the credits.
*/
const BOARDID = 'board-0';
const board = JXG.JSXGraph.initBoard(BOARDID, {
boundingbox: [-2, 2, 2, -2],
keepaspectratio: true
});
var b0, c0, c1, c2, c3,
a, p1,
solveQ2, thirdCircleX, thirdCircleY, thirdCircleRadius,
otherCirc;
solveQ2 = function(x1, x2, x3, off) {
var a, b, c, d;
a = 0.5;
b = -(x1 + x2 + x3);
c = x1 * x1 + x2 * x2 + x3 * x3 - 0.5 * (x1 + x2 + x3) * (x1 + x2 + x3) - off;
d = b * b - 4 * a * c;
if (Math.abs(d) < 0.00000001) d = 0.0;
return [(-b + Math.sqrt(d)) / (2.0 * a), (-b - Math.sqrt(d)) / (2.0 * a)];
}
a = board.create('segment', [
[0, 0],
[2, 0]
], {
visible: false
});
p1 = board.create('glider', [1.3, 0, a], {
name: 'Drag me'
});
b0 = -0.5;
c0 = board.create('circle', [
[0, 0], Math.abs(1.0 / b0)
], {
strokeWidth: 1
});
c1 = board.create('circle', [p1, function() {
return 2 - p1.X();
}], {
strokeWidth: 1
});
c2 = board.create('circle', [
[function() {
return p1.X() - 2;
}, 0],
function() {
return p1.X();
}
], {
strokeWidth: 1
});
// Constant curvature
c0.curvature = function() {
return b0;
};
c1.curvature = function() {
return 1 / (2 - p1.X());
};
c2.curvature = function() {
return 1 / (p1.X());
};
thirdCircleX = function() {
var b0, b1, b2, x0, x1, x2, b3, bx3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
x0 = c0.midpoint.X();
x1 = c1.midpoint.X();
x2 = c2.midpoint.X();
b3 = solveQ2(b0, b1, b2, 0);
bx3 = solveQ2(b0 * x0, b1 * x1, b2 * x2, 2);
return bx3[0] / b3[0];
}
thirdCircleY = function() {
var b0, b1, b2, y0, y1, y2, b3, by3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
y0 = c0.midpoint.Y();
y1 = c1.midpoint.Y();
y2 = c2.midpoint.Y();
b3 = solveQ2(b0, b1, b2, 0);
by3 = solveQ2(b0 * y0, b1 * y1, b2 * y2, 2);
return by3[0] / b3[0];
}
thirdCircleRadius = function() {
var b0, b1, b2, b3, bx3, by3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
b3 = solveQ2(b0, b1, b2, 0);
return 1.0 / b3[0];
}
c3 = board.create('circle', [
[thirdCircleX, thirdCircleY], thirdCircleRadius
], {
strokeWidth: 1
});
c3.curvature = function() {
return 1.0 / this.radius;
};
otherCirc = function(circs, level) {
var c, fx, fy, fr;
if (level <= 0) return;
fx = function() {
var b, x, i;
b = [];
x = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
x[i] = circs[i].midpoint.X();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
x[4] = (2 * (b[0] * x[0] + b[1] * x[1] + b[2] * x[2]) - b[3] * x[3]) / b[4];
return x[4];
}
fy = function() {
var b, y, i;
b = [];
y = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
y[i] = circs[i].midpoint.Y();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
y[4] = (2 * (b[0] * y[0] + b[1] * y[1] + b[2] * y[2]) - b[3] * y[3]) / b[4];
return y[4];
}
fr = function() {
var b, i;
b = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
if (isNaN(b[4])) {
return 1000.0;
} else {
return 1 / b[4];
}
}
c = board.create('circle', [
[fx, fy], fr
], {
strokeWidth: 1,
name: '',
fillColor: JXG.hsv2rgb(50 * level, 0.8, 0.8),
highlightFillColor: JXG.hsv2rgb(50 * level, 0.5, 0.8),
fillOpacity: 0.5,
highlightFillOpacity: 0.5
});
c.curvature = function() {
return 1 / this.radius;
};
// Recursion
otherCirc([circs[0], circs[1], c, circs[2]], level - 1);
otherCirc([circs[0], circs[2], c, circs[1]], level - 1);
otherCirc([circs[1], circs[2], c, circs[0]], level - 1);
return c;
}
//-------------------------------------------------------
var level = 4;
otherCirc([c0, c1, c2, c3], level);
otherCirc([c3, c1, c2, c0], level);
otherCirc([c0, c2, c3, c1], level);
otherCirc([c0, c1, c3, c2], level);
</script>
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Apollonian circle packing" description="This construction was copied from JSXGraph examples database: https://jsxgraph.org/share/" useGlobalJS="false">
/*
This example is licensed under a
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
Please note that you have to mention
The Center of Mobile Learning with Digital Technology
in the credits.
*/
const board = JXG.JSXGraph.initBoard(BOARDID, {
boundingbox: [-2, 2, 2, -2],
keepaspectratio: true
});
var b0, c0, c1, c2, c3,
a, p1,
solveQ2, thirdCircleX, thirdCircleY, thirdCircleRadius,
otherCirc;
solveQ2 = function(x1, x2, x3, off) {
var a, b, c, d;
a = 0.5;
b = -(x1 + x2 + x3);
c = x1 * x1 + x2 * x2 + x3 * x3 - 0.5 * (x1 + x2 + x3) * (x1 + x2 + x3) - off;
d = b * b - 4 * a * c;
if (Math.abs(d) < 0.00000001) d = 0.0;
return [(-b + Math.sqrt(d)) / (2.0 * a), (-b - Math.sqrt(d)) / (2.0 * a)];
}
a = board.create('segment', [
[0, 0],
[2, 0]
], {
visible: false
});
p1 = board.create('glider', [1.3, 0, a], {
name: 'Drag me'
});
b0 = -0.5;
c0 = board.create('circle', [
[0, 0], Math.abs(1.0 / b0)
], {
strokeWidth: 1
});
c1 = board.create('circle', [p1, function() {
return 2 - p1.X();
}], {
strokeWidth: 1
});
c2 = board.create('circle', [
[function() {
return p1.X() - 2;
}, 0],
function() {
return p1.X();
}
], {
strokeWidth: 1
});
// Constant curvature
c0.curvature = function() {
return b0;
};
c1.curvature = function() {
return 1 / (2 - p1.X());
};
c2.curvature = function() {
return 1 / (p1.X());
};
thirdCircleX = function() {
var b0, b1, b2, x0, x1, x2, b3, bx3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
x0 = c0.midpoint.X();
x1 = c1.midpoint.X();
x2 = c2.midpoint.X();
b3 = solveQ2(b0, b1, b2, 0);
bx3 = solveQ2(b0 * x0, b1 * x1, b2 * x2, 2);
return bx3[0] / b3[0];
}
thirdCircleY = function() {
var b0, b1, b2, y0, y1, y2, b3, by3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
y0 = c0.midpoint.Y();
y1 = c1.midpoint.Y();
y2 = c2.midpoint.Y();
b3 = solveQ2(b0, b1, b2, 0);
by3 = solveQ2(b0 * y0, b1 * y1, b2 * y2, 2);
return by3[0] / b3[0];
}
thirdCircleRadius = function() {
var b0, b1, b2, b3, bx3, by3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
b3 = solveQ2(b0, b1, b2, 0);
return 1.0 / b3[0];
}
c3 = board.create('circle', [
[thirdCircleX, thirdCircleY], thirdCircleRadius
], {
strokeWidth: 1
});
c3.curvature = function() {
return 1.0 / this.radius;
};
otherCirc = function(circs, level) {
var c, fx, fy, fr;
if (level <= 0) return;
fx = function() {
var b, x, i;
b = [];
x = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
x[i] = circs[i].midpoint.X();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
x[4] = (2 * (b[0] * x[0] + b[1] * x[1] + b[2] * x[2]) - b[3] * x[3]) / b[4];
return x[4];
}
fy = function() {
var b, y, i;
b = [];
y = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
y[i] = circs[i].midpoint.Y();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
y[4] = (2 * (b[0] * y[0] + b[1] * y[1] + b[2] * y[2]) - b[3] * y[3]) / b[4];
return y[4];
}
fr = function() {
var b, i;
b = [];
for (i = 0; i < 4; i++) {
b[i] = circs[i].curvature();
}
b[4] = 2 * (b[0] + b[1] + b[2]) - b[3];
if (isNaN(b[4])) {
return 1000.0;
} else {
return 1 / b[4];
}
}
c = board.create('circle', [
[fx, fy], fr
], {
strokeWidth: 1,
name: '',
fillColor: JXG.hsv2rgb(50 * level, 0.8, 0.8),
highlightFillColor: JXG.hsv2rgb(50 * level, 0.5, 0.8),
fillOpacity: 0.5,
highlightFillOpacity: 0.5
});
c.curvature = function() {
return 1 / this.radius;
};
// Recursion
otherCirc([circs[0], circs[1], c, circs[2]], level - 1);
otherCirc([circs[0], circs[2], c, circs[1]], level - 1);
otherCirc([circs[1], circs[2], c, circs[0]], level - 1);
return c;
}
//-------------------------------------------------------
var level = 4;
otherCirc([c0, c1, c2, c3], level);
otherCirc([c3, c1, c2, c0], level);
otherCirc([c0, c2, c3, c1], level);
otherCirc([c0, c1, c3, c2], level);
</jsxgraph>