[从头学数学] 第139节 二次根式 小结与复习题

剧情提要：

[机器小伟]在[工程师阿伟]的陪同下进入了筑基中期的修炼，

这次要修炼的目标是[二次根式 小结与复习题]。

正剧开始：

星历2016年03月18日 12:19:31, 银河系厄尔斯星球中华帝国江南行省。

[工程师阿伟]正在和[机器小伟]一起研究[二次根式 小结与复习题]。

<span style="font-size:18px;">			'x>=-3',
'x>1/2',
'x<2/3',
'x!=1',
'10*5^[0.5]',
'2*3x^[0.5]',
'2*(2/3)^[0.5]',
'(2/3)^[0.5]/a',
'xy*2y^[0.5]',
'(5a/6)^[0.5]a^[2]',
</span>

<span style="font-size:18px;">function myDraw(xGlobal, yGlobal) {
var config = new PlotConfiguration();
config.init();

config.setPreference();
var r = 20;
//config.setSector(1,1,1,1);
//config.graphPaper2D(0, 0, r);
//config.axis3D(0, 0,0,180);

plot.setFillStyle('blue');
var mathText = new MathText();
var s = [
'(24^[0.5]-(1/2)^[0.5])-((1/8)^[0.5]+6^[0.5])',
'2*12^[0.5]*3^[0.5]/4/(5*2^[0.5])',
'(2*3^[0.5]+6^[0.5])*(2*3^[0.5]-6^[0.5])',
'(2*48^[0.5]-3*27^[0.5])/6^[0.5]',
'(2*2^[0.5]+3*3^[0.5])^[2]',
'(3/2*(5/3)^[0.5]-(5/4)^[0.5])^[2]',

];
var x =40, y=40;

var len = s.length;
for (var i = 0; i < len; i++) {

if (s[i] == '') {
if (x < 100) {
x += 300;
y-=30*3;
}
else {
x = 20;
y += 30;
}
}
else {
mathText.print(s[i], x, y);
y+=30;
}
}

}</span>

<span style="font-size:18px;">def tmp():
s = ['(24^[0.5]-(1/2)^[0.5])-((1/8)^[0.5]+6^[0.5])',
'2*12^[0.5]*3^[0.5]/4/(5*2^[0.5])',
'(2*3^[0.5]+6^[0.5])*(2*3^[0.5]-6^[0.5])',
'(2*48^[0.5]-3*27^[0.5])/6^[0.5]',
'(2*2^[0.5]+3*3^[0.5])^[2]',
'(3/2*(5/3)^[0.5]-(5/4)^[0.5])^[2]'];
for i in range(len(s)):
s1 = s[i].replace('^[', '**');
s1 = s1.replace(']', '');
print('{0} = {1}'.format(s1, round(eval(s1), 3)));</span>

<span style="font-size:18px;">>>>
(24**0.5-(1/2)**0.5)-((1/8)**0.5+6**0.5) = 1.389
2*12**0.5*3**0.5/4/(5*2**0.5) = 0.424
(2*3**0.5+6**0.5)*(2*3**0.5-6**0.5) = 6.0
(2*48**0.5-3*27**0.5)/6**0.5 = -0.707
(2*2**0.5+3*3**0.5)**2 = 64.394
(3/2*(5/3)**0.5-(5/4)**0.5)**2 = 0.67</span>

<span style="font-size:18px;">>>> f = lambda x : x**2+5*x-6;
>>> f(5**0.5-1);
1.7082039324993694
>>> f2 = lambda x : (7+4*3**0.5)*x**2+(2+3**0.5)*x+3**0.5;
>>> f2(2-3**0.5);
3.732050807568878
>>> I = lambda Q, R, t: (Q/R/t)**0.5;
>>> I(30, 5, 1);
2.449489742783178</span>

<span style="font-size:18px;">function myDraw(xGlobal, yGlobal) {
var config = new PlotConfiguration();
config.init();

config.setPreference();
var r = 20;
//config.setSector(1,1,1,1);
//config.graphPaper2D(0, 0, r);
//config.axis3D(0, 0,0,180);

plot.setFillStyle('red');
var mathText = new MathText();
var s = [
'PI*R_[1]^[2] = PI*R_[0]^[2]/4 => R_[1] = 1/2*R_[0]',
'PI*(R_[2]^[2]-R_[1]^[2]) = PI*R_[0]^[2]/4 => R_[2] = 2^[0.5]/2*R_[0]',
'R_[3] = 3^[0.5]/2*R_[0]',

'OA = R_[0]',
'OD = R_[1]',
'OC = R_[2]',
'OB = R_[3]',

];
var x =40, y=40;
var r1 = 40;

var len = s.length;
for (var i = 0; i < len; i++) {

if (s[i] == '') {
if (x < 100) {
x += 300;
y-=r1*3;
}
else {
x = 20;
y += r1;
}
}
else {
mathText.print(s[i], x, y);
y+=r1;
}
}

}</span>

<span style="font-size:18px;">def tmp():
s = ['(24^[0.5]-(1/2)^[0.5])-((1/8)^[0.5]+6^[0.5])',
'2*12^[0.5]*3^[0.5]/4/(5*2^[0.5])',
'(2*3^[0.5]+6^[0.5])*(2*3^[0.5]-6^[0.5])',
'(2*48^[0.5]-3*27^[0.5])/6^[0.5]',
'(2*2^[0.5]+3*3^[0.5])^[2]',
'(3/2*(5/3)^[0.5]-(5/4)^[0.5])^[2]'];
for i in range(len(s)):
s1 = s[i].replace('^[', '**');
s1 = s1.replace(']', '');
print('{0} = {1}'.format(s1, round(eval(s1), 3)));

def tmp():
for i in range(1, 189):
n = (189*i)**0.5;
if (abs(n-round(n)) < 0.0001):
print(i);
break;

>>>
21</span>

为了增加这个下标，小伟的工具又进化了一下：

<span style="font-size:18px;">/**
* @usage   数学表达式，代数式的书写
* @author  mw
* @date    2016年03月12日  星期六  11:05:12
* @param
* @return
*
*/
function MathText() {
//上标标记形式为...^[内容]...
//分数不进行处理， 根式不进行处理，都转成指数式进行
//特殊数学符号设想加\[alpha]进行转义，待续
//可以进行指数上标代数式的书写
//可扩展下标，待续

this.setNormalFont = function() {
plot.setFont("normal normal normal 24px Times Lt Std");
}

this.setScriptFont = function() {
plot.setFont("italic normal bold 16px Dark Courier ");
}

this.print = function(text, xPos, yPos) {
xPos = xPos ? xPos : 0;
yPos = yPos ? yPos : 0;

plot.save();

var s = text ? text : '';

if (s != '') {
s = s.replace(/\/\//ig, '÷');
s = s.replace(/>=/ig, '≥');
s = s.replace(/<=/ig, '≤');
s = s.replace(/!=/ig, '≠');
s = s.replace(/pi/ig, 'π');
}

//字符串长度
var len = s.length;
//不同字体大小设置在此
var r1 = 20;
//单个字符暂存处
var c;
//文本显示位置
var x = xPos, y = yPos;
//正常文本暂存
var s0 = '';
//字符串打印长度
var measure;
//记录上一个x位置,可记录三层
var xMem = [x, x, x];
//记录每一层的左括号位置
var bracketPos = [x, x, x];
//记录括号层次
var bracketsLevel = 0;
//记录根号层次
var radicalLevel = 0;

//设置正常字体
this.setNormalFont();

for (var i = 0; i < len; i++) {
if (s[i] == '_') {
//下标开始
//下标标记形式为..._[内容]...

if (s0 != '') { //先把正常字符打印出
if (r1 != 20) { //字体字号大小还在上标状态
r1 = 20;
this.setNormalFont();
}

measure = plot.measureText(s0);
plot.fillText(s0, x, y, measure);
s0 = '';

x += measure;

}

var subScript = '';
var j = 0;
for (j = i+1; s[j]!=']'; j++) {
if (s[j] != '[') {
subScript+=s[j];
}
}

if (r1 != 10) {//正常字体状态，需要改为上标字体
r1 = 10;
this.setScriptFont();

}

measure = plot.measureText(subScript);
plot.fillText(subScript, x, y+8, measure);

if (j < len-1 && s[j+1] == '^') {

}
else {
x += 1.2*measure;
}

i = j;

}
else if (s[i] == '^') {
//上标开始
//上标标记形式为...^[内容]...

if (s0 != '') { //先把正常字符打印出
if (r1 != 20) { //字体字号大小还在上标状态
r1 = 20;
this.setNormalFont();
}

measure = plot.measureText(s0);
plot.fillText(s0, x, y, measure);
s0 = '';

x += measure;

}

var upperScript = '';
var j = 0;
for (j = i+1; s[j]!=']'; j++) {
if (s[j] != '[') {
upperScript+=s[j];
}
}

var x1, y1;
if (i > 0 && s[i-1] == ')') {
x1 = bracketPos[bracketsLevel], y1 = y-20-5*radicalLevel;
}
else {
x1 = xMem[bracketsLevel], y1 = y-20-5*radicalLevel;
}

//二次根式
if (upperScript == '1/2' || upperScript == '0.5') {

plot.save()
.setLineWidth(1);
plot.beginPath()
.moveTo(x1-5, y+5)
.lineTo(x1-8, y-3)
.moveTo(x1-5, y+5)
.lineTo(x1+5, y1)
.moveTo(x1+5, y1)
.lineTo(x, y1)
.closePath()
.stroke();
plot.restore();

}
else {

if (r1 != 10) {//正常字体状态，需要改为上标字体
r1 = 10;
this.setScriptFont();

}

measure = plot.measureText(upperScript);
plot.fillText(upperScript, x, y-8, measure);

if (j < len-1 && s[j+1] == '_') {

}
else {
x += 1.2*measure;
}
}

//直接跳跃过上标字符区段
i = j;
}
else {
c = s[i];

if (c == ')') {
s0 += c;
bracketsLevel -= 1;

}
else if (c == '(') {
//如果整个括号被开根式，根号在括号左边
bracketPos[bracketsLevel] = x + plot.measureText(s0);
s0 += c;

bracketsLevel+=1;
//过了括号就是过了一道关，要刷新坐标
xMem[bracketsLevel] = x + plot.measureText(s0);

}
else if (c == '+' || c == '-' || c == '*' || c == '/' || c == '÷'
|| c == '=' || c == ' ') {

if (c == '*') {
if (i > 0 && /[0-9]/.test(s[i-1]) && /[0-9]/.test(s[i+1])) {
//对于乘号前后都是数字的情况，把乘号改成叉号
c = ' \u00D7 ';
}
else {
//对于代数式中，乘号改为点号
c = ' \u00B7 ';
}
}

//如果是运算符后的数被开根式，根号在运算符右边
if (c == '-' || c == '/') {
s0 += ' '+c+' ';
}
else {
s0 += c;
}

if (bracketsLevel < 3) {
xMem[bracketsLevel] = x+plot.measureText(s0);
}
}
else {
s0 += c;
}

}
}

if (s0 != '') { //先把正常字符打印出
if (r1 != 20) { //字体字号大小还在上标状态
r1 = 20;
this.setNormalFont();
}
measure = plot.measureText(s0);
plot.fillText(s0, x, y, measure);
x += measure;
}

plot.restore();
}

}
</span>

基本上到这里也是个底了吧，再向里塞功能怕要撑破肚皮了。



本节到此结束，欲知后事如何，请看下回分解。