2018年12月23日日曜日


数学読本〈1〉
楽天ブックス(Kobo) Yahoo!

学習環境

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33.を取り組んでみる。


  1. 問題のある長方形の横の長さを x、縦の長さを y とする。

    x + 5 y - 4 = x y x - 5 y + 4 = 2 3 x y - 4 x + 5 y - 20 = 0 4 x + x y - 5 y - 20 = 2 3 x y y = 4 x + 20 5 4 x + 4 x + 20 5 x - 4 x - 20 - 20 = 2 3 x · 4 x + 20 5 4 x + 20 5 x - 40 = 2 3 x 4 x + 20 5 x + 5 5 x - 10 = 2 3 x · x + 5 5 3 x + 15 x - 150 = 2 x x + 5 3 x 2 + 15 x - 150 = 2 x 2 + 10 x x 2 + 5 x - 150 = 0 x + 15 x - 10 = 0 y = 40 + 20 5 = 8 + 4 = 12

    よって、長方形の2辺の長さは、 縦12 cm、横10 cmである。

コード(Emacs)

Python 3

#!/usr/bin/env python3
from sympy import pprint, symbols, solve, Rational, plot

print('33.')

x, y = symbols('x, y', positive=True)
eqs = [(x + 5) * (y - 4) - x * y,
       (x - 5) * (y + 4) - Rational(2, 3) * x * y]

pprint(solve(eqs, dict=True))

fs = [solve(eq, y)[0] for eq in eqs]

p = plot(*fs, legend=True, show=False)
colors = ['red', 'green']

for i, color in enumerate(colors):
    p[i].line_color = color

p.save('sample33.png')

入出力結果(Terminal, Jupyter(IPython))

$ ./sample33.py
33.
[{x: 10, y: 12}]
$

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="0.005">
<br>
<label for="x1">x1 = </label>
<input id="x1" type="number" value="-15">
<label for="x2">x2 = </label>
<input id="x2" type="number" value="15">
<br>
<label for="y1">y1 = </label>
<input id="y1" type="number" value="-15">
<label for="y2">y2 = </label>
<input id="y2" type="number" value="15">

<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="sample33.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 = [];
    
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 = [[0, 0, x0, 0, 'red'],
                 [x0, 0, x0, y0, 'red'],
                 [x0, y0, 0, y0, 'red'],
                 [0, y0, 0, 0, 'red'],
                 [0, 0, x0 + 5, 0, 'green'],
                 [x0 + 5, 0, x0 + 5, y0 - 4, 'green'],
                 [x0 + 5, y0 - 4, 0, y0 - 4, 'green'],
                 [0, y0 - 4, 0, 0, 'green'],                 
                 [0, 0, x0 - 5, 0, 'blue'],
                 [x0 - 5, 0, x0 - 5, y0 + 4, 'blue'],
                 [x0 - 5, y0 + 4, 0, y0 + 4, 'blue'],
                 [0, y0 + 4, 0, 0, 'blue']];
        
    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();



































						












時刻:


12:00




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