[从头学数学] 第188节 千军阅尽还复来（全）

剧情提要：
[机器小伟]在[project师阿伟]的陪同下进入了[九转金丹]之第四转的修炼。
这次要研究的是[复习题]。

正剧開始：
星历2016年04月21日 15:22:06, 银河系厄尔斯星球中华帝国江南行省。

[project师阿伟]正在和[机器小伟]一起研究[复习题]。

<span style="font-size:18px;">#7
def incomeTax(x):
    #不用交所得税的上限
    bound = 2000;
    #超过部分
    over = x - bound;
    #应交税额：
    tax = 0;
    
    if over <= 500:
        tax = over * 0.05;
    elif over <= 2000:
        tax = 500*0.05 + (over-500) * 0.1;
    elif over <= 5000:
        tax = 500*0.05 + 1500*0.1 + (over-2000) * 0.15;
    else:
        pass;

    return tax;</span>

<span style="font-size:18px;">	if (1) {    
         var r = 20;          
        config.setSector(1,1,1,1);            
        config.graphPaper2D(0, 0, r);          
        config.axis2D(0, 0,180, 1);            
              
        //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 = [];     
                
        //须要显示的函数说明      
        var f1 = 'y=2x^3-4x^2-3x+1';  
        //函数描点      
        for (var x = xS; x <= xE; x+=0.3) {        
            if (x != 0) {      
                a.push([x, funTask(x)]);      
    
    
    
    
            }      
        }        
    
        //二分法求函数的零点    
        //区间的最小值和最大值    
        var minX = 2, maxX = 4;    
        var y1 = y2 = 0;    
        x = minX;    
        y1 = funTask(x);    
        x = maxX;    
        y2 = funTask(x);    
            
        //假设在给定区间上存在有零点    
        if (y1 * y2 < 0) {    
            var epsilon = 0.000001;    
            while (Math.abs(y1-y2) > epsilon) {    
                
                x = minX;    
                y1 = funTask(x);    
                x = maxX;    
                y2 = funTask(x);    
                    
                    
                x = (minX+maxX)/2;    
                y = funTask(x);    
                    
                if (y * y1 < 0) {    
                    maxX = x;    
                }    
                else {    
                    minX = x;    
                }    
                    
    
            }    
            plot.setFillStyle('blue')    
                .fillText('零点：x = '+ ((minX+maxX)/2).toFixed(3), -200, -60, 120);    
        }    
               
               
        //存放暂时数组      
        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;">	 if (1) {  
        var r = 20;  
        config.setSector(1,1,1,1);  
        config.graphPaper2D(0, 0, r);  
        config.axis3D(0, 0, 0, 180);  
          
        var transform = new Transform();  
          
        var a = 2*r, b = 1*r, h = 4*r;  
        var array = shape.ellipse(a, b);  
          
        var size = array.length;  
          
        var topFace = [], bottomFace = [];  
        for (var i = 0; i < size; i++) {  
            topFace.push([array[i][0], array[i][1]]);  
            bottomFace.push([array[i][0], array[i][1]-1.5*h]);  
        }  
          
        //topFace = transform.flipY(topFace);  
        //bottomFace = transform.flipY(bottomFace);  
          
        //垂直側面的处理  
        var size = topFace.length;  
          
        var vertFace = [];  
        for (var i = 0; i < size; i++) {  
            vertFace.push([topFace[i][0], topFace[i][1], bottomFace[i][0], bottomFace[i][1]]);  
        }  
          
		  
        //圆柱
        shape.faceDraw(vertFace, 'blue', 1);  
        shape.strokeDraw([].concat(bottomFace), 'pink');  
        shape.fillDraw([].concat(topFace), 'red');  
  
  
		//圆锥
		topFace = transform.scale(topFace, 2);
         
		shape.fillDraw([].concat(topFace), 'red');  
		
		vertFace = [];  
        for (var i = 0; i < size; i++) {  
            vertFace.push([topFace[i][0], topFace[i][1], 0, 2*h]);  
        }  
      
		shape.faceDraw(vertFace, 'red', 1); 
    }
	</span>

<span style="font-size:18px;">	 if (1) {  
        var r = 20;  
        config.setSector(1,1,1,1);  
        config.graphPaper2D(0, 0, r);  
        config.axis3D(0, 0, 0, 180);  
          
        var transform = new Transform();  
          
        var a = 6*r, b = 1*r, h = 4*r;  
        var array = shape.nEdge(0, 0, a, 4);  
		var array2 = transform.scale(array, 0.6);
          
        var size = array.length;  
          
        var topFace = [], bottomFace = [];  
        for (var i = 0; i < size; i++) {  
            topFace.push(shape.point3D(array[i][0], h, array[i][1]));  
            bottomFace.push(shape.point3D(array2[i][0], -h, array2[i][1]));  
        }  
          
        //topFace = transform.flipY(topFace);  
        //bottomFace = transform.flipY(bottomFace);  
          
        //垂直側面的处理  
        var size = topFace.length;  
          
        var vertFace = [];  
        for (var i = 0; i < size; i++) {  
            vertFace.push([topFace[i][0], topFace[i][1], bottomFace[i][0], bottomFace[i][1]]);  
        }  
          
		  
        //台柱
        shape.faceDraw(vertFace, 'blue', 1);  
        shape.strokeDraw([].concat(bottomFace), 'pink');  
        shape.fillDraw([].concat(topFace), 'red');  
  

    }
	</span>

<span style="font-size:18px;">>>> 
共同拥有64个小正方体。
0面着色的有 8 个面。

1面着色的有 24 个面。

2面着色的有 24 个面。

3面着色的有 8 个面。
4面着色的有 0 个面。
5面着色的有 0 个面。

6面着色的有 0 个面。

#9 正方体着色统计  
def cubicPaint(N):
    #N为每条棱长切割的段数
    a = [];  
  
    for z in range(N):  
        for y in range(N):  
            for x in range(N):  
                a.append([x, y, z]);  

    #print(a);  
  
    size = len(a);  
    b = [6]*size;  
    #print(b);  
      
    for i in range(size):  
        for j in range(i, size):  
            xdiff = abs(a[i][0] - a[j][0]);  
            ydiff = abs(a[i][1] - a[j][1]);  
            zdiff = abs(a[i][2] - a[j][2]);  
            #对于相邻的立方体仅仅有一个坐标相差1。其余都同样。  
            if (xdiff + ydiff + zdiff == 1):  
                b[i]-=1;  
                b[j]-=1;  
  
    #统计n面涂色的数量。

    b1 = [0]*7;
      
    for i in range(size):
        for j in range(7):
            if (b[i] == j):
                b1[j]+=1;
                break;  
 

    print('共同拥有{0}个小正方体。
'.format(size));
    for i in range(7):
        print('{0}面着色的有 {1} 个面。'.format(i, b1[i]));
		</span>

<span style="font-size:18px;">#题5
>>> 
等比数列：  [100, 50.0, 25.0, 12.5, 6.25, 3.125, 1.5625, 0.78125, 0.390625, 0.1953125]
前10项和是：199.8046875
>>> 0.1953125/2
0.09765625
>>> 199.8046875*2-100
299.609375

#等比数列  
def geometricSequence(a0, q, N):  
    seq = [];  
    for i in range(N):  
        seq.append(a0);  
        a0 *= q;  
  
    print('等比数列： ', seq);  
    print('前{0}项和是：{1}'.format(N, sum(seq)));  
    #return sum(seq);  
	
def tmp():
    a0 = 100;
    q = 0.5;
    N = 10;
    geometricSequence(a0, q, N)
	</span>

<span style="font-size:18px;">#1
def weekday(N):
    days = ['Sun', 'Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat'];

    return days[N%7];

#2
def fun(x):  
    return 2*x**3-4*x**2-3*x+1;
  
def bisection(xMin, xMax):  
    if fun(xMin)*fun(xMax) > 0:  
        return float('inf');  
    elif fun(xMin) == 0:  
        return xMin;  
    elif fun(xMax) == 0:  
        return xMax;  
    else:  
        epsilon = 10e-6;  
          
        while (abs(xMin-xMax)> epsilon):  
            xMid = (xMin+xMax)/2;  
            if (fun(xMid)*fun(xMin)< 0):  
                xMax = xMid;  
            elif (fun(xMid)*fun(xMax) < 0):  
                xMin = xMid;  
            else:  
                return xMid;  
  
        return xMid;


#3
def palindrome(N):
    s = str(N);
    size = len(s);

    if (size < 2):
        return False;

    for i in range(size//2):
        if (s[i] != s[-(i+1)]):
            print('第{0}位： {1}和{2}不同样'.format(i, s[i], s[-(i+1)]));
            return False;

    return True;

def tmp():
    a = [123, 1234, 1221, 10011001, 132434231];
    for i in range(len(a)):
        print(a[i], '-->', palindrome(a[i]));
		
</span>

<span style="font-size:18px;">	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 = 5, spaceY = 1000;         
        var xS = -10, xE = 30;        
        var yS = -5000, yE = 5000;        
        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 = [];     
                
        //须要显示的函数说明      
        var f1 = 'y=1.3*x^3-26.013*x^2+0.975*x-19.50975';  
        //函数描点      
        for (var x = xS; x <= xE; x+=0.3) {        
            if (x != 0) {      
                a.push([x, funTask(x)]);      
    
    
    
    
            }      
        }        
    
        //二分法求函数的零点    
        //区间的最小值和最大值    
        var minX = 20, maxX = 21;    
        var y1 = y2 = 0;    
        x = minX;    
        y1 = funTask(x);    
        x = maxX;    
        y2 = funTask(x);    
            
        //假设在给定区间上存在有零点    
        if (y1 * y2 < 0) {    
            var epsilon = 0.000001;    
            while (Math.abs(y1-y2) > epsilon) {    
                
                x = minX;    
                y1 = funTask(x);    
                x = maxX;    
                y2 = funTask(x);    
                    
                    
                x = (minX+maxX)/2;    
                y = funTask(x);    
                    
                if (y * y1 < 0) {    
                    maxX = x;    
                }    
                else {    
                    minX = x;    
                }    
                    
    
            }    
            plot.setFillStyle('blue')    
                .fillText('零点：x = '+ ((minX+maxX)/2).toFixed(3), -200, -60, 120);    
        }    
               
               
        //存放暂时数组      
        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);        
        }      
              
      
    }
	
	

}


function funTask(x) {
	return 1.3*x*x*x-26.013*x*x+0.975*x-19.50975;
}</span>

至此为止。

<span style="font-size:18px;">	if (1) {
		var r = 20;
        
        var stat = new Statistic();            
        var data = [
			[10,7],
			[10,6],
			[9,2],
			//
			[10,4],
			[10,2],
			[12,10],
			[8,6],
			//
			[5,3],
			[8,2],
			[6,4],
			//
			[18,9],
			[14,9],
			[13,8],
			//
			[7,3],
			[11,7],
			[8,6]
			
		
		];
		
		
		text = ['集', '函', '用', '体', '面', '线', '圆', '算', '统', '率', '三', '向', '变', '解', '列', '式'];  
			
		var len = data.length;  
		var data2 = new Array(len);

		for (var i = 0; i < len; i++) {
			data2[i] = 0;
			for (var j = 0; j < 2; j++) {
				data2[i] += data[i][j];
			}
		}
  
        var sum = 0;
		for (var i = 0; i < len; i++) {
			sum += data2[i];

		}
 
		        stat.init(data, '章节', '复习题数', 2);       
        stat.multiBarChart(text, ['A组', 'B组'], -10, 0);     
          
        plot.setFillStyle('blue')  
            .fillText('总计：'+sum.toFixed(0), 60, 30, 200); 
	
	}
	
</span>

至此，[人叫板老师]赐给[机器小伟]的主修功法[天地人正冊]， 小伟已经所有修炼完成了。

当中共同拥有题：

>>> 245+548+247
1040

[人叫板老师]称其为千人斩。

本节到此结束，欲知后事怎样，请看下回分解。