[从头学数学] 第140节 勾股定理

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[勾股定理]。

正剧开始：

星历2016年03月19日 10:03:20, 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[勾股定理]。

<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.axis2D(0, 0,180);  var triangle = new Triangle();var array = triangle.know3edges([3, 4, 5]);var tmp = [];plot.translate(r, -r).save();for (var i = 0; i < 4; i++) {tmp = [].concat(array);shape.angleDraw(tmp, 'red', 2*r, 'ABC');plot.rotate(Math.PI/2);plot.translate(2*r, 0);}plot.restore();}</span>

这里是小伟用到的工具：

<span style="font-size:18px;">function Triangle() {this.edges = [];this.angles = [];//已知三条边this.know3edges = function(edges) {this.edges = [];this.angles = [];this.edges = edges;//角度为弧度单位//a边对应角this.angles.push(Math.acos((edges[1]*edges[1] + edges[2]*edges[2]-edges[0]*edges[0])/(2*edges[1]*edges[2])));//b边对应角this.angles.push(Math.acos((edges[0]*edges[0] + edges[2]*edges[2]-edges[1]*edges[1])/(2*edges[0]*edges[2])));//c边对应角this.angles.push(Math.acos((edges[0]*edges[0] + edges[1]*edges[1]-edges[2]*edges[2])/(2*edges[0]*edges[1])));var x0 = 0, y0 = 0;var x1 = x0 + this.edges[0], y1 = y0;var x2 = x0 + this.edges[1] * Math.cos(-this.angles[2]),y2 = y0 + this.edges[1] * Math.sin(-this.angles[2]);var retArray = new Array();retArray.push([x0, y0]);retArray.push([x1, y1]);retArray.push([x2, y2]);return retArray;}//已知两个角this.know2angles = function(angles, r) {this.edges = [];this.angles = [];this.angles = [angles[0]/180*Math.PI, angles[1]/180*Math.PI,   (180-(angles[0]+angles[1]))/180*Math.PI];//设其中一边长度为10r = r > 0 ? r : 10;//A边this.edges.push(r);var angleA = this.angles[0];angleB = this.angles[1];angleC = this.angles[2];//B边this.edges.push(Math.sin(angleB)/Math.sin(angleA)*r);//C边this.edges.push(Math.sin(angleC)/Math.sin(angleA)*r);var x0 = 0, y0 = 0;var x1 = x0 + this.edges[0], y1 = y0;var x2 = x0 + this.edges[1] * Math.cos(-this.angles[2]),y2 = y0 + this.edges[1] * Math.sin(-this.angles[2]);var retArray = new Array();retArray.push([x0, y0]);retArray.push([x1, y1]);retArray.push([x2, y2]);return retArray;}//已知2条边this.know2edges = function(edges, angle) {this.edges = [];this.angles = [];//如果没有指定两边的夹角，默认为90度angle = angle ? angle/180*Math.PI : Math.PI/2;var edgeC = Math.sqrt(edges[0]*edges[0]+edges[1]*edges[1]-2*edges[0]*edges[1]*Math.cos(angle));this.edges = [edges[0], edges[1], edgeC];var edgeA = this.edges[0],edgeB = this.edges[1];//角度为弧度单位//a边对应角this.angles.push(Math.acos((edgeB*edgeB + edgeC*edgeC-edgeA*edgeA)/(2*edgeB*edgeC)));//b边对应角this.angles.push(Math.acos((edgeA*edgeA + edgeC*edgeC-edgeB*edgeB)/(2*edgeA*edgeC)));//c边对应角this.angles.push(angle);var x0 = 0, y0 = 0;var x1 = x0 + this.edges[0], y1 = y0;var x2 = x0 + this.edges[1] * Math.cos(-this.angles[2]),y2 = y0 + this.edges[1] * Math.sin(-this.angles[2]);var retArray = new Array();retArray.push([x0, y0]);retArray.push([x1, y1]);retArray.push([x2, y2]);return retArray;}//返回角度和边信息的字符串this.info = function() {var angleLabel = ['C', 'A', 'B'];var edgeLabel = ['ab', 'bc', 'ac'];var s = '';for (var i = 0; i < 3; i++) {s += edgeLabel[i]+' : ';s += this.edges[i].toFixed(2)+' ; ';}for (var i = 0; i < 3; i++) {s += angleLabel[i]+' : ';s += (this.angles[i]*180/Math.PI).toFixed(2) + ' ; ';}return s;}}</span>

还有：

<span style="font-size:18px;">this.angleDraw = function(array, style, scale, vertexLabel) {//vertexLabel是顶点编号顺序字符串 ABC,...style = style ? style : 'black';//array是一个存放二维坐标点序列的数组var a0 = new Array();a0 = [].concat(array);scale = scale ? scale : 1;var len = a0.length;if (scale != 1 && scale > 0) {for (var i = 0; i < len; i++) {for (var j = 0; j < 2; j++) {a0[i][j]*=scale;}}}//进行环状排序，这样传入的array就可以任意顺序放置坐标点。var a = this.angularSort(a0);//分两次绘点和连线var tmp = [].concat(a);this.pointDraw(tmp, style);tmp = [].concat(a);this.strokeDraw(tmp, style);var d1, d2, d3, angle;var x1,y1, x2, y2, x3, y3;var s;//坐标点编号var s0 = vertexLabel ? vertexLabel : 'ABCDEFGHIJKLMNOPQRSTUVWXYZ';//标记边的长度var edgeLong = 0;var measure = 0;//为每个点利用余弦定理求角for (var i = 0; i < len; i++) {if (i == 0) {x1 = a[len-1][0];y1 = a[len-1][1];x3 = a[i+1][0];y3 = a[i+1][1];}else if (i == len-1) {x1 = a[i-1][0];y1 = a[i-1][1];x3 = a[0][0];y3 = a[0][1];}else {x1 = a[i-1][0];y1 = a[i-1][1];x3 = a[i+1][0];y3 = a[i+1][1];}x2 = a[i][0];y2 = a[i][1];d1 = (x1-x2)*(x1-x2)+(y1-y2)*(y1-y2);d2 = (x2-x3)*(x2-x3)+(y2-y3)*(y2-y3);d3 = (x1-x3)*(x1-x3)+(y1-y3)*(y1-y3);angle = Math.acos((d1+d2-d3)/(2*Math.sqrt(d1*d2)))/Math.PI*180;s = angle.toFixed(2)+'°';//document.write(s+'<p>');//标注角度和顶点编号plot.setFillStyle('purple');plot.fillText(s, x2, -y2-5, 100);plot.setFillStyle(style);plot.fillText(s0[i], x2, -y2+20, 20);edgeLong = (Math.sqrt(d1)/scale).toFixed(2);measure = plot.measureText(edgeLong);plot.setFillStyle('blue');plot.fillText(edgeLong, (x1+x2-measure)/2, -(y1+y2)/2+20, measure);}//由于处理会改变原矩阵，看以下操作能否恢复原矩阵if (scale != 1 && scale > 0) {for (var i = 0; i < len; i++) {for (var j = 0; j < 2; j++) {a0[i][j]/=scale;}}}}</span>

看到这个题，阿伟就想笑，这个对角线就比木板多了4个毫米，如果这块板太薄，过门时很容易折坏，

如果稍微厚那么一点，就等着撞门框吧，这理论的数据可当不的真的哦。

<span style="font-size:18px;">function myDraw(xGlobal, yGlobal) {  var config = new PlotConfiguration();      config.init();  config.setPreference();  var r = 80;config.setSector(1,1,1,1);  config.graphPaper2D(0, 0, r/4);config.axis2D(0, 0,180);  var triangle = new Triangle();var array = triangle.know2edges([Math.sqrt(2.6*2.6-2.4*2.4), 2.4]);var tmp = [];config.setSector(1,3,1,1); tmp = [].concat(array);shape.angleDraw(tmp, 'red', r);array = triangle.know2edges([Math.sqrt(2.6*2.6-1.9*1.9), 1.9]);config.setSector(1,3,1,2); tmp = [].concat(array);shape.angleDraw(tmp, 'green', r);}</span>

<span style="font-size:18px;">function myDraw(xGlobal, yGlobal) {  var config = new PlotConfiguration();      config.init();  config.setPreference();  var r = 25;config.setSector(1,1,1,1);  config.graphPaper2D(0, 0, r);config.axis2D(0, 0,180);  /*var triangle = new Triangle();var array = triangle.know2edges([Math.sqrt(2.6*2.6-2.4*2.4), 2.4]);var tmp = [];config.setSector(2,3,1,1); tmp = [].concat(array);shape.angleDraw(tmp, 'red', r);array = triangle.know2edges([Math.sqrt(2.6*2.6-1.9*1.9), 1.9]);config.setSector(2,3,1,2); tmp = [].concat(array);shape.angleDraw(tmp, 'green', r);*/var array = [];var thita = 0;var rho = 0;var x, y;for (var i = 0; i < 36; i++) {rho = Math.sqrt(i);x = rho*Math.cos(thita);y = rho*Math.sin(thita);array.push([x, -y]);thita += Math.PI/12;}var tmp = [];tmp = [].concat(array);shape.pointDraw(tmp, 'red', r);tmp = [].concat(array);shape.multiLineDraw(tmp, 'pink', r);}</span>

<span style="font-size:18px;">function myDraw(xGlobal, yGlobal) {  var config = new PlotConfiguration();      config.init();  config.setPreference();  var r = 50;config.setSector(1,1,1,1);  config.graphPaper2D(0, 0, r/2);config.axis2D(0, 0,180);  var triangle = new Triangle();var array = triangle.know2edges([3, 4]);var tmp = [];config.setSector(2,3,1,1); tmp = [].concat(array);shape.angleDraw(tmp, 'red', r);array = triangle.know2edges([2.4, 0.7]);config.setSector(2,3,1,2); tmp = [].concat(array);shape.angleDraw(tmp, 'red', 2*r, 'AOB');}</span>

<span style="font-size:18px;">function myDraw(xGlobal, yGlobal) {  var config = new PlotConfiguration();      config.init();  config.setPreference();  var r = 50;config.setSector(1,1,1,1);  config.graphPaper2D(0, 0, r/2);config.axis2D(0, 0,180);  var triangle = new Triangle();var array = triangle.know2edges([19, 39]);var tmp = [];config.setSector(2,3,1,1); tmp = [].concat(array);shape.angleDraw(tmp, 'red', 6);array = triangle.know2edges([Math.sqrt(7*7-5*5), 5]);config.setSector(2,3,1,2); tmp = [].concat(array);shape.angleDraw(tmp, 'red', 20);}</span>

<span style="font-size:18px;">function myDraw(xGlobal, yGlobal) {  var config = new PlotConfiguration();      config.init();  config.setPreference();  var r = 50;config.setSector(1,1,1,1);  config.graphPaper2D(0, 0, r/2);config.axis2D(0, 0,180);  var triangle = new Triangle();var array = triangle.know2edges([Math.sqrt(88*88-32*32), 32]);var tmp = [];config.setSector(2,3,1,1); tmp = [].concat(array);shape.angleDraw(tmp, 'red', 2);array = triangle.know2edges([5, 12]);config.setSector(2,3,1,2); tmp = [].concat(array);shape.angleDraw(tmp, 'green', 50);}</span>

<span style="font-size:18px;">var mathText = new MathText();var s = ['AE = DB','AD^[2]+DB^[2] = AB^[2]','AB^[2] = AC^[2]+BC^[2] = 2*AC^[2]'];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;">var triangle = new Triangle();var array = [];var tmp = [];array = triangle.know3edges([15, 8, 17]);config.setSector(2,3,1,1); tmp = [].concat(array);shape.angleDraw(tmp, 'red', 10);array = triangle.know3edges([13, 14, 15]);config.setSector(2,3,1,2); tmp = [].concat(array);shape.angleDraw(tmp, 'green', 10);</span>

<span style="font-size:18px;">var triangle = new Triangle();var array = [];var tmp = [];array = triangle.know3edges([18, 24, 30]);config.setSector(2,3,1,1); tmp = [].concat(array);shape.angleDraw(tmp, 'red', 10);</span>

本节到此结束，欲知后事如何，请看下回分解。