学習環境
- Surface Go、タイプ カバー、ペン(端末)
- Windows 10 Pro (OS)
- Nebo(Windows アプリ)
- iPad Pro + Apple Pencil
- MyScript Nebo - MyScript(iPad アプリ(iOS))
- 参考書籍
数学読本〈1〉数・式の計算/方程式/不等式 (松坂 和夫(著)、岩波書店)の第3章(数学の威力を発揮する - 方程式)、3.3(高次方程式)、連立2次方程式の問34.を取り組んでみる。
2辺の長さ を x cm、 y cm とする。
周の長さは42 cm なので
円の直径は15 cm なので、
2次方程式の解の係数の関係により、 求める2辺の長さは、
コード(Emacs)
Python 3
#!/usr/bin/env python3 from sympy import pprint, symbols, sqrt, solve, plot print('34.') x, y = symbols('x, y', positive=True) eqs = (2 * (x + y) - 42, sqrt(x ** 2 + y ** 2) - 15) pprint(solve(eqs, dict=True)) fs = solve(eqs[0], y) + solve(eqs[1], y) pprint(fs) p = plot(*fs, (x, -25, 25), ylim=(-25, 25), legend=True, show=False) colors = ['red', 'green', 'green'] for i, color in enumerate(colors): p[i].line_color = color p.save('sample34.png')
入出力結果(Terminal, Jupyter(IPython))
$ ./sample34.py 34. [{x: 9, y: 12}, {x: 12, y: 9}] ⎡ ____________ ____________⎤ ⎢ ╱ 2 ╱ 2 ⎥ ⎣-x + 21, -╲╱ - x + 225 , ╲╱ - x + 225 ⎦ $
HTML5
<div id="graph0"></div> <pre id="output0"></pre> <label for="r0">r = </label> <input id="r0" type="number" min="0" value="1"> <label for="dx">dx = </label> <input id="dx" type="number" min="0" step="0.001" value="0.01"> <br> <label for="x1">x1 = </label> <input id="x1" type="number" value="-20"> <label for="x2">x2 = </label> <input id="x2" type="number" value="20"> <br> <label for="y1">y1 = </label> <input id="y1" type="number" value="-20"> <label for="y2">y2 = </label> <input id="y2" type="number" value="20"> <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="sample34.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'), inputs = [input_r, input_dx, input_x1, input_x2, input_y1, input_y2], p = (x) => pre0.textContent += x + '\n'; let fns = [[x => -x + 21, 'red'], [x => -Math.sqrt(-(x ** 2) + 225), 'green'], [x => Math.sqrt(-(x ** 2) + 225), 'green']]; 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); if (r === 0 || dx === 0 || x1 > x2 || y1 > y2) { return; } let points = [], x0 = 10, y0 = 12, lines = [[9, y1, 9, y2, 'blue'], [12, y1, 12, y2, 'brown']]; fns .forEach((o) => { let [f, color] = o; for (let x = x1; x <= x2; x += dx) { let y = f(x); points.push([x, y, 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].forEach((fs) => p(fs.join('\n'))); }; inputs.forEach((input) => input.onchange = draw); btn0.onclick = draw; btn1.onclick = () => pre0.textContent = ''; draw();
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