[从头学数学] 第216节 带着计算机去高考（八）

剧情提要：
[机器小伟]在[工程师阿伟]的陪同下进入了[九转金丹]之第八转的修炼。设想一个场景：
如果允许你带一台不连网的计算机去参加高考，你会放弃选择一个手拿计算器和草稿本吗
？阿伟决定和小伟来尝试一下用计算机算高考题会是怎样的感觉。

正剧开始：

星历2016年05月21日 11:31:19, 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]一起做着2007年的江苏省数学高考题]。

这一年的卷子又回到了比较低的难度，感觉这就是正弦曲线的节奏。

<span style="font-size:18px;">//题1
	if (1) {      
        var r = 20;            
        config.setSector(1,1,1,1);              
        config.graphPaper2D(0, 0, r);            
        config.axis2D(0, 0,180);              
                
        //坐标轴设定        
        var scaleX = 2*r, scaleY = 2*r;          
        var spaceX = 90, spaceY = 0.5;           
        var xS = -720, xE = 720;          
        var yS = -10, yE = 10;          
        config.axisSpacing(xS, xE, spaceX, scaleX, 'X');            
        config.axisSpacing(yS, yE, spaceY, scaleY, 'Y');            
                    
        var transform = new Transform();            
        //存放函数图像上的点        
        var a = [], b = [], c = [], d = [];          
                  
        //需要显示的函数说明    
                    //希腊字母表(存此用于Ctrl C/V  
            //ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ  
            //αβγδεζηθικλμνξοπρστυφχψω  
        var f1 = 'y = sinx/2', f2 = 'y = sin2x', f3 = 'y = cosx/4', f4 = 'y = cos4x';        
        var  y1 = y2 = y3 = y4 = 0;
		var  x1 = 0;
		//(1-(x+2)^2)^0.5
		for (var x = xS; x <= xE; x+=10) { 
				x1 = x/180*Math.PI;
				
				y1 = Math.sin(x1/2);
				y2 = Math.sin(2*x1);
				y3 = Math.cos(x1/4);
				y4 = Math.cos(4*x1);
				
				a.push([x, y1]);
				b.push([x, y2]);
				c.push([x, y3]);
				d.push([x, y4]);

        }  
          
                  
        //存放临时数组        
        var tmp = [];        
                  
         //显示变换    
        if (a.length > 0) {    
            a = transform.scale(transform.translate(a, 0, 0), scaleX/spaceX, scaleY/spaceY);     
            //函数1    
            tmp = [].concat(a);        
            shape.pointDraw(tmp, 'red');        
            tmp = [].concat(a);        
            shape.multiLineDraw(tmp, 'pink');      
                  
            plot.setFillStyle('red');    
            plot.fillText(f1, 100, -90, 200);      
        }    
            
        if (b.length > 0) {    
            b = transform.scale(transform.translate(b, 0, 0), scaleX/spaceX, scaleY/spaceY);                
            //函数2    
            tmp = [].concat(b);        
            shape.pointDraw(tmp, 'blue');        
            tmp = [].concat(b);        
            shape.multiLineDraw(tmp, '#22CCFF');     
                
            plot.setFillStyle('blue');    
            plot.fillText(f2, 100, -120, 200);     
    
        }    
               
        if (c.length > 0) {    
            c = transform.scale(transform.translate(c, 0, 0), scaleX/spaceX, scaleY/spaceY);      
            tmp = [].concat(c);        
            shape.pointDraw(tmp, 'green');        
            tmp = [].concat(c);        
            shape.multiLineDraw(tmp, '#CCFF22');      
            plot.setFillStyle('green');      
            plot.fillText(f3, 100, -150, 200);     
        }    
            
        if (d.length > 0) {    
            d = transform.scale(transform.translate(d, 0, 0), scaleX/spaceX, scaleY/spaceY);      
            tmp = [].concat(d);        
            shape.pointDraw(tmp, 'orange');        
            tmp = [].concat(d);        
            shape.multiLineDraw(tmp, '#CC8800');      
            plot.setFillStyle('orange');      
            plot.fillText(f4, 100, -180, 200);     
        }    

    } </span>

<span style="font-size:18px;">//题3
	if (1) {      
        var r = 20;            
        config.setSector(1,1,1,1);              
        config.graphPaper2D(0, 0, r);            
        config.axis2D(0, 0,180);              
                
        //坐标轴设定        
        var scaleX = 2*r, scaleY = 2*r;          
        var spaceX = 2, spaceY = 2;           
        var xS = -10, xE = 10;          
        var yS = -10, yE = 10;          
        config.axisSpacing(xS, xE, spaceX, scaleX, 'X');            
        config.axisSpacing(yS, yE, spaceY, scaleY, 'Y');            
                    
        var transform = new Transform();            
        //存放函数图像上的点        
        var a = [], b = [], c = [], d = [];          
                  
        //需要显示的函数说明    
                    //希腊字母表(存此用于Ctrl C/V  
            //ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ  
            //αβγδεζηθικλμνξοπρστυφχψω  
        var f1 = 'y^2 - x^2/4 = 1', f2 = '', f3 = '', f4 = '';        
        var  y1 = y2 = y3 = y4 = 0;
		var  x1 = 0;
		var asqare = 4, bsqare = 1;
		//(1-(x+2)^2)^0.5
		for (var x = xS; x <= xE; x+=0.5) { 
				y1 = Math.pow((x*x/asqare+1)*bsqare, 0.5);
				
				a.push([x, y1]);
				a.push([x, -y1]);


        }  
          
                  
        //存放临时数组        
        var tmp = [];        
                  
         //显示变换    
        if (a.length > 0) {    
            a = transform.scale(transform.translate(a, 0, 0), scaleX/spaceX, scaleY/spaceY);     
            //函数1    
            tmp = [].concat(a);        
            shape.pointDraw(tmp, 'red');        
            tmp = [].concat(a);        
            shape.multiLineDraw(tmp, 'pink');      
                  
            plot.setFillStyle('red');    
            plot.fillText(f1, 30, -90, 200);      
        }   
	}</span>

<span style="font-size:18px;">//题5
	if (1) {      
        var r = 20;            
        config.setSector(1,1,1,1);              
        config.graphPaper2D(0, 0, r);            
        config.axis2D(0, 0,180);              
                
        //坐标轴设定        
        var scaleX = 2*r, scaleY = 2*r;          
        var spaceX = 90, spaceY = 0.5;           
        var xS = -720, xE = 720;          
        var yS = -10, yE = 10;          
        config.axisSpacing(xS, xE, spaceX, scaleX, 'X');            
        config.axisSpacing(yS, yE, spaceY, scaleY, 'Y');            
                    
        var transform = new Transform();            
        //存放函数图像上的点        
        var a = [], b = [], c = [], d = [];          
                  
        //需要显示的函数说明    
                    //希腊字母表(存此用于Ctrl C/V  
            //ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ  
            //αβγδεζηθικλμνξοπρστυφχψω  
        var f1 = 'y = sinx-1.732cosx', f2 = '', f3 = '', f4 = '';        
        var  y1 = y2 = y3 = y4 = 0;
		var  x1 = 0;

		//(1-(x+2)^2)^0.5
		for (var x = xS; x <= xE; x+=10) { 
				x1 = x/180*Math.PI;
				y1 = Math.sin(x1) - 1.732*Math.cos(x1);
				
				a.push([x, y1]);


        }  
          
                  
        //存放临时数组        
        var tmp = [];        
                  
         //显示变换    
        if (a.length > 0) {    
            a = transform.scale(transform.translate(a, 0, 0), scaleX/spaceX, scaleY/spaceY);     
            //函数1    
            tmp = [].concat(a);        
            shape.pointDraw(tmp, 'red');        
            tmp = [].concat(a);        
            shape.multiLineDraw(tmp, 'pink');      
                  
            plot.setFillStyle('#880000');    
            plot.fillText(f1, 100, -90, 200);      
        }    </span>

<span style="font-size:18px;">#题7
def tmp7():
    A_0 = alg.strformat(['a_[0]']);
    A_1 = alg.strformat(['a_[1]']);
    A_2 = alg.strformat(['a_[2]']);
    A_3 = alg.strformat(['a_[3]']);
    
    C_1 = alg.strformat(['x', '-2']);
    C_2 = alg.strcombine(alg.strpow_n(C_1, 2));
    C_3 = alg.strcombine(alg.strpow_n(C_1, 3));

    D = A_0 + alg.strdot(A_1, C_1)+alg.strdot(A_2, C_2)+alg.strdot(A_3, C_3);
    D = alg.strcombine(D);
    print(D);

    '''
    ['(1)*a_[0]^[1]', '(1)*a_[1]^[1]*x^[1]', '(-2)*a_[1]^[1]', '(1)*a_[2]^[1]*x^[2]', '(-4)*a_[2]^[1]*x^[1]',
    '(4)*a_[2]^[1]', '(1)*a_[3]^[1]*x^[3]',
    '(-6)*a_[3]^[1]*x^[2]', '(12)*a_[3]^[1]*x^[1]', '(-8)*a_[3]^[1]']
    '''

    E = ['(1)*a_[0]^[1]', '(1)*a_[1]^[1]*x^[1]', '(-2)*a_[1]^[1]', '(1)*a_[2]^[1]*x^[2]', '(-4)*a_[2]^[1]*x^[1]',
    '(4)*a_[2]^[1]', '(1)*x^[3]', '(-6)*x^[2]', '(12)*x^[1]', '(-8)'];

    E = alg.strcombine(E);
    print(E);

    F = ['(1)*a_[0]^[1]', '(1)*a_[1]^[1]*x^[1]', '(-2)*a_[1]^[1]', '(1)*a_[2]^[1]*x^[2]', '(-4)*a_[2]^[1]*x^[1]',
         '(4)*a_[2]^[1]', '(1)*x^[3]', '(-6)*x^[2]', '(12)*x^[1]', '(-8)']

    #-6 + a_[2] = 0;</span>

<span style="font-size:18px;">//题8
	if (1) {      
        var r = 20;            
        config.setSector(1,1,1,1);              
        config.graphPaper2D(0, 0, r);            
        config.axis2D(0, 0,180);              
                
        //坐标轴设定        
        var scaleX = 2*r, scaleY = 2*r;          
        var spaceX = 2, spaceY = 0.5;           
        var xS = -10, xE = 10;          
        var yS = -20, yE = 20;          
        config.axisSpacing(xS, xE, spaceX, scaleX, 'X');            
        config.axisSpacing(yS, yE, spaceY, scaleY, 'Y');            
                    
        var transform = new Transform();            
        //存放函数图像上的点        
        var a = [], b = [], c = [], d = [];          
                  
        //需要显示的函数说明    
                    //希腊字母表(存此用于Ctrl C/V  
            //ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ  
            //αβγδεζηθικλμνξοπρστυφχψω  
        var f1 = 'y = log(2/(1-x))', f2 = '', f3 = '', f4 = '';        
        var  y1 = y2 = 0;
		//(1-(x+2)^2)^0.5
		for (var x = xS; x <= xE; x+=0.2) { 
				y1 = Math.log(2/(1-x))/Math.log(10);
				
				a.push([x, y1]);


        }  
          
                  
        //存放临时数组        
        var tmp = [];        
                  
        //显示变换        
        if (a.length > 0) {        
            a = transform.scale(transform.translate(a, 0, 0), scaleX/spaceX, scaleY/spaceY);         
            //函数1        
            tmp = [].concat(a);            
            shape.pointDraw(tmp, 'red');            
           
			tmp = [].concat(a);            
            shape.multiLineDraw(tmp, 'pink');          
                      
            plot.setFillStyle('red');        
            plot.fillText(f1, 100, -90, 200);          
        }  
	}</span>

<span style="font-size:18px;">//题8
	if (1) {      
        var r = 20;            
        config.setSector(1,1,1,1);              
        config.graphPaper2D(0, 0, r);            
        config.axis2D(0, 0,180);              
                
        //坐标轴设定        
        var scaleX = 2*r, scaleY = 2*r;          
        var spaceX = 2, spaceY = 0.5;           
        var xS = -10, xE = 10;          
        var yS = -20, yE = 20;          
        config.axisSpacing(xS, xE, spaceX, scaleX, 'X');            
        config.axisSpacing(yS, yE, spaceY, scaleY, 'Y');            
                    
        var transform = new Transform();            
        //存放函数图像上的点        
        var a = [], b = [], c = [], d = [];          
                  
        //需要显示的函数说明    
                    //希腊字母表(存此用于Ctrl C/V  
            //ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ  
            //αβγδεζηθικλμνξοπρστυφχψω  
        var f1 = 'y = log(2/(1-x))', f2 = '', f3 = '', f4 = '';        
        var  y1 = y2 = 0;
		//(1-(x+2)^2)^0.5
		for (var x = xS; x <= xE; x+=0.2) { 
				y1 = Math.log(2/(1-x))/Math.log(10);
				
				a.push([x, y1]);


        }  
          
                  
        //存放临时数组        
        var tmp = [];        
                  
        //显示变换        
        if (a.length > 0) {        
            a = transform.scale(transform.translate(a, 0, 0), scaleX/spaceX, scaleY/spaceY);         
            //函数1        
            tmp = [].concat(a);            
            shape.pointDraw(tmp, 'red');            
           
			tmp = [].concat(a);            
            shape.multiLineDraw(tmp, 'pink');          
                      
            plot.setFillStyle('red');        
            plot.fillText(f1, 100, -90, 200);          
        }  
	}</span>

<span style="font-size:18px;">//题15
	if (1) {      
        var r = 20;            
        config.setSector(1,1,1,1);              
        config.graphPaper2D(0, 0, r);            
        config.axis2D(0, 0,180);              
                
        //坐标轴设定        
        var scaleX = 2*r, scaleY = 2*r;          
        var spaceX = 2, spaceY = 10;           
        var xS = -10, xE = 10;          
        var yS = -50, yE = 50;          
        config.axisSpacing(xS, xE, spaceX, scaleX, 'X');            
        config.axisSpacing(yS, yE, spaceY, scaleY, 'Y');            
                    
        var transform = new Transform();            
        //存放函数图像上的点        
        var a = [], b = [], c = [], d = [];          
                  
        //需要显示的函数说明    
                    //希腊字母表(存此用于Ctrl C/V  
            //ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ  
            //αβγδεζηθικλμνξοπρστυφχψω  
        var f1 = 'y = x^3-12x+8', f2 = '', f3 = '', f4 = '';        
        var  y1 = y2 = 0;
		//(1-(x+2)^2)^0.5
		for (var x = xS; x <= xE; x+=0.2) { 
				y1 = Math.pow(x, 3) - 12 * x + 8;
				
				a.push([x, y1]);


        }  
          
                  
        //存放临时数组        
        var tmp = [];        
                  
        //显示变换        
        if (a.length > 0) {        
            a = transform.scale(transform.translate(a, 0, 0), scaleX/spaceX, scaleY/spaceY);         
            //函数1        
            tmp = [].concat(a);            
            shape.pointDraw(tmp, 'red');            
           
			tmp = [].concat(a);            
            shape.multiLineDraw(tmp, 'pink');          
                      
            plot.setFillStyle('red');        
            plot.fillText(f1, 100, -90, 200);          
        }  </span>

<span style="font-size:18px;">#题16
def tmp16():
    #写出边长和坐标点
    AB = AC = BC = 2 *1.732;
    A, B, C = [0, 0, 0], [AB, 0, 0], [AB/2, AB*1.732/2, 0];
    P = [AB/2, AB*1.732/6, 2];

    panel = geo.Panel();
    d = panel.pt2panel(A, [P, B, C]);
    print(d);
	
>>> 
2.6832028613289456

>>> 6/5*5**0.5
2.6832815729997477</span>

本节到此结束，欲知后事如何，请看下回分解。