31:[] 2f:{"title":"Inequality of the Pythagorean Means","cells":[{"id":0,"value":"# Inequality of the Pythagorean Means","pinned":false,"hidden":false,"mode":"md"},{"id":40,"value":"html`\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":11,"value":"viewof a = Inputs.range([1, (width/2)-1], {label: \"a\", step: 1, value: 200})","pinned":false,"hidden":false,"mode":"ojs"},{"id":14,"value":"viewof b = Inputs.range([1, width/2], {label: \"b\", step: 1, value: 50})","pinned":false,"hidden":false,"mode":"ojs"},{"id":257,"value":"For a=${a} and b=${b}:\n- The sum is ${d}.\n- The quadratic mean is ${meanQuadratic([a,b]).toFixed(2)}.\n- The arithmetic mean is ${meanArithmetic([a,b]).toFixed(2)}.\n- The geometric mean is ${meanGeometric([a,b]).toFixed(2)}.\n- The harmonic mean is ${meanHarmonic([a,b]).toFixed(2)}.\n- H < G < A < Q is ${meanHarmonic([a,b]) < meanGeometric([a,b]) && meanGeometric([a,b]) < meanArithmetic([a,b]) && meanArithmetic([a,b]) < meanQuadratic([a,b])}.","pinned":false,"hidden":false,"mode":"md"},{"id":32,"value":"### Calculations","pinned":false,"hidden":false,"mode":"md"},{"id":44,"value":"width = 500","pinned":false,"hidden":false,"mode":"ojs"},{"id":34,"value":"height = 500","pinned":false,"hidden":false,"mode":"ojs"},{"id":154,"value":"d = a+b","pinned":false,"hidden":false,"mode":"ojs"},{"id":42,"value":"c = Object.create({x: (d/2)+1, y: height/2, r: d/2})","pinned":false,"hidden":false,"mode":"ojs"},{"id":414,"value":"point_A = Object.create({x: meanArithmetic([a,b]), y: height/2})","pinned":false,"hidden":false,"mode":"ojs"},{"id":406,"value":"point_ab = Object.create({x: a, y: height/2})","pinned":false,"hidden":false,"mode":"ojs"},{"id":421,"value":"point_G = Object.create({\n x: a, \n y: c.y - meanGeometric([a,b])\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":545,"value":"// scale the endpoint of the harmonic mean line on the coordinate plane\nharmonicScalingFactor = meanHarmonic([a,b]) / Math.sqrt(Math.pow(c.x-point_G.x,2)+Math.pow(c.y-point_G.y,2))","pinned":false,"hidden":false,"mode":"ojs"},{"id":426,"value":"point_harmonicTriangle = Object.create({\n x: point_G.x + (c.x - point_G.x) * harmonicScalingFactor,\n y: point_G.y + (c.y - point_G.y) * harmonicScalingFactor\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":91,"value":"// from the start of the chart, length a\nline_a = Object.create({x1: 0, y1: c.y, x2: a, y2: c.y, style: \"stroke: orange\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":94,"value":"// from the end of a, for length b\nline_b = Object.create({x1: a, y1: c.y, x2: a+b, y2: c.y, style: \"stroke: brown\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":270,"value":"// arithmetic mean, from the midpoint of the circle straight down\nlineA = Object.create({x1: meanArithmetic([a,b]), x2: meanArithmetic([a,b]), y1: height/2, y2: (height/2)-(d/2), style: \"stroke: red\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":251,"value":"// geometric mean, from the intersection of ab straight up to the intersection with the circle\nlineG = Object.create({x1: a, y1: c.y, x2: a, y2: c.y-meanGeometric([a,b]), style: \"stroke: blue\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":283,"value":"// harmonic mean, from the top of G, partially to the bottom of A\nlineH = Object.create({\n x1: point_G.x, \n y1: point_G.y, \n x2: point_harmonicTriangle.x, \n y2: point_harmonicTriangle.y, style: \"stroke: purple\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":288,"value":"// quadratic mean, or root mean square (RMS), from ab to the top of A\nlineQ = Object.create({x1: a, x2: meanArithmetic([a,b]), y1: height/2, y2: (height/2)-meanArithmetic([a,b]), style: \"stroke: green\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":331,"value":"harmonicTriangleHyp = Object.create({\n x1: meanArithmetic([a,b]), \n y1: height/2, \n x2: point_harmonicTriangle.x, \n y2: point_harmonicTriangle.y,\n style: \"stroke: black; stroke-dasharray: 2 2\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":338,"value":"harmonicTriangleLine = Object.create({\n x1: a, y1: height/2, \n x2: point_harmonicTriangle.x, y2: point_harmonicTriangle.y,\n style: \"stroke: black; stroke-dasharray: 2 2\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":26,"value":"### Formulas","pinned":false,"hidden":false,"mode":"md"},{"id":160,"value":"lineGenerator = (lineObj) => {\n return ``\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":5,"value":"// the harmonic mean should be used for ratios and rates\n// for example, different speeds for the same distance, the density of alloys, resistors in parallel, and price/earnings ratios.\nmeanHarmonic = (arr) => {\n let d = 0\n arr.forEach(i => {\n d += 1/i\n })\n return arr.length / d\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":294,"value":"meanGeometric = (arr) => {\n let p = 1\n arr.forEach(i => {p = p*i})\n return Math.pow(Math.abs(p),1/arr.length)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":220,"value":"meanArithmetic = (arr) => {\n let n = 0\n arr.forEach(i => {n += i})\n return n/arr.length\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":296,"value":"meanQuadratic = (arr) => {\n let p = 1\n arr.forEach(i => {p += i**2})\n return Math.sqrt((1/arr.length)*p)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":588,"value":"// tweaked from https://stackoverflow.com/a/53660837\nfunction median(arr) {\n const sorted = Array.from(arr).sort((a, b) => a - b);\n const middle = Math.floor(sorted.length / 2);\n\n if (sorted.length % 2 === 0) {\n return (sorted[middle - 1] + sorted[middle]) / 2;\n }\n\n return sorted[middle];\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":592,"value":"sum = (arr) => {\n let s = 0\n arr.forEach(i => s += Number(i))\n return s\n}","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}