学習環境
- Surface 3 (4G LTE)、Surface 3 タイプ カバー、Surface ペン(端末)
- Windows 10 Pro (OS)
- 数式入力ソフト(TeX, MathML): MathType
- MathML対応ブラウザ: Firefox、Safari
- MathML非対応ブラウザ(Internet Explorer, Microsoft Edge, Google Chrome...)用JavaScript Library: MathJax
- 参考書籍
解析入門 原書第3版 (S.ラング(著)、松坂 和夫(翻訳)、片山 孝次(翻訳)、岩波書店)の第2部(微分と基本的な関数)、第7章(逆関数)、4(逆正接関数)、練習問題24.を取り組んでみる。
時間をt秒、高原に最も近い歩道上の点から人までの距離をxメートル、人、光源、高原に最も近い歩道上の点のなす角をθとする。
コード(Emacs)
Python 3
#!/usr/bin/env python3 from sympy import pprint, symbols, tan, Derivative, pi θ = symbols('θ') x = 1500 / tan(θ) Dθ = Derivative(x, θ, 1) Dt = Dθ * -0.05 for t in [Dθ, Dθ.doit(), Dt, Dt.doit(), Dt.doit().subs({θ: pi / 4})]: pprint(t) print()
入出力結果(Terminal, Jupyter(IPython))
$ ./sample24.py d ⎛ ⎛x⎞⎞ ──⎜atan⎜─⎟⎟ dx⎝ ⎝9⎠⎠ 1 ────────── ⎛ 2 ⎞ ⎜x ⎟ 9⋅⎜── + 1⎟ ⎝81 ⎠ d ⎛ ⎛x⎞⎞ 3⋅──⎜atan⎜─⎟⎟ dx⎝ ⎝9⎠⎠ ───────────── 2 1 ────────── ⎛ 2 ⎞ ⎜x ⎟ 6⋅⎜── + 1⎟ ⎝81 ⎠ 3/26 $
HTML5
<div id="graph0"></div> <pre id="output0"></pre> <label for="r0">r = </label> <input id="r0" type="number" min="0" value="0.5"> <label for="dx">dx = </label> <input id="dx" type="number" min="0" step="0.0001" value="0.1"> <br> <label for="x1">x1 = </label> <input id="x1" type="number" value="-50"> <label for="x2">x2 = </label> <input id="x2" type="number" value="50"> <br> <label for="y1">y1 = </label> <input id="y1" type="number" value="0"> <label for="y2">y2 = </label> <input id="y2" type="number" value="10"> <br> <label for="x0">x = </label> <input id="x0" type="number" step="1.5" value="1.5"> <button id="draw0">draw</button> <button id="clear0">clear</button> <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/d3/4.2.6/d3.min.js" integrity="sha256-5idA201uSwHAROtCops7codXJ0vja+6wbBrZdQ6ETQc=" crossorigin="anonymous"></script> <script src="sample24.js"></script>
JavaScript
let div0 = document.querySelector('#graph0'), pre0 = document.querySelector('#output0'), width = 600, height = 600, padding = 50, btn0 = document.querySelector('#draw0'), btn1 = document.querySelector('#clear0'), input_r = document.querySelector('#r0'), input_dx = document.querySelector('#dx'), input_x1 = document.querySelector('#x1'), input_x2 = document.querySelector('#x2'), input_y1 = document.querySelector('#y1'), input_y2 = document.querySelector('#y2'), input_x0 = document.querySelector('#x0'), inputs = [input_r, input_dx, input_x1, input_x2, input_y1, input_y2, input_x0], p = (x) => pre0.textContent += x + '\n', range = (start, end, step=1) => { let res = []; for (let i = start; i < end; i += step) { res.push(i); } return res; }; let draw = () => { pre0.textContent = ''; let r = parseFloat(input_r.value), dx = parseFloat(input_dx.value), x1 = parseFloat(input_x1.value), x2 = parseFloat(input_x2.value), y1 = parseFloat(input_y1.value), y2 = parseFloat(input_y2.value), x0 = parseFloat(input_x0.value); if (r === 0 || dx === 0 || x1 > x2 || y1 > y2) { return; } let points = [], lines = [[x1, 6, x2, 6, 'red'], [9, y1, 9, y2, 'green']], f = (x) => 6 / x0 * x, fns = [], fns1 = [[f, 'blue']], fns2 = []; fns .forEach((o) => { let [f, color] = o; for (let x = x1; x <= x2; x += dx) { let y = f(x); points.push([x, y, color]); } }); fns1 .forEach((o) => { let [f, color] = o; lines.push([x1, f(x1), x2, f(x2), color]); }); fns2 .forEach((o) => { let [f, color] = o; for (let x = x1; x <= x2; x += dx0) { let g = f(x); lines.push([x1, g(x1), x2, g(x2), color]); } }); let xscale = d3.scaleLinear() .domain([x1, x2]) .range([padding, width - padding]); let yscale = d3.scaleLinear() .domain([y1, y2]) .range([height - padding, padding]); let xaxis = d3.axisBottom().scale(xscale); let yaxis = d3.axisLeft().scale(yscale); div0.innerHTML = ''; let svg = d3.select('#graph0') .append('svg') .attr('width', width) .attr('height', height); svg.selectAll('line') .data([[x1, 0, x2, 0], [0, y1, 0, y2]].concat(lines)) .enter() .append('line') .attr('x1', (d) => xscale(d[0])) .attr('y1', (d) => yscale(d[1])) .attr('x2', (d) => xscale(d[2])) .attr('y2', (d) => yscale(d[3])) .attr('stroke', (d) => d[4] || 'black'); svg.selectAll('circle') .data(points) .enter() .append('circle') .attr('cx', (d) => xscale(d[0])) .attr('cy', (d) => yscale(d[1])) .attr('r', r) .attr('fill', (d) => d[2] || 'green'); svg.append('g') .attr('transform', `translate(0, ${height - padding})`) .call(xaxis); svg.append('g') .attr('transform', `translate(${padding}, 0)`) .call(yaxis); [fns, fns1, fns2].forEach((fs) => p(fs.join('\n'))); }; inputs.forEach((input) => input.onchange = draw); btn0.onclick = draw; btn1.onclick = () => pre0.textContent = ''; draw();
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