<!DOCTYPE html>
<html lang="zh-CN">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>圆的面积教学工具</title>
<style>
* {
box-sizing: border-box;
margin: 0;
padding: 0;
}
body {
font-family: 'Microsoft YaHei', sans-serif;
line-height: 1.6;
color: #333;
background: linear-gradient(135deg, #f5f7fa 0%, #c3cfe2 100%);
min-height: 100vh;
padding: 20px;
overflow-x: hidden;
}
.container {
max-width: 1200px;
margin: 0 auto;
padding: 20px;
}
header {
text-align: center;
margin-bottom: 30px;
}
h1 {
color: #2c3e50;
margin-bottom: 10px;
font-size: 2.5rem;
}
.subtitle {
color: #7f8c8d;
font-size: 1.2rem;
}
.main-content {
display: flex;
flex-wrap: wrap;
gap: 30px;
justify-content: center;
}
.circle-container {
flex: 1;
min-width: 300px;
max-width: 500px;
background: white;
border-radius: 15px;
box-shadow: 0 10px 30px rgba(0, 0, 0, 0.1);
padding: 20px;
text-align: center;
}
#circle-wrapper {
width: 240px;
height: 240px;
margin: 20px auto;
position: relative;
}
#circle {
width: 100%;
height: 100%;
position: relative;
border-radius: 50%;
background: #e0e0e0;
box-shadow: inset 0 0 20px rgba(0, 0, 0, 0.1);
}
.sector {
position: absolute;
top: 0;
left: 0;
width: 100%;
height: 100%;
transform-origin: center;
cursor: grab;
transition: transform 0.3s ease;
}
.sector:hover {
filter: brightness(1.1);
}
.sector.dragging {
cursor: grabbing;
z-index: 100;
filter: brightness(1.2);
box-shadow: 0 0 15px rgba(0, 0, 0, 0.2);
}
.instructions {
flex: 1;
min-width: 300px;
max-width: 600px;
background: white;
border-radius: 15px;
box-shadow: 0 10px 30px rgba(0, 0, 0, 0.1);
padding: 25px;
}
h2 {
color: #3498db;
margin-bottom: 15px;
border-bottom: 2px solid #eee;
padding-bottom: 10px;
}
p {
margin-bottom: 15px;
}
.controls {
display: flex;
justify-content: center;
gap: 15px;
margin-top: 20px;
flex-wrap: wrap;
}
button {
padding: 12px 25px;
border: none;
border-radius: 50px;
background: #3498db;
color: white;
font-size: 1rem;
cursor: pointer;
transition: all 0.3s;
box-shadow: 0 4px 6px rgba(0, 0, 0, 0.1);
}
button:hover {
background: #2980b9;
transform: translateY(-2px);
box-shadow: 0 6px 8px rgba(0, 0, 0, 0.15);
}
.formula {
background: #f8f9fa;
padding: 15px;
border-radius: 10px;
margin: 20px 0;
text-align: center;
font-size: 1.2rem;
border-left: 4px solid #3498db;
}
.highlight {
color: #e74c3c;
font-weight: bold;
}
footer {
text-align: center;
margin-top: 40px;
color: #7f8c8d;
font-size: 0.9rem;
}
.rotation-info {
margin-top: 15px;
font-size: 0.9rem;
color: #7f8c8d;
}
.rotation-controls {
display: flex;
justify-content: center;
gap: 10px;
margin-top: 15px;
}
.rot-btn {
padding: 8px 15px;
font-size: 0.9rem;
}
@media (max-width: 768px) {
.main-content {
flex-direction: column;
align-items: center;
}
.circle-container, .instructions {
width: 100%;
}
}
</style>
</head>
<body>
<div class="container">
<header>
<h1>圆的面积公式推导</h1>
<p class="subtitle">通过分割和重组圆形来理解面积公式</p>
</header>
<div class="main-content">
<div class="circle-container">
<h2>圆形分割演示</h2>
<div id="circle-wrapper">
<div id="circle">
<!-- 扇形将通过JavaScript动态生成 -->
</div>
</div>
<div class="controls">
<button id="resetBtn">重置圆形</button>
</div>
<div class="rotation-controls">
<button class="rot-btn" id="rotateAllLeft">全部左转10°</button>
<button class="rot-btn" id="rotateAllRight">全部右转10°</button>
</div>
<p class="rotation-info">提示：可以拖动每个扇形到任意位置，点击扇形可旋转10°</p>
</div>
<div class="instructions">
<h2>教学说明</h2>
<p>这个交互式工具有助于理解圆的面积公式推导过程：</p>
<div class="formula">
圆的面积 = π × r²
</div>
<p>1. 将一个圆平均分成16个相等的扇形。</p>
<p>2. 将这些扇形重新排列，可以组合成一个近似长方形。</p>
<p>3. 这个近似长方形的长度大约是圆周长的一半（πr），宽度大约是圆的半径（r）。</p>
<p>4. 因此，圆的面积可以近似为：πr × r = πr²。</p>
<h2>操作指南</h2>
<p>• <span class="highlight">拖动</span>：点击并拖动每个扇形到页面任意位置</p>
<p>• <span class="highlight">旋转</span>：点击扇形可以将其旋转10度</p>
<p>• <span class="highlight">批量旋转</span>：使用按钮可以同时旋转所有扇形</p>
<p>• 使用重置按钮可以恢复圆形</p>
<div class="formula">
分割越多，近似程度越高！
</div>
</div>
</div>
<footer>
<p>圆的面积教学工具 © 2023 | 设计用于数学教育</p>
</footer>
</div>
<script>
document.addEventListener('DOMContentLoaded', function() {
const circle = document.getElementById('circle');
const resetBtn = document.getElementById('resetBtn');
const rotateAllLeftBtn = document.getElementById('rotateAllLeft');
const rotateAllRightBtn = document.getElementById('rotateAllRight');
const sectors = [];
const sectorCount = 16;
const radius = 120; // 圆的半径
const center = { x: radius, y: radius }; // 圆心坐标
// 创建扇形
function createSectors() {
circle.innerHTML = '';
sectors.length = 0;
for (let i = 0; i < sectorCount; i++) {
const sector = document.createElement('div');
sector.className = 'sector';
sector.dataset.index = i;
sector.dataset.rotation = 0;
// 计算扇形角度
const startAngle = (i * 2 * Math.PI) / sectorCount;
const endAngle = ((i + 1) * 2 * Math.PI) / sectorCount;
// 设置扇形样式
sector.style.clipPath = generateClipPath(startAngle, endAngle);
sector.style.backgroundColor = getColor(i);
// 添加事件监听器
sector.addEventListener('click', rotateSector);
sector.addEventListener('mousedown', startDrag);
circle.appendChild(sector);
sectors.push({
element: sector,
startAngle: startAngle,
endAngle: endAngle,
x: 0,
y: 0,
rotation: 0,
originalPosition: true
});
}
}
// 生成扇形的clip-path
function generateClipPath(startAngle, endAngle) {
// 计算扇形的起点和终点坐标
const x1 = center.x + radius * Math.cos(startAngle);
const y1 = center.y + radius * Math.sin(startAngle);
const x2 = center.x + radius * Math.cos(endAngle);
const y2 = center.y + radius * Math.sin(endAngle);
// 判断是否大于半圆
const largeArcFlag = (endAngle - startAngle) <= Math.PI ? 0 : 1;
return `path('M ${center.x} ${center.y} L ${x1} ${y1} A ${radius} ${radius} 0 ${largeArcFlag} 1 ${x2} ${y2} Z')`;
}
// 获取颜色
function getColor(index) {
const hue = (index * 360 / sectorCount) % 360;
return `hsl(${hue}, 80%, 65%)`;
}
// 旋转单个扇形 (每次10度)
function rotateSector(e) {
// 防止拖动时触发旋转
if (e.target.classList.contains('dragging')) return;
const sector = e.target;
const index = parseInt(sector.dataset.index);
const rotation = (parseInt(sector.dataset.rotation) + 10) % 360;
sector.dataset.rotation = rotation;
sector.style.transform = `translate(${sectors[index].x}px, ${sectors[index].y}px) rotate(${rotation}deg)`;
sectors[index].rotation = rotation;
e.stopPropagation();
}
// 旋转所有扇形
function rotateAll(degrees) {
sectors.forEach((sectorData, index) => {
const rotation = (parseInt(sectorData.element.dataset.rotation) + degrees) % 360;
sectorData.element.dataset.rotation = rotation;
sectorData.element.style.transform = `translate(${sectorData.x}px, ${sectorData.y}px) rotate(${rotation}deg)`;
sectorData.rotation = rotation;
});
}
// 开始拖动
function startDrag(e) {
if (e.button !== 0) return; // 只响应左键
const sector = e.target;
const index = parseInt(sector.dataset.index);
const sectorData = sectors[index];
// 标记为拖动状态
sector.classList.add('dragging');
// 保存初始位置
const startX = e.clientX;
const startY = e.clientY;
const initialX = sectorData.x;
const initialY = sectorData.y;
// 拖动函数
function drag(e) {
const dx = e.clientX - startX;
const dy = e.clientY - startY;
sectorData.x = initialX + dx;
sectorData.y = initialY + dy;
sectorData.originalPosition = false;
// 只更新位置，不更新旋转
sector.style.transform = `translate(${sectorData.x}px, ${sectorData.y}px) rotate(${sectorData.rotation}deg)`;
sector.style.zIndex = 1000;
}
// 停止拖动
function stopDrag() {
document.removeEventListener('mousemove', drag);
document.removeEventListener('mouseup', stopDrag);
sector.classList.remove('dragging');
sector.style.zIndex = 1;
}
document.addEventListener('mousemove', drag);
document.addEventListener('mouseup', stopDrag);
e.preventDefault();
}
// 重置圆形
function resetCircle() {
sectors.forEach(sectorData => {
sectorData.x = 0;
sectorData.y = 0;
sectorData.rotation = 0;
sectorData.originalPosition = true;
sectorData.element.style.transform = '';
sectorData.element.dataset.rotation = 0;
sectorData.element.style.zIndex = 1;
});
}
// 添加按钮事件监听器
resetBtn.addEventListener('click', resetCircle);
rotateAllLeftBtn.addEventListener('click', () => rotateAll(-10));
rotateAllRightBtn.addEventListener('click', () => rotateAll(10));
// 初始化
createSectors();
});
</script>
</body>
</html>
index.html