<iframe src="https://jsxgraph.org/share/iframe/apollonian-circle-packing" style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" name="JSXGraph example: Apollonian circle packing" allowfullscreen ></iframe>
<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 you have to mention The Center of Mobile Learning with Digital Technology in the credits. */ const BOARDID = 'board-0'; var brd = JXG.JSXGraph.initBoard(BOARDID, { boundingbox: [-2.5, 2.5, 2.5, -2.5], showNavigation: false, pan: { enabled: false }, zoom: { enabled: false }}), 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)]; }; var a = brd.create('line', [[0, 0], [2, 0]], {straightFirst: false, straightLast: false, visible: false}), p0 = brd.create('point', [0, 0], {name: '', visible: false}), p1 = brd.create('glider', [1.3, 0, a], {name: 'drag me', showInfobox: false, label: { offset: [-20, 15]}}), b0 = -0.5, r1 = 2 - p1.X(), b1 = 1.0 / r1, r2 = (2.0 - r1), b2 = 1.0 / r2, p2 = brd.create('point', [function () { return p1.X() - 2; }, 0], {name: '', visible: false}), c0 = brd.create('circle', [p0, Math.abs(1.0 / b0)], {strokeWidth: 1, withLabel: false}), c1 = brd.create('circle', [p1, function () { return 2 - p1.X(); }], {strokeWidth: 1, withLabel: false}), c2 = brd.create('circle', [p2, function () { return p1.X(); }], {strokeWidth: 1, withLabel: false}); c0.curvature = function () { return b0; }; // constant c1.curvature = function () { return 1 / (2 - p1.X()); }; c2.curvature = function () { return 1 / (p1.X()); }; var 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]; }; var p3 = brd.create('point', [thirdCircleX, thirdCircleY], {name: '', visible: false}), c3 = brd.create('circle', [p3, thirdCircleRadius], {strokeWidth: 1, withLabel: false}); c3.curvature = function () { return 1.0 / this.radius; }; var otherCirc = function (circs, level) { var p, 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]; } }; p = brd.create('point', [fx, fy], {name: '', visible: false}); c = brd.create('circle', [p, fr], { strokeWidth: 1, fillColor: JXG.hsv2rgb((70 * level) % 360, 0.9, 1), highlightFillColor: JXG.hsv2rgb((70 * level) % 360, 0.9, 0.6), fillOpacity: 0.7, withLabel: false, }); 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 = 3; 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>
/* This example is licensed under a Creative Commons Attribution 4.0 International License. https://creativecommons.org/licenses/by/4.0/ Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits. */ const BOARDID = 'your_div_id'; // Insert your id here! var brd = JXG.JSXGraph.initBoard(BOARDID, { boundingbox: [-2.5, 2.5, 2.5, -2.5], showNavigation: false, pan: { enabled: false }, zoom: { enabled: false }}), 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)]; }; var a = brd.create('line', [[0, 0], [2, 0]], {straightFirst: false, straightLast: false, visible: false}), p0 = brd.create('point', [0, 0], {name: '', visible: false}), p1 = brd.create('glider', [1.3, 0, a], {name: 'drag me', showInfobox: false, label: { offset: [-20, 15]}}), b0 = -0.5, r1 = 2 - p1.X(), b1 = 1.0 / r1, r2 = (2.0 - r1), b2 = 1.0 / r2, p2 = brd.create('point', [function () { return p1.X() - 2; }, 0], {name: '', visible: false}), c0 = brd.create('circle', [p0, Math.abs(1.0 / b0)], {strokeWidth: 1, withLabel: false}), c1 = brd.create('circle', [p1, function () { return 2 - p1.X(); }], {strokeWidth: 1, withLabel: false}), c2 = brd.create('circle', [p2, function () { return p1.X(); }], {strokeWidth: 1, withLabel: false}); c0.curvature = function () { return b0; }; // constant c1.curvature = function () { return 1 / (2 - p1.X()); }; c2.curvature = function () { return 1 / (p1.X()); }; var 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]; }; var p3 = brd.create('point', [thirdCircleX, thirdCircleY], {name: '', visible: false}), c3 = brd.create('circle', [p3, thirdCircleRadius], {strokeWidth: 1, withLabel: false}); c3.curvature = function () { return 1.0 / this.radius; }; var otherCirc = function (circs, level) { var p, 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]; } }; p = brd.create('point', [fx, fy], {name: '', visible: false}); c = brd.create('circle', [p, fr], { strokeWidth: 1, fillColor: JXG.hsv2rgb((70 * level) % 360, 0.9, 1), highlightFillColor: JXG.hsv2rgb((70 * level) % 360, 0.9, 0.6), fillOpacity: 0.7, withLabel: false, }); 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 = 3; 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 width="100%" aspect-ratio="1 / 1" title="Apollonian circle packing" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false"> /* This example is licensed under a Creative Commons Attribution 4.0 International License. https://creativecommons.org/licenses/by/4.0/ Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits. */ var brd = JXG.JSXGraph.initBoard(BOARDID, { boundingbox: [-2.5, 2.5, 2.5, -2.5], showNavigation: false, pan: { enabled: false }, zoom: { enabled: false }}), 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)]; }; var a = brd.create('line', [[0, 0], [2, 0]], {straightFirst: false, straightLast: false, visible: false}), p0 = brd.create('point', [0, 0], {name: '', visible: false}), p1 = brd.create('glider', [1.3, 0, a], {name: 'drag me', showInfobox: false, label: { offset: [-20, 15]}}), b0 = -0.5, r1 = 2 - p1.X(), b1 = 1.0 / r1, r2 = (2.0 - r1), b2 = 1.0 / r2, p2 = brd.create('point', [function () { return p1.X() - 2; }, 0], {name: '', visible: false}), c0 = brd.create('circle', [p0, Math.abs(1.0 / b0)], {strokeWidth: 1, withLabel: false}), c1 = brd.create('circle', [p1, function () { return 2 - p1.X(); }], {strokeWidth: 1, withLabel: false}), c2 = brd.create('circle', [p2, function () { return p1.X(); }], {strokeWidth: 1, withLabel: false}); c0.curvature = function () { return b0; }; // constant c1.curvature = function () { return 1 / (2 - p1.X()); }; c2.curvature = function () { return 1 / (p1.X()); }; var 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]; }; var p3 = brd.create('point', [thirdCircleX, thirdCircleY], {name: '', visible: false}), c3 = brd.create('circle', [p3, thirdCircleRadius], {strokeWidth: 1, withLabel: false}); c3.curvature = function () { return 1.0 / this.radius; }; var otherCirc = function (circs, level) { var p, 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]; } }; p = brd.create('point', [fx, fy], {name: '', visible: false}); c = brd.create('circle', [p, fr], { strokeWidth: 1, fillColor: JXG.hsv2rgb((70 * level) % 360, 0.9, 1), highlightFillColor: JXG.hsv2rgb((70 * level) % 360, 0.9, 0.6), fillOpacity: 0.7, withLabel: false, }); 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 = 3; 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>
// Define the id of your board in BOARDID var brd = JXG.JSXGraph.initBoard(BOARDID, { boundingbox: [-2.5, 2.5, 2.5, -2.5], showNavigation: false, pan: { enabled: false }, zoom: { enabled: false }}), 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)]; }; var a = brd.create('line', [[0, 0], [2, 0]], {straightFirst: false, straightLast: false, visible: false}), p0 = brd.create('point', [0, 0], {name: '', visible: false}), p1 = brd.create('glider', [1.3, 0, a], {name: 'drag me', showInfobox: false, label: { offset: [-20, 15]}}), b0 = -0.5, r1 = 2 - p1.X(), b1 = 1.0 / r1, r2 = (2.0 - r1), b2 = 1.0 / r2, p2 = brd.create('point', [function () { return p1.X() - 2; }, 0], {name: '', visible: false}), c0 = brd.create('circle', [p0, Math.abs(1.0 / b0)], {strokeWidth: 1, withLabel: false}), c1 = brd.create('circle', [p1, function () { return 2 - p1.X(); }], {strokeWidth: 1, withLabel: false}), c2 = brd.create('circle', [p2, function () { return p1.X(); }], {strokeWidth: 1, withLabel: false}); c0.curvature = function () { return b0; }; // constant c1.curvature = function () { return 1 / (2 - p1.X()); }; c2.curvature = function () { return 1 / (p1.X()); }; var 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]; }; var p3 = brd.create('point', [thirdCircleX, thirdCircleY], {name: '', visible: false}), c3 = brd.create('circle', [p3, thirdCircleRadius], {strokeWidth: 1, withLabel: false}); c3.curvature = function () { return 1.0 / this.radius; }; var otherCirc = function (circs, level) { var p, 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]; } }; p = brd.create('point', [fx, fy], {name: '', visible: false}); c = brd.create('circle', [p, fr], { strokeWidth: 1, fillColor: JXG.hsv2rgb((70 * level) % 360, 0.9, 1), highlightFillColor: JXG.hsv2rgb((70 * level) % 360, 0.9, 0.6), fillOpacity: 0.7, withLabel: false, }); 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 = 3; 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 you have to mention The Center of Mobile Learning with Digital Technology in the credits.