Including all physical drafting steps as in http://www.mathopenref.com/printinpentagon.html
See also http://bl.ocks.org/garciadelcastillo/f0dc5b79d02775317041
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August 29, 2015 14:13
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Pentagon inscribed in circle 1
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| <!DOCTYPE html> | |
| <meta charset="utf-8"> | |
| <html> | |
| <head> | |
| <style> | |
| body { | |
| margin: 0; | |
| padding: 0; | |
| } | |
| #sketchpadDiv { | |
| position: absolute; | |
| width: 100%; | |
| height: 100%; | |
| border: 1px solid #000; | |
| -webkit-box-sizing: border-box; | |
| -moz-box-sizing: border-box; | |
| box-sizing: border-box; | |
| } | |
| #sketchpadCanvas { | |
| position: absolute; | |
| } | |
| </style> | |
| </head> | |
| <body> | |
| <div id="sketchpadDiv"> | |
| <canvas id="sketchpadCanvas"></canvas> | |
| </div> | |
| </body> | |
| <script type="text/javascript" src="https://code.jquery.com/jquery-2.1.1.min.js"></script> | |
| <script type="text/javascript" src="http://www.garciadelcastillo.es/sketchpad/sketchpad-0.0.2.js"></script> | |
| <script> | |
| /** | |
| * CONSTRUCTION OF REGULAR PENTAGON INSCRIBED IN CIRCLE | |
| * Inspired by http://www.mathopenref.com/printinpentagon.html | |
| */ | |
| // Initialize Sketchpad | |
| var pad = new Sketchpad('sketchpadCanvas'); | |
| // Define some styles | |
| var node = new pad.Style({ | |
| fill: 'rgba(127, 127, 127, 0.3)' | |
| }); | |
| var thin = new pad.Style({ | |
| strokeWidth: 0.5 | |
| }); | |
| var thick = new pad.Style({ | |
| strokeWidth: 3.0 | |
| }); | |
| pad.currentStyle(thin); | |
| // Slider to control pentagon's radius | |
| var pentagonRadius = Slider(pad, 25, 25, 150, 0, 400, 200); // see below | |
| // Step 0: Draw circle | |
| var O = new pad.Node(pad.width.value / 2, pad.height.value / 2), | |
| circle = pad.Circle.centerRadius(O, pentagonRadius); | |
| M = pad.Node.along(circle, 0.25), | |
| node.applyTo(O, M); | |
| // Step 1: Draw diameter | |
| var OM = pad.Line.between(M, O), | |
| interOM = pad.Point.intersection(OM, circle), | |
| C = interOM.items[1], | |
| MC = pad.Line.between(M, C); | |
| // Step 2: Construct a perpendicular | |
| var doubleRadius = pad.Measure.compose(pentagonRadius, function() { | |
| return 2 * pentagonRadius.value; | |
| }), | |
| circleM = pad.Circle.centerRadius(M, doubleRadius), | |
| circleC = pad.Circle.centerRadius(C, doubleRadius), | |
| interMC = pad.Point.intersection(circleM, circleC), | |
| A1 = interMC.items[1], | |
| perpendicular = pad.Line.between(O, A1); | |
| // Step 3: Point crossing the circle | |
| var interA1O = pad.Point.intersection(perpendicular, circle), | |
| S = interA1O.items[1]; | |
| // Step 4: Find the midpoint | |
| var SO = pad.Line.between(S, O), | |
| L = pad.Point.along(SO, 0.5); | |
| // Step 5: Draw a circle | |
| var halfRadius = pad.Measure.compose(pentagonRadius, function() { | |
| return 0.5 * pentagonRadius.value; | |
| }), | |
| circleL = pad.Circle.centerRadius(L, halfRadius); | |
| // Step 6: Find ints from M | |
| var ML = pad.Line.between(M, L), | |
| interMLcircleL = pad.Point.intersection(ML, circleL), | |
| P = interMLcircleL.items[0], | |
| N = interMLcircleL.items[1]; | |
| // Step 7: Measure MP | |
| var MPdist = pad.Measure.distance(M, P); | |
| // Step 8: Find intersections with MP circle | |
| var circleMP = pad.Circle.centerRadius(M, MPdist), | |
| interAE = pad.Point.intersection(circleMP, circle), | |
| A = interAE.items[1], | |
| E = interAE.items[0]; | |
| // Step 9: Measure MN | |
| var MNdist = pad.Measure.distance(M, N); | |
| // Step 10: Find ints with MN circle | |
| var circleMN = pad.Circle.centerRadius(M, MNdist), | |
| interBD = pad.Point.intersection(circleMN, circle), | |
| B = interBD.items[1], | |
| D = interBD.items[0]; | |
| // Draw the pentagon | |
| pad.currentStyle(thick); | |
| var AB = pad.Line.between(A, B), | |
| BC = pad.Line.between(B, C), | |
| CD = pad.Line.between(C, D), | |
| DE = pad.Line.between(D, E), | |
| EA = pad.Line.between(E, A); | |
| pad.showPoints(); | |
| pad.tagPoints(); | |
| pad.update = function() { | |
| // do nothing | |
| }; | |
| /** | |
| * A quick implementation of a Slider class based on Sketchpad's capabilities | |
| * Returns a Measure object defined by the slider's state | |
| */ | |
| function Slider(pad, x, y, width, minValue, maxValue, startValue, options) { | |
| var axis = new pad.Line(x, y, x + width, y); | |
| var t = (startValue - minValue) / (maxValue - minValue); | |
| var handle = pad.Node.along(axis, t, {clamp: true}); | |
| var measure = pad.Measure.compose(handle, function() { | |
| return minValue + (maxValue - minValue) * (handle.x - x) / width; // handle gets scoped! serendipity! | |
| }); | |
| var label = pad.Label.from(measure, {round: true}), | |
| tag = new pad.Tag.on(handle, label); | |
| return measure; | |
| }; | |
| </script> | |
| </html> |
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