30:T545,function plot(functions, range, closed) { const fns = _.isArray(functions) ? functions : [functions]; // Native function if (_.isFunction(fns[0])) { if (!range) { throw new Error("Missing second parameter ([rangeMin, rangeMax])"); } // Generate x-axis const points = ((min, max) => { const p = []; const count = 1000; const step = (max - min) / count; for (let i = 0; i < count; ++i) { p.push(min + i * step); } return p; })(range[0], range[1]); const data = _.flatten( fns.map((fn, i) => { return points.map((x) => { return { x, y: fn(x), z: i, stroke: "s-" + i }; }); }) ); return Plot.plot({ width, grid: true, marks: [ Plot.line(data, { x: "x", y: "y", z: "z", stroke: "stroke" }) ] }); } // String function let target = DOM.element("div"); _functionPlot({ data: fns.map((fn) => { return { fn, range, closed: !!closed // derivative: { // fn: math.derivative(fn, "x").toString(), // updateOnMouseMove: true // } }; }), width, grid: true, target }); return target; }31:[{"id":"9614f18284f60b07ffcbbff3438c2133eddb193fa69dc6459c476b879276a68b8effb1f7610de8abdb382a0b1c6d084a2c014998752cc127966e746df9c6a273","href":"https://static.observableusercontent.com/files/9614f18284f60b07ffcbbff3438c2133eddb193fa69dc6459c476b879276a68b8effb1f7610de8abdb382a0b1c6d084a2c014998752cc127966e746df9c6a273","name":"image@6.png","type":"image/png","lastModified":1690046295764.444,"size":139457}] 2e:{"title":"Math","cells":[{"id":19,"value":"# Math","pinned":false,"hidden":false,"mode":"md"},{"id":438,"value":"Math utilities for cleaner notebooks.","pinned":false,"hidden":false,"mode":"md"},{"id":445,"value":"```js\nimport { roundTo, roundDownTo, roundUpTo, ... } from \"@jerryjappinen/math\"\n```","pinned":false,"hidden":false,"mode":"md"},{"id":2537,"value":"function convert(value, originUnitString, targetUnitString) {\n const mathjsOriginUnit = math.unit(originUnitString);\n const mathjsTargetUnit = math.unit(targetUnitString);\n const mathjsValue = math.unit(value, mathjsOriginUnit);\n return mathjsValue.toNumber(mathjsTargetUnit);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":2541,"value":"function accumulate(value, amount = 1, times = 1) {\n return times < 1 ? value : accumulate(value * amount, amount, times - 1);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":433,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":2374,"value":"### Formatting","pinned":false,"hidden":false,"mode":"md"},{"id":2397,"value":"formatNumber(1234.123456789)","pinned":true,"hidden":false,"mode":"ojs"},{"id":2392,"value":"formatCurrency(1234.123456789)","pinned":true,"hidden":false,"mode":"ojs"},{"id":2390,"value":"roundCurrency(1234.123456789)","pinned":true,"hidden":false,"mode":"ojs"},{"id":2383,"value":"function roundCurrency(value, rounding) {\n const r =\n rounding ||\n (value > 10000 ? 500 : value > 1000 ? 100 : value > 100 ? 10 : 1);\n return roundTo(value, r);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2381,"value":"function formatCurrency(value, rounding, currency) {\n const options = {\n style: \"currency\",\n currency: currency || \"EUR\"\n }\n\n // These options are needed to round to whole numbers if that's what you want.\n if (!rounding || rounding >= 1) {\n options.minimumFractionDigits = 0, // (this suffices for whole numbers, but will print 2500.10 as $2,500.1)\n options.maximumFractionDigits = 0 // (causes 2500.99 to be printed as $2,501)\n }\n\n const formatter = new Intl.NumberFormat(\"fi-FI\", options);\n\n return formatter.format(roundCurrency(value, rounding));\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2376,"value":"function formatNumber(value) {\n const options = {\n maximumSignificantDigits: 4\n }\n\n // These options are needed to round to whole numbers if that's what you want.\n // if (!rounding || rounding >= 1) {}\n options.minimumFractionDigits = 0 // (this suffices for whole numbers, but will print 2500.10 as $2,500.1)\n options.maximumFractionDigits = 0 // (causes 2500.99 to be printed as $2,501)\n\n const formatter = new Intl.NumberFormat(\"fi-FI\", options);\n\n return formatter.format(value);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2372,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":1965,"value":"# Random","pinned":false,"hidden":false,"mode":"md"},{"id":1986,"value":"Deal with pseudo-randomness.","pinned":false,"hidden":false,"mode":"md"},{"id":1974,"value":"function randomFloat () {\n return _.random(1, true)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1990,"value":"randomFloat()","pinned":true,"hidden":false,"mode":"ojs"},{"id":1978,"value":"function randomIndex (...arr) {\n const l = _.flatten(arr).length\n if (!l) {\n return null\n }\n return Math.round(randomFloat() * (l-1))\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1994,"value":"randomIndex(['a', 'b', 'c', 'd'])","pinned":true,"hidden":false,"mode":"ojs"},{"id":2424,"value":"function randomValue (...arr) {\n return _.flatten(arr)[randomIndex(...arr)]\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2426,"value":"randomValue(['a', 'b', 'c', 'd'])","pinned":true,"hidden":false,"mode":"ojs"},{"id":2434,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":1967,"value":"function getSeed (seed) {\n return seedrandom(seed)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1976,"value":"function seededRandomFloat (seed) {\n return getSeed(seed)()\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1992,"value":"seededRandomFloat('2023-01-01')","pinned":true,"hidden":false,"mode":"ojs"},{"id":1980,"value":"function seededRandomIndex (seed, ...arr) {\n const l = _.flatten(arr).length\n if (!l) {\n return null\n }\n return Math.round(seededRandomFloat(seed) * (l-1))\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1996,"value":"seededRandomIndex('2023-01-01', ['a', 'b', 'c', 'd'])","pinned":true,"hidden":false,"mode":"ojs"},{"id":2411,"value":"function seededRandomValue (seed, ...arr) {\n return _.flatten(arr)[seededRandomIndex(seed, ...arr)]\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2413,"value":"seededRandomValue('2023-01-01', ['a', 'b', 'c', 'd'])","pinned":true,"hidden":false,"mode":"ojs"},{"id":2188,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":2184,"value":"Simplified seeded shuffling. Note that this is not secure, and doesn't work with string seeds.\n\nhttps://stackoverflow.com/questions/16801687/javascript-random-ordering-with-seed","pinned":false,"hidden":false,"mode":"md"},{"id":2197,"value":"shuffleSeeded(_.range(0, 10), new Date())","pinned":true,"hidden":false,"mode":"ojs"},{"id":2182,"value":"function shuffleSeeded(array, seed) {\n var m = array.length,\n t,\n i;\n\n function getRand(seed) {\n var x = Math.sin(seed++) * 10000;\n return x - Math.floor(x);\n }\n\n // While there remain elements to shuffle\n while (m) {\n // Pick a remaining element\n i = Math.floor(getRand(seed) * m--);\n\n // And swap it with the current element\n t = array[m];\n array[m] = array[i];\n array[i] = t;\n ++seed;\n }\n\n return array;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1963,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":1330,"value":"# Plot","pinned":false,"hidden":false,"mode":"md"},{"id":1403,"value":"$30","pinned":false,"hidden":false,"mode":"ojs"},{"id":1894,"value":"plot([sin, cos], [-pi * 2, pi * 2])","pinned":true,"hidden":false,"mode":"ojs"},{"id":1812,"value":"plot(\n [\n pow,\n (x) => pow(x, 1.2),\n (x) => pow(x, 1.4),\n (x) => pow(x, 1.6),\n root\n ],\n [0, 20]\n)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1360,"value":"plot('0.5x^2 + 4x +2')","pinned":true,"hidden":false,"mode":"ojs"},{"id":1371,"value":"plot(\"0.75x^2 + 4x +2\", [-3, 2])","pinned":true,"hidden":false,"mode":"ojs"},{"id":1383,"value":"plot([\"0.75x^2 + 4x +2\", \"x^2 + 3x + 2\"], [-3, 2], true)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1325,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":187,"value":"# Constants","pinned":false,"hidden":false,"mode":"md"},{"id":427,"value":"e = 2.718281828459045","pinned":false,"hidden":false,"mode":"ojs"},{"id":199,"value":"pi = Math.PI","pinned":false,"hidden":false,"mode":"ojs"},{"id":732,"value":"[Golden ratio](https://en.wikipedia.org/wiki/Mathematical_constant#The_golden_ratio_%CF%86), ${tex`\\phi`}:","pinned":false,"hidden":false,"mode":"md"},{"id":468,"value":"phi = 1.61803398874989484820","pinned":false,"hidden":false,"mode":"ojs"},{"id":1674,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":1669,"value":"# Series","pinned":false,"hidden":false,"mode":"md"},{"id":1783,"value":"See something [you like](https://en.wikipedia.org/wiki/List_of_mathematical_series)? Leave a comment.","pinned":false,"hidden":false,"mode":"md"},{"id":1697,"value":"function fibonacci(n) {\n const series = fibonaccis(n);\n return series[series.length - 1];\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1686,"value":"function fibonaccis(n) {\n const numbers = [0, 1];\n\n if (n <= 1) {\n return n ? [0] : [];\n }\n\n for (let i = 0; i < n - 2; ++i) {\n numbers.push(\n nextFibonacci(numbers[numbers.length - 1], numbers[numbers.length - 2])\n );\n }\n\n return numbers;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1668,"value":"function nextFibonacci (prev1, prev2) {\n return prev1 + prev2\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1694,"value":"fibonaccis(14)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1702,"value":"fibonacci(14)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1709,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":1717,"value":"isPrime = math.isPrime","pinned":false,"hidden":false,"mode":"ojs"},{"id":1716,"value":"// NOTE: this is extremely naive and slow with larger numbers\nfunction nextPrime(n, iMax) {\n // Loop runs as long as prime is not found or we reach max number of iterations\n let i = n + 1;\n for (; !isPrime(i) && (!iMax || i < n + iMax); ++i) {}\n\n //\n return i;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1759,"value":"nextPrime(7)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1737,"value":"function primes (n, start) {\n const numbers = []\n\n for (let i = 0; i < n; ++i) {\n numbers.push(nextPrime(numbers[i-1] || start || 0))\n }\n\n return numbers\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1743,"value":"primes(10)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1741,"value":"primes(5, 100000)","pinned":true,"hidden":false,"mode":"ojs"},{"id":469,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":753,"value":"# SI prefixes","pinned":false,"hidden":false,"mode":"md"},{"id":693,"value":"yotta = Math.pow(10, 24)","pinned":false,"hidden":false,"mode":"ojs"},{"id":686,"value":"zetta = Math.pow(10, 21)","pinned":false,"hidden":false,"mode":"ojs"},{"id":684,"value":"exa = Math.pow(10, 18)","pinned":false,"hidden":false,"mode":"ojs"},{"id":683,"value":"peta = Math.pow(10, 15)","pinned":false,"hidden":false,"mode":"ojs"},{"id":176,"value":"tera = Math.pow(10, 12)","pinned":false,"hidden":false,"mode":"ojs"},{"id":175,"value":"giga = Math.pow(10, 9)","pinned":false,"hidden":false,"mode":"ojs"},{"id":160,"value":"mega = Math.pow(10, 6)","pinned":false,"hidden":false,"mode":"ojs"},{"id":161,"value":"kilo = Math.pow(10, 3)","pinned":false,"hidden":false,"mode":"ojs"},{"id":409,"value":"hecto = Math.pow(10, 2)","pinned":false,"hidden":false,"mode":"ojs"},{"id":227,"value":"desi = Math.pow(10, -1)","pinned":false,"hidden":false,"mode":"ojs"},{"id":225,"value":"centi = Math.pow(10, -2)","pinned":false,"hidden":false,"mode":"ojs"},{"id":169,"value":"milli = Math.pow(10, -3)","pinned":false,"hidden":false,"mode":"ojs"},{"id":170,"value":"micro = Math.pow(10, -6)","pinned":false,"hidden":false,"mode":"ojs"},{"id":150,"value":"nano = Math.pow(10, -9)","pinned":false,"hidden":false,"mode":"ojs"},{"id":153,"value":"pico = Math.pow(10, -12)","pinned":false,"hidden":false,"mode":"ojs"},{"id":155,"value":"femto = Math.pow(10, -15)","pinned":false,"hidden":false,"mode":"ojs"},{"id":700,"value":"atto = Math.pow(10, -18)","pinned":false,"hidden":false,"mode":"ojs"},{"id":701,"value":"zepto = Math.pow(10, -21)","pinned":false,"hidden":false,"mode":"ojs"},{"id":703,"value":"yocto = Math.pow(10, -24)","pinned":false,"hidden":false,"mode":"ojs"},{"id":748,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":457,"value":"# Rounding and manipulation","pinned":false,"hidden":false,"mode":"md"},{"id":2470,"value":"function fitToRange(floatValue, min, max) {\n return (max - min) * floatValue + min;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2478,"value":"function fitToFloat(value, min, max) {\n return (value - min) / (max - min);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2479,"value":"fitToFloat(25, 0, 75)","pinned":true,"hidden":false,"mode":"ojs"},{"id":2475,"value":"fitToRange(0.5, 100, 200)","pinned":true,"hidden":false,"mode":"ojs"},{"id":2471,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":289,"value":"function min (...components) {\n return Math.min(..._.flatten(components))\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1096,"value":"min(2, 4, 8)","pinned":true,"hidden":false,"mode":"ojs"},{"id":290,"value":"function max (...components) {\n return Math.max(..._.flatten(components))\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1097,"value":"max(2, 4, 8)","pinned":true,"hidden":false,"mode":"ojs"},{"id":405,"value":"function abs (...components) {\n return components.length > 1 ? components.map(Math.abs) : Math.abs(components[0])\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1106,"value":"abs(-90)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1147,"value":"abs(-90, 20, -20)","pinned":true,"hidden":false,"mode":"ojs"},{"id":817,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":69,"value":"function round(number) {\n return Math.round(number);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1110,"value":"round(2.1)","pinned":true,"hidden":false,"mode":"ojs"},{"id":66,"value":"function roundDown(number) {\n return Math.floor(number);\n}\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":1114,"value":"roundDown(2.8)","pinned":true,"hidden":false,"mode":"ojs"},{"id":71,"value":"function roundUp(number) {\n return Math.ceil(number);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1121,"value":"roundUp(2.2)","pinned":true,"hidden":false,"mode":"ojs"},{"id":843,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":103,"value":"Round to nearest `0.01`, `0.5`, `20` or whatever you like:","pinned":false,"hidden":false,"mode":"md"},{"id":34,"value":"function roundTo (number, roundTo) {\n return Math.round(number * getRoundingMultiplier(roundTo)) / getRoundingMultiplier(roundTo)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1254,"value":"roundTo(pi, 0.01)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1262,"value":"roundTo(82839, 1000)","pinned":true,"hidden":false,"mode":"ojs"},{"id":42,"value":"function roundDownTo (number, roundTo) {\n return Math.floor(number * getRoundingMultiplier(roundTo)) / getRoundingMultiplier(roundTo)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":44,"value":"function roundUpTo (number, roundTo) {\n return Math.ceil(number * getRoundingMultiplier(roundTo)) / getRoundingMultiplier(roundTo)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":0,"value":"function getRoundingMultiplier (roundTo) {\n return 10 / (10 * roundTo)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2153,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":2157,"value":"Present a base-ten number with a different digit placement. So for example, present `100000` as `100` k instead.","pinned":false,"hidden":false,"mode":"md"},{"id":2066,"value":"function toDigit(number, base, decimalBases) {\n if (decimalBases === 0) {\n return roundTo(number, base) / base;\n }\n\n if (decimalBases) {\n const rounding = ten(decimalBases);\n\n if (decimalBases > 0) {\n return roundTo(number, base / rounding) / base;\n }\n\n if (decimalBases < 0) {\n return roundTo(number, base / rounding) / base;\n }\n }\n\n return number / base;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2072,"value":"toDigit(123000, 1000)","pinned":true,"hidden":false,"mode":"ojs"},{"id":2161,"value":"toDigit(256000, thousand)","pinned":false,"hidden":false,"mode":"ojs"},{"id":2079,"value":"toDigit(0.0123456, 0.001)","pinned":true,"hidden":false,"mode":"ojs"},{"id":2095,"value":"toDigit(0.0123456, 0.001, 2)","pinned":true,"hidden":false,"mode":"ojs"},{"id":2138,"value":"toDigit(0.0123456, ten(-6), 0)","pinned":true,"hidden":false,"mode":"ojs"},{"id":2250,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":2234,"value":"Sometimes numbers in JavaScript suffer from a floating point precision problem and you will see very long decimals where you expect something else. But if you sacrifice some precision, they will go away:","pinned":false,"hidden":false,"mode":"md"},{"id":2331,"value":"viewof _example_x = Inputs.range([0.01, 10], {step: 0.01})","pinned":false,"hidden":false,"mode":"ojs"},{"id":2254,"value":"_example_x * 0.2","pinned":true,"hidden":false,"mode":"ojs"},{"id":2268,"value":"fix(_example_x * 0.2)","pinned":true,"hidden":false,"mode":"ojs"},{"id":2238,"value":"fix = stabilizeNumber","pinned":true,"hidden":false,"mode":"ojs"},{"id":2231,"value":"stabilizeNumber = (num) => {\n // return parseFloat(num).toPrecision(12);\n return roundTo(num, 0.00000000000001)\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":302,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":794,"value":"# Common calculations","pinned":false,"hidden":false,"mode":"md"},{"id":231,"value":"function pow (x, a) {\n return math.pow(x, typeof a === 'undefined' ? 2 : a)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":849,"value":"pow(2)","pinned":true,"hidden":false,"mode":"ojs"},{"id":898,"value":"pow(3, 4)","pinned":true,"hidden":false,"mode":"ojs"},{"id":892,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":886,"value":"Powers of two, eight and ten:","pinned":false,"hidden":false,"mode":"md"},{"id":1292,"value":"function two (power) {\n return pow(2, power || 1)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1301,"value":"two(6)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1293,"value":"function eight (power) {\n return pow(8, power || 1)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1307,"value":"eight(4)","pinned":true,"hidden":false,"mode":"ojs"},{"id":413,"value":"function ten (power) {\n return pow(10, power || 1)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":856,"value":"ten(3)","pinned":true,"hidden":false,"mode":"ojs"},{"id":2033,"value":"thousand = ten(3)","pinned":true,"hidden":false,"mode":"ojs"},{"id":2036,"value":"million = ten(6)","pinned":true,"hidden":false,"mode":"ojs"},{"id":2040,"value":"billion = ten(9)","pinned":true,"hidden":false,"mode":"ojs"},{"id":2042,"value":"trillion = ten(12)","pinned":true,"hidden":false,"mode":"ojs"},{"id":905,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":907,"value":"Square, cubic or any other roots:","pinned":false,"hidden":false,"mode":"md"},{"id":258,"value":"function root (x, a) {\n return math.nthRoot(x, typeof a === 'undefined' ? 2 : a)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":860,"value":"root(4)","pinned":true,"hidden":false,"mode":"ojs"},{"id":864,"value":"root(81, 4)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1029,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":1026,"value":"function sum (...components) {\n const arr = _.isArray(components[0]) ? components[0] : components\n\n return arr.reduce((total, c) => {\n return total + c\n }, 0)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1036,"value":"sum(1, 2, 3, 4)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1058,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":56,"value":"function sums(...components) {\n const arr = _.isArray(components[0]) ? components[0] : components\n \n let result = [];\n \n arr.reduce(function(a, b, i) {\n return (result[i] = a + b);\n }, 0);\n \n return result;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1043,"value":"sums(1, 2, 3, 4)","pinned":true,"hidden":false,"mode":"ojs"},{"id":2350,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":2360,"value":"Σ = sigma","pinned":true,"hidden":false,"mode":"ojs"},{"id":2351,"value":"// https://betterprogramming.pub/maths-sigma-%CF%83-symbol-explained-with-javascript-a10f78c9786f\nfunction sigma (lowerBound, upperBoundInclusive, iterator) {\n let accumulator = 0;\n\n for(let i = lowerBound; i <= upperBoundInclusive; ++i) {\n accumulator += iterator(i);\n }\n\n return accumulator;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2364,"value":"sigma(1, 10, (i) => { return i * 2 })","pinned":true,"hidden":false,"mode":"ojs"},{"id":1656,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":1658,"value":"function avg(...inputs) {\n const arr = _.isArray(inputs[0]) ? inputs[0] : inputs\n \n return sum(arr) / arr.length;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1680,"value":"avg(1, 3, 5)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1940,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":1946,"value":"function median(...inputs) {\n const arr = _.isArray(inputs[0]) ? inputs[0] : inputs;\n\n const quickselect = (arr, k) => {\n // Select the kth element in arr\n // arr: List of numerics\n // k: Index\n // return: The kth element (in numerical order) of arr\n if (arr.length == 1) return arr[0];\n else {\n const pivot = arr[0];\n const lows = arr.filter((e) => e < pivot);\n const highs = arr.filter((e) => e > pivot);\n const pivots = arr.filter((e) => e == pivot);\n if (k < lows.length)\n // the pivot is too high\n return quickselect(lows, k);\n else if (k < lows.length + pivots.length)\n // We got lucky and guessed the median\n return pivot;\n // the pivot is too low\n else return quickselect(highs, k - lows.length - pivots.length);\n }\n };\n\n const L = arr.length,\n halfL = L / 2;\n if (L % 2 == 1) return quickselect(arr, halfL);\n else return 0.5 * (quickselect(arr, halfL - 1) + quickselect(arr, halfL));\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1953,"value":"median(1, 2, 2, 2, 2, 9, 100)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1060,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":1049,"value":"function product (...components) {\n const arr = _.isArray(components[0]) ? components[0] : components\n\n return arr.reduce((total, c) => {\n return total * c\n }, 1)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1053,"value":"product(1, 2, 3, 4)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1453,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":1470,"value":"log = math.log","pinned":false,"hidden":false,"mode":"ojs"},{"id":1475,"value":"function ln (val) {\n return log(val, e)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1795,"value":"function log10 (val) {\n return log(val, 10)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1802,"value":"logTen = log10","pinned":false,"hidden":false,"mode":"ojs"},{"id":1507,"value":"log(10000, 10)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1797,"value":"log10(10000)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1502,"value":"ln(e)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1517,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":1467,"value":"factorial = math.factorial","pinned":false,"hidden":false,"mode":"ojs"},{"id":1495,"value":"factorial(4)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1468,"value":"gamma = math.gamma","pinned":false,"hidden":false,"mode":"ojs"},{"id":1485,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":1451,"value":"More functions (powered by [math.js](https://mathjs.org/))","pinned":false,"hidden":false,"mode":"md"},{"id":1479,"value":"math.matrix([1, 4, 9, 16, 25])","pinned":false,"hidden":false,"mode":"ojs"},{"id":1523,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":1529,"value":"# Matrices","pinned":false,"hidden":false,"mode":"md"},{"id":1531,"value":"Use matrix functionality from [math.js](https://mathjs.org/docs/datatypes/matrices.html):","pinned":false,"hidden":false,"mode":"md"},{"id":1553,"value":"math.matrix([1, 2, 3, 4])","pinned":true,"hidden":false,"mode":"ojs"},{"id":1557,"value":"root(math.matrix([[1, 2], [3, 4]]), 2).valueOf()","pinned":true,"hidden":false,"mode":"ojs"},{"id":1600,"value":"pow(math.matrix([[1, 2], [3, 4]]), 2).valueOf()","pinned":true,"hidden":false,"mode":"ojs"},{"id":296,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":788,"value":"# Trigonometry","pinned":false,"hidden":false,"mode":"md"},{"id":915,"value":"All JavaScript math functions use radians by default. Convert radians to degrees and vice versa:","pinned":false,"hidden":false,"mode":"md"},{"id":82,"value":"function toDeg(radians) {\n return radians * (180 / Math.PI);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1275,"value":"toDeg(pi)","pinned":true,"hidden":false,"mode":"ojs"},{"id":84,"value":"function toRad(degrees) {\n return degrees * (Math.PI / 180);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1271,"value":"toRad(180)","pinned":false,"hidden":false,"mode":"ojs"},{"id":191,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":935,"value":"Trigonometry using radians:","pinned":false,"hidden":false,"mode":"md"},{"id":315,"value":"cos = Math.cos","pinned":false,"hidden":false,"mode":"ojs"},{"id":955,"value":"cos(pi)","pinned":true,"hidden":false,"mode":"ojs"},{"id":317,"value":"sin = Math.sin","pinned":false,"hidden":false,"mode":"ojs"},{"id":965,"value":"sin(pi / 2)","pinned":true,"hidden":false,"mode":"ojs"},{"id":319,"value":"tan = Math.tan","pinned":false,"hidden":false,"mode":"ojs"},{"id":382,"value":"acos = Math.acos","pinned":false,"hidden":false,"mode":"ojs"},{"id":380,"value":"asin = Math.asin","pinned":false,"hidden":false,"mode":"ojs"},{"id":364,"value":"atan = Math.atan","pinned":false,"hidden":false,"mode":"ojs"},{"id":807,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":939,"value":"Trigonometry using degrees:","pinned":false,"hidden":false,"mode":"md"},{"id":321,"value":"function cosDeg (degrees) {\n return cos(toRadians(degrees))\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1010,"value":"cosDeg(180)","pinned":true,"hidden":false,"mode":"ojs"},{"id":323,"value":"function sinDeg (degrees) {\n return sin(toRadians(degrees))\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1019,"value":"sinDeg(90)","pinned":true,"hidden":false,"mode":"ojs"},{"id":325,"value":"function tanDeg (degrees) {\n return tan(toRadians(degrees))\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":388,"value":"function acosDeg (s) {\n return toDegrees(acos(s))\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":386,"value":"function asinDeg (s) {\n return toDegrees(asin(s))\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":366,"value":"function atanDeg (degrees) {\n return atan(toRadians(degrees))\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":94,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":372,"value":"# Vectors","pinned":false,"hidden":false,"mode":"md"},{"id":493,"value":"Magnitude of a vector:","pinned":false,"hidden":false,"mode":"md"},{"id":376,"value":"function magnitude(...components) {\n const vector = _.isArray(components[0]) ? components[0] : components\n\n const sum = vector.reduce((tally, c) => {\n return tally + pow(c, 2)\n }, 0)\n\n return root(sum, 2);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":505,"value":"magnitude([2, 4, 9])","pinned":true,"hidden":false,"mode":"ojs"},{"id":532,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":534,"value":"Dot product of two vectors:","pinned":false,"hidden":false,"mode":"md"},{"id":210,"value":"function dotProduct (vector1, vector2, exactResult) {\n return calculate(nerdamer(`dot([${vector1[0]}, ${vector1[1]}, ${vector1[2]}], [${vector2[0]}, ${vector2[1]}, ${vector2[2]}])`).evaluate().text(), exactResult)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":211,"value":"dotProduct([0, 4, 0], [1, 2, 3])","pinned":true,"hidden":false,"mode":"ojs"},{"id":541,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":544,"value":"Cross product of two vectors:","pinned":false,"hidden":false,"mode":"md"},{"id":238,"value":"function crossProduct(vector1, vector2, exactResult) {\n const result = nerdamer(\n `cross([${vector1[0]}, ${vector1[1]}, ${vector1[2]}], [${vector2[0]}, ${vector2[1]}, ${vector2[2]}])`\n ).evaluate();\n\n if (!exactResult) {\n return eval(result.text());\n }\n\n return result.toString();\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":243,"value":"crossProduct([0, 5, 0.2732723], [1, 2, 0.2732723])","pinned":true,"hidden":false,"mode":"ojs"},{"id":1238,"value":"crossProduct([0, 5, 0.2732723], [1, 2, 0.2732723], true)","pinned":true,"hidden":false,"mode":"ojs"},{"id":2487,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":2548,"value":"## Calculus","pinned":false,"hidden":false,"mode":"md"},{"id":2550,"value":"function diff(...args) {\n return nerdamer(`diff(${args.join(\", \")})`).toString();\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":2572,"value":"diff(\"x^2\")","pinned":true,"hidden":false,"mode":"ojs"},{"id":2563,"value":"function integral(...args) {\n return nerdamer(`integrate(${args.join(\", \")})`).toString();\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":2580,"value":"integral(\"x^2\")","pinned":true,"hidden":false,"mode":"ojs"},{"id":2546,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":2488,"value":"## Calculate with units","pinned":false,"hidden":false,"mode":"md"},{"id":2506,"value":"calculate_units(\"12 MPa + 1999 Pa\")","pinned":true,"hidden":false,"mode":"ojs"},{"id":2517,"value":"calculate_units(\"x MPa + y Pa\", { x: 12, y: 1999 })","pinned":true,"hidden":false,"mode":"ojs"},{"id":2504,"value":"calculate_units(`${12} MPa + ${1999} Pa`)","pinned":true,"hidden":false,"mode":"ojs"},{"id":2502,"value":"// calculate_units(\"x + y\", { x: \"12 MPa\", y: \"1999 Pa\" }) // won't work","pinned":true,"hidden":false,"mode":"ojs"},{"id":2531,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":2522,"value":"expr = calculate_units","pinned":true,"hidden":false,"mode":"ojs"},{"id":2494,"value":"function calculate_units(expr, variables) {\n return math.evaluate(expr, variables || {}).value;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":98,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":73,"value":"# Libraries","pinned":false,"hidden":false,"mode":"md"},{"id":660,"value":"These external libraries can be imported directly from this notebook.","pinned":false,"hidden":false,"mode":"md"},{"id":1090,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":133,"value":"import {\n equation,\n equationWolfram,\n equationExpanded,\n calculate,\n place,\n solve,\n solved,\n wolframSolve,\n wolframSolveExpanded,\n nerdamer\n} with { equations as equations } from \"@jerryjappinen/equations\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":137,"value":"equations = ({})","pinned":false,"hidden":false,"mode":"ojs"},{"id":2403,"value":"solve(`a^2 + b^2 = c^2`, {\n a: 1,\n b: 2,\n c: undefined\n})","pinned":true,"hidden":false,"mode":"ojs"},{"id":653,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":1970,"value":"seedrandom = require('https://unpkg.com/seedrandom@3.0.5/seedrandom.min.js')","pinned":false,"hidden":false,"mode":"ojs"},{"id":1354,"value":"_functionPlot = require(\"https://unpkg.com/function-plot@1/dist/function-plot.js\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":57,"value":"math = require(\"mathjs\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":62,"value":"statistics = require(\"simple-statistics\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":584,"value":"---","pinned":false,"hidden":false,"mode":"md"},{"id":581,"value":"# Aliases","pinned":false,"hidden":false,"mode":"md"},{"id":1079,"value":"Offered only for backwards-compatibility. Will eventually be removed.","pinned":false,"hidden":false,"mode":"md"},{"id":591,"value":"vectorLength = magnitude","pinned":false,"hidden":false,"mode":"ojs"},{"id":632,"value":"cumulativeSum = sums","pinned":false,"hidden":false,"mode":"ojs"},{"id":1151,"value":"toDegrees = toDeg","pinned":false,"hidden":false,"mode":"ojs"},{"id":1158,"value":"toRadians = toRad","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}