神奇的阿基米德螺线
今天在读数学史,正巧读到阿基米德螺线,于是写了一段js代码,生成螺线。
See the Pen Spiral by gangtao (@gangtao) on CodePen.
更多的有趣内容请参考这篇文章
代码如下(需要jquery和d3):
HTML
<div id="chart"></div>
CSS
body { background-color:#000000; }
JS
function drawCircile(pc, r, container) { var circle = container.append("circle").attr("cx", pc.x).attr("cy", pc.y).attr("r", r) .attr("stroke", "#fa6900").attr("stroke-width", 1).attr("fill", "none"); return circle; } function drawLine(p1, p2, c, isDash) { var line = c.append("line").attr("x1", p1.x).attr("y1", p1.y) .attr("x2", p2.x).attr("y2", p2.y) .style("stroke", "#ccc").style("stroke-width", 1); if (isDash) { line.style("stroke-dasharray", "5,5"); } return line; } $(function () { var center = {x: 300, y :300}; var l = 250; var a = 0, b = 0, p0, p1, line; var v = 0.3; //直线移动速度 var f = 360; //转动速度 var root = d3.select("#chart").append("svg").append("g"); drawCircile(center,3,root) var timer = setInterval(function(){ a = a + Math.PI / f; b = b + v; p0 = {x:center.x+ l * Math.sin(a), y:center.y - l * Math.cos(a) }; p1 = {x:center.x + b * Math.sin(a), y:center.y - b * Math.cos(a) }; drawCircile(p1,1,root) if( b > l ) { clearInterval(timer); } else { if(!line) { line = drawLine(center, p0, root); } else { line.transition().duration(10).attr("x2",p0.x).attr("y2",p0.y); } } },10); });
改变v和f的值分别改变点在直线上的移动过速度和直线转动的角速度,会得到不同的结果。
我拿给我还在读一年级的女儿看,她很是入迷,不断要求我修改参数,结果得到许多有趣的图形,大家可以通过这个链接自己试试看。
f=2.5 海星
f=3 雪花
f=1.414
f = 0.618
f=8.8
f = 12.12
更多的结果,大家可以自己去探索。
感叹于数学的神奇和美丽,感叹于小孩子的探索精神, 感叹于计算机和编程使得数学的探索变得简单和有趣!
2022年8月19日 08:32
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2023年1月17日 02:06
The Archimedes spiral, named after the ancient Greek mathematician Archimedes of Syracuse, is a type of spiral that can be described by the polar equation r = a?, where r is the distance from real estate services Dallas the origin, ? is the angle from the positive x-axis, and a is a constant. It is also called the "Magical Archimedes Spiral" because of the unique mathematical properties of the spiral. Good to see the details you have shared here.