<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.8/dist/katex.min.css">
  <script src="https://cdn.jsdelivr.net/npm/katex@0.16.8/dist/katex.min.js"></script>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: transparent;
      color: #0f172a;
      padding: 8px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 8px;
      user-select: none;
    }

    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      flex-wrap: wrap;
      gap: 4px;
      background: #f1f5f9;
      padding: 3px 6px;
      border-radius: 20px;
      max-width: 100%;
    }
    .btn-angle {
      border: none;
      background: transparent;
      padding: 4px 8px;
      border-radius: 14px;
      font-size: 12px;
      font-weight: 600;
      color: #334155;
      cursor: pointer;
      transition: background-color 0.15s ease, color 0.15s ease;
    }
    .btn-angle.active {
      background: #ffffff;
      color: #0f172a;
      box-shadow: 0 1px 3px rgba(0,0,0,0.15);
    }

    .shared-pill {
      display: inline-flex;
      align-items: center;
      gap: 6px;
      background: #f5f3ff;
      border: 1.5px dashed #7c3aed;
      border-radius: 8px;
      padding: 3px 10px;
      font-size: 13px;
      color: #5b21b6;
      font-weight: 700;
    }

    .panels {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 8px;
      width: 100%;
      max-width: 580px;
    }

    @media (max-width: 500px) {
      .panels {
        grid-template-columns: 1fr;
      }
      .panel {
        display: grid !important;
        grid-template-columns: 90px 1fr;
        grid-template-rows: auto auto;
        align-items: center;
        text-align: left;
        column-gap: 12px;
        row-gap: 4px;
        padding: 6px 10px !important;
      }
      .panel-header {
        grid-column: 1 / -1;
        justify-content: flex-start;
      }
      .svg-wrap {
        grid-row: 2;
        grid-column: 1;
        max-width: 90px !important;
      }
      .formula-box {
        grid-row: 2;
        grid-column: 2;
        min-height: 42px !important;
        padding: 4px 6px !important;
      }
    }

    .panel {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      border-radius: 10px;
      padding: 8px;
      display: flex;
      flex-direction: column;
      align-items: center;
      text-align: center;
      gap: 6px;
      box-shadow: 0 1px 2px rgba(0,0,0,0.04);
    }

    .panel-header {
      font-size: 13px;
      font-weight: 800;
      display: flex;
      align-items: center;
      gap: 6px;
    }
    .panel-arc .panel-header { color: #0369a1; }
    .panel-sector .panel-header { color: #c2410c; }

    .tag-1d {
      font-size: 11px;
      font-weight: 800;
      padding: 1px 6px;
      border-radius: 4px;
      background: #e0f2fe;
      color: #0369a1;
      border: 1px solid #bae6fd;
    }
    .tag-2d {
      font-size: 11px;
      font-weight: 800;
      padding: 1px 6px;
      border-radius: 4px;
      background: #ffedd5;
      color: #c2410c;
      border: 1px solid #fed7aa;
    }

    .svg-wrap {
      width: 100%;
      max-width: 130px;
      aspect-ratio: 1;
      display: flex;
      align-items: center;
      justify-content: center;
    }
    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
    }

    .formula-box {
      background: #f8fafc;
      border: 1px solid #cbd5e1;
      border-radius: 6px;
      padding: 4px 6px;
      width: 100%;
      font-size: 13px;
      display: flex;
      align-items: center;
      justify-content: center;
      min-height: 44px;
      overflow-x: auto;
    }
  </style>
</head>
<body>

  <div class="controls">
    <button class="btn-angle" data-deg="45">45° (⅛)</button>
    <button class="btn-angle active" data-deg="90">90° (¼)</button>
    <button class="btn-angle" data-deg="120">120° (⅓)</button>
    <button class="btn-angle" data-deg="180">180° (½)</button>
  </div>

  <div class="shared-pill">
    <span>Fraction of Circle:</span>
    <span id="fracLabel"></span>
  </div>

  <div class="panels">
    
    <div class="panel panel-arc">
      <div class="panel-header">
        <span>Arc Length</span>
        <span class="tag-1d">1D</span>
      </div>
      <div class="svg-wrap">
        <svg viewBox="0 0 160 160">
          
          <circle cx="80" cy="80" r="60" fill="none" stroke="#cbd5e1" stroke-width="2" stroke-dasharray="4 3" />
          
          <line id="arcR1" x1="80" y1="80" x2="140" y2="80" stroke="#475569" stroke-width="1.75" />
          <line id="arcR2" x1="80" y1="80" x2="80" y2="20" stroke="#475569" stroke-width="1.75" />
          
          <path id="arcAngle" fill="none" stroke="#5b21b6" stroke-width="2" />
          <text id="arcAngleTxt" fill="#5b21b6" font-size="11" font-weight="800" text-anchor="middle"></text>
          
          <text x="110" y="74" fill="#1e293b" font-size="12" font-weight="700" font-style="italic" text-anchor="middle">r</text>
          
          <circle cx="80" cy="80" r="3" fill="#1e293b" />
          
          <path id="arcPath" fill="none" stroke="#0284c7" stroke-width="5.5" stroke-linecap="round" />
        </svg>
      </div>
      <div class="formula-box" id="arcFormula"></div>
    </div>

    
    <div class="panel panel-sector">
      <div class="panel-header">
        <span>Sector Area</span>
        <span class="tag-2d">2D</span>
      </div>
      <div class="svg-wrap">
        <svg viewBox="0 0 160 160">
          
          <circle cx="80" cy="80" r="60" fill="none" stroke="#cbd5e1" stroke-width="2" stroke-dasharray="4 3" />
          
          <path id="sectorPath" fill="#fdba74" fill-opacity="0.65" stroke="#c2410c" stroke-width="2" />
          
          <line id="secR1" x1="80" y1="80" x2="140" y2="80" stroke="#475569" stroke-width="1.75" />
          <line id="secR2" x1="80" y1="80" x2="80" y2="20" stroke="#475569" stroke-width="1.75" />
          
          <path id="secAngle" fill="none" stroke="#5b21b6" stroke-width="2" />
          <text id="secAngleTxt" fill="#5b21b6" font-size="11" font-weight="800" text-anchor="middle"></text>
          
          <text x="110" y="74" fill="#1e293b" font-size="12" font-weight="700" font-style="italic" text-anchor="middle">r</text>
          
          <circle cx="80" cy="80" r="3" fill="#1e293b" />
        </svg>
      </div>
      <div class="formula-box" id="sectorFormula"></div>
    </div>
  </div>

  <script>
    const CX = 80, CY = 80, R = 60, ANGLE_R = 20;

    function polarToCartesian(cx, cy, r, angleInDegrees) {
      const rad = (angleInDegrees * Math.PI) / 180.0;
      return {
        x: cx + (r * Math.cos(rad)),
        y: cy - (r * Math.sin(rad))
      };
    }

    function describeArc(cx, cy, r, startAngle, endAngle) {
      const start = polarToCartesian(cx, cy, r, endAngle);
      const end = polarToCartesian(cx, cy, r, startAngle);
      const largeArcFlag = endAngle - startAngle <= 180 ? "0" : "1";
      return [
        "M", start.x, start.y,
        "A", r, r, 0, largeArcFlag, 1, end.x, end.y
      ].join(" ");
    }

    function describeSector(cx, cy, r, startAngle, endAngle) {
      const start = polarToCartesian(cx, cy, r, endAngle);
      const end = polarToCartesian(cx, cy, r, startAngle);
      const largeArcFlag = endAngle - startAngle <= 180 ? "0" : "1";
      return [
        "M", cx, cy,
        "L", end.x, end.y,
        "A", r, r, 0, largeArcFlag, 0, start.x, start.y,
        "Z"
      ].join(" ");
    }

    function renderDiagram(theta) {
      const endPt = polarToCartesian(CX, CY, R, theta);

      // Left: Arc diagram
      document.getElementById('arcR2').setAttribute('x2', endPt.x);
      document.getElementById('arcR2').setAttribute('y2', endPt.y);
      document.getElementById('arcPath').setAttribute('d', describeArc(CX, CY, R, 0, theta));
      document.getElementById('arcAngle').setAttribute('d', describeArc(CX, CY, ANGLE_R, 0, theta));

      // Right: Sector diagram
      document.getElementById('secR2').setAttribute('x2', endPt.x);
      document.getElementById('secR2').setAttribute('y2', endPt.y);
      document.getElementById('sectorPath').setAttribute('d', describeSector(CX, CY, R, 0, theta));
      document.getElementById('secAngle').setAttribute('d', describeArc(CX, CY, ANGLE_R, 0, theta));

      // Angle texts position
      const midAngle = theta / 2;
      const textPt = polarToCartesian(CX, CY, ANGLE_R + 13, midAngle);
      
      const arcTxt = document.getElementById('arcAngleTxt');
      arcTxt.setAttribute('x', textPt.x);
      arcTxt.setAttribute('y', textPt.y + 4);
      arcTxt.textContent = theta + '°';

      const secTxt = document.getElementById('secAngleTxt');
      secTxt.setAttribute('x', textPt.x);
      secTxt.setAttribute('y', textPt.y + 4);
      secTxt.textContent = theta + '°';

      // KaTeX formulas
      if (window.katex) {
        katex.render(
          `\\frac{${theta}^\\circ}{360^\\circ}`,
          document.getElementById('fracLabel'),
          { throwOnError: false }
        );
        katex.render(
          `s = {\\color{#5b21b6}\\frac{${theta}^\\circ}{360^\\circ}} \\cdot {\\color{#0369a1}2\\pi r}`,
          document.getElementById('arcFormula'),
          { throwOnError: false }
        );
        katex.render(
          `A = {\\color{#5b21b6}\\frac{${theta}^\\circ}{360^\\circ}} \\cdot {\\color{#c2410c}\\pi r^2}`,
          document.getElementById('sectorFormula'),
          { throwOnError: false }
        );
      } else {
        document.getElementById('fracLabel').textContent = `${theta}° / 360°`;
        document.getElementById('arcFormula').innerHTML = `s = <b>(${theta}°/360°)</b> · <span style="color:#0369a1; font-weight:700;">2πr</span>`;
        document.getElementById('sectorFormula').innerHTML = `A = <b>(${theta}°/360°)</b> · <span style="color:#c2410c; font-weight:700;">πr²</span>`;
      }
    }

    // Button interactions
    const buttons = document.querySelectorAll('.btn-angle');
    buttons.forEach(btn => {
      btn.addEventListener('click', () => {
        buttons.forEach(b => b.classList.remove('active'));
        btn.classList.add('active');
        renderDiagram(parseInt(btn.getAttribute('data-deg'), 10));
      });
    });

    // Initial render
    renderDiagram(90);
  </script>
</body>
</html>

Arc Length and Sector Area

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Sector Area and Arc Length</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      background: #ffffff;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: flex-start;
      min-height: 100vh;
      padding: 10px 12px;
      user-select: none;
    }

    .main-wrap {
      width: 100%;
      max-width: 460px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 8px;
    }

    /* Fraction Header Banner */
    .fraction-banner {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 6px 14px;
      font-size: 14px;
      font-weight: 600;
      color: #1e2945;
      width: 100%;
    }

    /* HTML Fraction Formatting */
    .math-expr {
      display: inline-flex;
      align-items: center;
      gap: 4px;
      font-weight: 700;
      color: #0369a1;
    }
    .math-frac {
      display: inline-flex;
      flex-direction: column;
      vertical-align: middle;
      text-align: center;
      font-size: 0.9em;
      line-height: 1.05;
      padding: 0 2px;
    }
    .math-num {
      border-bottom: 1.5px solid currentColor;
      padding-bottom: 1px;
    }
    .math-den {
      padding-top: 1px;
    }

    /* Diagram Canvas */
    .svg-container {
      width: 100%;
      max-width: 320px;
      aspect-ratio: 16 / 13;
      position: relative;
    }
    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
      display: block;
    }

    /* Cards / Formulas */
    .cards-row {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 8px;
      width: 100%;
    }
    .info-card {
      border-radius: 8px;
      padding: 6px 10px;
      display: flex;
      flex-direction: column;
      gap: 2px;
    }
    .card-arc {
      background: #f0f9ff;
      border: 1px solid #bae6fd;
      border-left: 4px solid #0284c7;
    }
    .card-sector {
      background: #fff7ed;
      border: 1px solid #fed7aa;
      border-left: 4px solid #ea580c;
    }
    .card-title {
      font-size: 11px;
      font-weight: 700;
      display: flex;
      align-items: center;
      gap: 4px;
    }
    .card-arc .card-title { color: #0284c7; }
    .card-sector .card-title { color: #ea580c; }
    .card-formula {
      font-size: 13px;
      color: #1e2945;
      display: flex;
      align-items: center;
      gap: 4px;
      min-height: 28px;
    }

    /* Interactive Buttons */
    .preset-row {
      display: flex;
      flex-wrap: wrap;
      justify-content: center;
      gap: 6px;
      width: 100%;
      margin-top: 2px;
    }
    .preset-btn {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      border-radius: 16px;
      padding: 4px 10px;
      font-size: 12px;
      font-weight: 600;
      color: #475569;
      cursor: pointer;
      transition: background 0.15s, border-color 0.15s, color 0.15s;
    }
    .preset-btn:hover {
      background: #e2e8f0;
      color: #1e2945;
    }
    .preset-btn.active {
      background: #1e2945;
      border-color: #1e2945;
      color: #ffffff;
    }

    @media (max-width: 380px) {
      .cards-row {
        grid-template-columns: 1fr;
        gap: 6px;
      }
      .fraction-banner {
        font-size: 13px;
        padding: 5px 10px;
      }
      .preset-btn {
        padding: 3px 8px;
        font-size: 11px;
      }
    }
  </style>
</head>
<body>

<div class="main-wrap">
  
  <div class="fraction-banner">
    <span>Fraction of Circle:</span>
    <span class="math-expr" id="fracEquation"></span>
  </div>

  
  <div class="svg-container">
    <svg viewBox="0 0 320 260">
      
      <circle cx="160" cy="130" r="100" fill="#f8fafc" stroke="#cbd5e1" stroke-width="1.5" stroke-dasharray="4 4" />
      
      
      <g id="spokesGroup"></g>

      
      <path id="sectorPath" fill="#fed7aa" fill-opacity="0.75" stroke="#f97316" stroke-width="2" />

      
      <path id="angleArc" fill="none" stroke="#ea580c" stroke-width="2" />
      <text id="angleText" fill="#ea580c" font-size="12" font-weight="700" text-anchor="middle" dominant-baseline="middle"></text>

      
      <line x1="160" y1="130" x2="260" y2="130" stroke="#1e2945" stroke-width="2" />
      <text x="210" y="145" fill="#1e2945" font-size="12" font-weight="700" text-anchor="middle">radius (r)</text>
      
      
      <circle cx="160" cy="130" r="3.5" fill="#1e2945" />

      
      <path id="arcPath" fill="none" stroke="#0284c7" stroke-width="4.5" stroke-linecap="round" />
    </svg>
  </div>

  
  <div class="cards-row">
    <div class="info-card card-arc">
      <div class="card-title" id="arcTitle">● Arc Length</div>
      <div class="card-formula" id="arcEquation"></div>
    </div>
    <div class="info-card card-sector">
      <div class="card-title" id="sectorTitle">■ Sector Area</div>
      <div class="card-formula" id="sectorEquation"></div>
    </div>
  </div>

  
  <div class="preset-row">
    <button class="preset-btn active" data-angle="60">60° (¹/₆)</button>
    <button class="preset-btn" data-angle="90">90° (¹/₄)</button>
    <button class="preset-btn" data-angle="120">120° (¹/₃)</button>
    <button class="preset-btn" data-angle="180">180° (¹/₂)</button>
  </div>
</div>

<script>
  const cx = 160, cy = 130, r = 100;

  function gcd(a, b) {
    return b === 0 ? a : gcd(b, a % b);
  }

  function getFraction(deg) {
    const divisor = gcd(deg, 360);
    const num = deg / divisor;
    const den = 360 / divisor;
    return { num, den };
  }

  function makeFracHTML(num, den) {
    return `<span class="math-frac"><span class="math-num">${num}</span><span class="math-den">${den}</span></span>`;
  }

  function polarToCartesian(centerX, centerY, radius, angleInDegrees) {
    const angleInRadians = (angleInDegrees * Math.PI) / 180.0;
    return {
      x: centerX + radius * Math.cos(-angleInRadians),
      y: centerY + radius * Math.sin(-angleInRadians)
    };
  }

  function updateDiagram(deg) {
    const pStart = polarToCartesian(cx, cy, r, 0);
    const pEnd = polarToCartesian(cx, cy, r, deg);
    const largeArcFlag = deg > 180 ? 1 : 0;

    // Sector path (fill)
    const sectorD = `M ${cx} ${cy} L ${pStart.x} ${pStart.y} A ${r} ${r} 0 ${largeArcFlag} 0 ${pEnd.x} ${pEnd.y} Z`;
    document.getElementById('sectorPath').setAttribute('d', sectorD);

    // Arc path (blue curve)
    const arcD = `M ${pStart.x} ${pStart.y} A ${r} ${r} 0 ${largeArcFlag} 0 ${pEnd.x} ${pEnd.y}`;
    document.getElementById('arcPath').setAttribute('d', arcD);

    // Angle Arc Indicator
    const angleRadius = 32;
    const aStart = polarToCartesian(cx, cy, angleRadius, 0);
    const aEnd = polarToCartesian(cx, cy, angleRadius, deg);
    const angleArcD = `M ${aStart.x} ${aStart.y} A ${angleRadius} ${angleRadius} 0 ${largeArcFlag} 0 ${aEnd.x} ${aEnd.y}`;
    document.getElementById('angleArc').setAttribute('d', angleArcD);

    // Angle text position
    const textPos = polarToCartesian(cx, cy, angleRadius + 15, deg / 2);
    const angleText = document.getElementById('angleText');
    angleText.setAttribute('x', textPos.x);
    angleText.setAttribute('y', textPos.y);
    angleText.textContent = `${deg}°`;

    // Spokes for slices
    const spokesGroup = document.getElementById('spokesGroup');
    spokesGroup.innerHTML = '';
    const { num, den } = getFraction(deg);
    if (den <= 12) {
      for (let i = 1; i < den; i++) {
        const spokeP = polarToCartesian(cx, cy, r, i * (360 / den));
        const line = document.createElementNS('http://www.w3.org/2000/svg', 'line');
        line.setAttribute('x1', cx);
        line.setAttribute('y1', cy);
        line.setAttribute('x2', spokeP.x);
        line.setAttribute('y2', spokeP.y);
        line.setAttribute('stroke', '#cbd5e1');
        line.setAttribute('stroke-width', '1.2');
        line.setAttribute('stroke-dasharray', '3 3');
        spokesGroup.appendChild(line);
      }
    }

    // Formulas & Labels
    const fracStr = `${num}/${den}`;
    const fracHTML = makeFracHTML(num, den);
    const angleFracHTML = makeFracHTML(`${deg}°`, '360°');

    document.getElementById('fracEquation').innerHTML = `${angleFracHTML} = ${fracHTML}`;

    document.getElementById('arcTitle').textContent = `● Arc Length (${fracStr} of Circumference)`;
    document.getElementById('arcEquation').innerHTML = `${fracHTML} × 2πr`;

    document.getElementById('sectorTitle').textContent = `■ Sector Area (${fracStr} of Area)`;
    document.getElementById('sectorEquation').innerHTML = `${fracHTML} × πr²`;
  }

  // Button interactivity
  document.querySelectorAll('.preset-btn').forEach(btn => {
    btn.addEventListener('click', () => {
      document.querySelectorAll('.preset-btn').forEach(b => b.classList.remove('active'));
      btn.classList.add('active');
      const angle = parseInt(btn.dataset.angle, 10);
      updateDiagram(angle);
    });
  });

  // Initial draw
  updateDiagram(60);
</script>

</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      background: #ffffff;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      user-select: none;
    }

    /* Formula Header */
    .formula-card {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      flex-wrap: wrap;
      margin-bottom: 8px;
      width: 100%;
    }

    .formula-main {
      font-size: 20px;
      font-weight: 700;
      display: flex;
      align-items: center;
      gap: 6px;
    }

    .block {
      display: inline-flex;
      flex-direction: column;
      align-items: center;
      padding: 4px 10px;
      border-radius: 8px;
      position: relative;
    }

    .block.purple {
      background: rgba(136, 84, 208, 0.12);
      border: 1.5px solid #8854d0;
      color: #8854d0;
    }

    .block.blue {
      background: rgba(34, 183, 255, 0.12);
      border: 1.5px solid #22b7ff;
      color: #0284c7;
    }

    .fraction {
      display: inline-flex;
      flex-direction: column;
      align-items: center;
      vertical-align: middle;
      line-height: 1;
      font-size: 16px;
    }

    .fraction .top {
      border-bottom: 1.5px solid currentColor;
      padding: 0 3px 2px;
    }

    .fraction .bottom {
      padding: 2px 3px 0;
    }

    .tag {
      font-size: 11px;
      font-weight: 600;
      letter-spacing: 0.2px;
      margin-top: 2px;
      white-space: nowrap;
    }

    /* Interactive / Stage Area */
    .stage {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 16px;
      width: 100%;
      max-width: 540px;
      flex-wrap: wrap;
    }

    .svg-wrap {
      width: 190px;
      height: 190px;
      flex-shrink: 0;
    }

    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
    }

    /* Calculation Display */
    .calc-panel {
      display: flex;
      flex-direction: column;
      gap: 8px;
      font-size: 15px;
      font-weight: 600;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 10px;
      padding: 10px 14px;
      min-width: 180px;
    }

    .calc-row {
      display: flex;
      align-items: center;
      gap: 6px;
    }

    .num-purple { color: #8854d0; font-weight: 700; }
    .num-blue { color: #0284c7; font-weight: 700; }

    /* Angle Toggle Buttons */
    .controls {
      display: flex;
      gap: 6px;
      margin-top: 8px;
    }

    .btn {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      border-radius: 6px;
      padding: 5px 10px;
      font-size: 13px;
      font-weight: 600;
      color: #475569;
      cursor: pointer;
      transition: all 0.2s ease;
    }

    .btn.active {
      background: #8854d0;
      border-color: #8854d0;
      color: #ffffff;
    }
  </style>
</head>
<body>

  
  <div class="formula-card">
    <div class="formula-main">
      <span>s =</span>
      
      <div class="block purple">
        <div class="fraction">
          <span class="top">θ</span>
          <span class="bottom">360°</span>
        </div>
        <span class="tag">Fraction of full turn</span>
      </div>

      <span>×</span>

      <div class="block blue">
        <span>2πr</span>
        <span class="tag">Total Circumference</span>
      </div>
    </div>
  </div>

  
  <div class="stage">
    <div class="svg-wrap">
      <svg viewBox="0 0 200 200" id="circleSvg">
        
        <circle cx="100" cy="100" r="75" fill="none" stroke="#22b7ff" stroke-width="2.5" stroke-dasharray="4 3" opacity="0.6"/>
        
        
        <path id="sectorFill" fill="rgba(136, 84, 208, 0.1)" stroke="none"/>
        
        
        <line x1="100" y1="100" x2="175" y2="100" stroke="#64748b" stroke-width="2"/>
        <line id="radius2" x1="100" y1="100" x2="100" y2="25" stroke="#64748b" stroke-width="2"/>
        
        
        <path id="angleArc" fill="none" stroke="#8854d0" stroke-width="2"/>
        <text id="angleLabel" x="118" y="86" fill="#8854d0" font-size="13" font-weight="700">90°</text>

        
        <text x="135" y="116" fill="#475569" font-size="12" font-weight="600">r = 6 cm</text>

        
        <path id="arcPath" fill="none" stroke="#8854d0" stroke-width="5" stroke-linecap="round"/>
        
        
        <circle cx="100" cy="100" r="3.5" fill="#1e2945"/>
      </svg>
    </div>

    
    <div class="calc-panel">
      <div class="calc-row">
        <span>s =</span>
        <span class="num-purple" id="calcFrac">(90° / 360°)</span>
        <span>×</span>
        <span class="num-blue">2π(6)</span>
      </div>
      <div class="calc-row">
        <span>s =</span>
        <span class="num-purple" id="calcReduced">¼</span>
        <span>×</span>
        <span class="num-blue">12π</span>
      </div>
      <div class="calc-row" style="padding-top: 4px; border-top: 1px solid #e2e8f0;">
        <span>s =</span>
        <span style="color: #8854d0;" id="calcExact">3π cm</span>
        <span style="color: #64748b; font-weight: 500;" id="calcApprox">≈ 9.42 cm</span>
      </div>
    </div>
  </div>

  
  <div class="controls">
    <button class="btn" onclick="setAngle(60, '⅙', '2π', '6.28')">60° (⅙ turn)</button>
    <button class="btn active" onclick="setAngle(90, '¼', '3π', '9.42')">90° (¼ turn)</button>
    <button class="btn" onclick="setAngle(180, '½', '6π', '18.85')">180° (½ turn)</button>
    <button class="btn" onclick="setAngle(270, '¾', '9π', '28.27')">270° (¾ turn)</button>
  </div>

  <script>
    const cx = 100, cy = 100, r = 75;

    function polarToCartesian(angleDeg) {
      // SVG 0 deg is at (cx + r, cy) - standard 3 o'clock position, moving counter-clockwise
      const rad = (-angleDeg) * Math.PI / 180;
      return {
        x: cx + r * Math.cos(rad),
        y: cy + r * Math.sin(rad)
      };
    }

    function setAngle(deg, fracText, exactText, approxText) {
      // Update Buttons
      document.querySelectorAll('.btn').forEach(b => {
        b.classList.toggle('active', b.textContent.includes(deg + '°'));
      });

      const p0 = { x: cx + r, y: cy }; // 0 degrees
      const p1 = polarToCartesian(deg);
      const largeArc = deg > 180 ? 1 : 0;

      // Arc path: sweep-flag = 0 for counter-clockwise in SVG
      const arcD = `M ${p0.x} ${p0.y} A ${r} ${r} 0 ${largeArc} 0 ${p1.x} ${p1.y}`;
      document.getElementById('arcPath').setAttribute('d', arcD);

      // Sector fill
      const sectorD = `M ${cx} ${cy} L ${p0.x} ${p0.y} A ${r} ${r} 0 ${largeArc} 0 ${p1.x} ${p1.y} Z`;
      document.getElementById('sectorFill').setAttribute('d', sectorD);

      // Second radius line
      const rad2 = document.getElementById('radius2');
      rad2.setAttribute('x2', p1.x);
      rad2.setAttribute('y2', p1.y);

      // Angle indicator
      const ar = 24;
      const ap = {
        x: cx + ar * Math.cos((-deg) * Math.PI / 180),
        y: cy + ar * Math.sin((-deg) * Math.PI / 180)
      };
      const angleD = `M ${cx + ar} ${cy} A ${ar} ${ar} 0 ${largeArc} 0 ${ap.x} ${ap.y}`;
      document.getElementById('angleArc').setAttribute('d', angleD);

      // Angle Label Position
      const midRad = (-deg / 2) * Math.PI / 180;
      const lr = 38;
      const lx = cx + lr * Math.cos(midRad);
      const ly = cy + lr * Math.sin(midRad) + 4;
      const label = document.getElementById('angleLabel');
      label.setAttribute('x', lx);
      label.setAttribute('y', ly);
      label.textContent = deg + '°';

      // Update text calculations
      document.getElementById('calcFrac').textContent = `(${deg}° / 360°)`;
      document.getElementById('calcReduced').textContent = fracText;
      document.getElementById('calcExact').textContent = `${exactText} cm`;
      document.getElementById('calcApprox').textContent = `≈ ${approxText} cm`;
    }

    // Init 90°
    setAngle(90, '¼', '3π', '9.42');
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      width: 100%;
      background: #ffffff;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 8px 4px;
    }
    .diagram-svg {
      width: 100%;
      max-width: 350px;
      height: auto;
      display: block;
    }
    .callout {
      margin-top: 6px;
      background: #f0f7ff;
      border: 1.5px solid #22b7ff;
      border-radius: 8px;
      padding: 6px 14px;
      font-size: 15px;
      font-weight: 700;
      color: #1e2945;
      text-align: center;
      display: flex;
      align-items: center;
      gap: 6px;
    }
    .callout span {
      color: #0284c7;
    }
  </style>
</head>
<body>

  <svg class="diagram-svg" viewBox="0 0 350 310" xmlns="http://www.w3.org/2000/svg">
    <defs>
      
      <linearGradient id="rightCyl" x1="0%" y1="0%" x2="100%" y2="0%">
        <stop offset="0%" stop-color="#e0f2fe" />
        <stop offset="50%" stop-color="#f0f9ff" />
        <stop offset="100%" stop-color="#bae6fd" />
      </linearGradient>
      <linearGradient id="obliqueCyl" x1="0%" y1="0%" x2="100%" y2="0%">
        <stop offset="0%" stop-color="#e0f2fe" />
        <stop offset="50%" stop-color="#f0f9ff" />
        <stop offset="100%" stop-color="#bae6fd" />
      </linearGradient>
      
      <linearGradient id="sliceGrad" x1="0%" y1="0%" x2="100%" y2="0%">
        <stop offset="0%" stop-color="#bae6fd" stop-opacity="0.9" />
        <stop offset="100%" stop-color="#7dd3fc" stop-opacity="0.9" />
      </linearGradient>
    </defs>

    
    <line x1="20" y1="65" x2="330" y2="65" stroke="#94a3b8" stroke-width="1.2" stroke-dasharray="4,4" />
    <line x1="20" y1="215" x2="330" y2="215" stroke="#94a3b8" stroke-width="1.2" stroke-dasharray="4,4" />

    
    
    
    <path d="M 40,65 L 40,215 A 40 14 0 0 0 120,215 L 120,65 Z" fill="url(#rightCyl)" stroke="#0284c7" stroke-width="1.5" />
    
    
    <path d="M 40,215 A 40 14 0 0 1 120,215" fill="none" stroke="#0284c7" stroke-width="1.2" stroke-dasharray="3,3" />
    
    
    <path d="M 40,140 A 40 14 0 1 0 120,140 A 40 14 0 1 0 40,140" fill="url(#sliceGrad)" stroke="#0284c7" stroke-width="1" stroke-dasharray="2,2" />
    <text x="80" y="144" font-size="11" font-weight="700" fill="#0369a1" text-anchor="middle">Area = B</text>

    
    <ellipse cx="80" cy="65" rx="40" ry="14" fill="#e0f2fe" stroke="#0284c7" stroke-width="1.5" />

    
    <path d="M 80,205 L 90,205 L 90,215" fill="none" stroke="#1e2945" stroke-width="1.4" />
    
    
    <line x1="80" y1="65" x2="80" y2="215" stroke="#1e2945" stroke-width="1.4" />
    
    
    <line x1="80" y1="215" x2="120" y2="215" stroke="#1e2945" stroke-width="1.5" />
    <circle cx="80" cy="215" r="2.5" fill="#1e2945" />
    <circle cx="120" cy="215" r="2" fill="#1e2945" />
    <text x="100" y="211" font-size="13" font-weight="700" fill="#1e2945" text-anchor="middle">r</text>
    
    
    <text x="72" y="185" font-size="14" font-weight="700" fill="#1e2945" text-anchor="end">h</text>
    <text x="80" y="245" font-size="13" font-weight="700" fill="#1e2945" text-anchor="middle">Right Cylinder</text>
    <text x="80" y="263" font-size="12" font-weight="600" fill="#475569" text-anchor="middle">Base B = πr²</text>


    
    
    
    <path d="M 222,65 L 180,215 A 40 14 0 0 0 260,215 L 302,65 Z" fill="url(#obliqueCyl)" stroke="#0284c7" stroke-width="1.5" />
    
    
    <path d="M 180,215 A 40 14 0 0 1 260,215" fill="none" stroke="#0284c7" stroke-width="1.2" stroke-dasharray="3,3" />

    
    <path d="M 201,140 A 40 14 0 1 0 281,140 A 40 14 0 1 0 201,140" fill="url(#sliceGrad)" stroke="#0284c7" stroke-width="1" stroke-dasharray="2,2" />
    <text x="241" y="144" font-size="11" font-weight="700" fill="#0369a1" text-anchor="middle">Area = B</text>

    
    <ellipse cx="262" cy="65" rx="40" ry="14" fill="#e0f2fe" stroke="#0284c7" stroke-width="1.5" />

    
    <line x1="220" y1="215" x2="260" y2="215" stroke="#1e2945" stroke-width="1.5" />
    <circle cx="220" cy="215" r="2.5" fill="#1e2945" />
    <circle cx="260" cy="215" r="2" fill="#1e2945" />
    <text x="240" y="211" font-size="13" font-weight="700" fill="#1e2945" text-anchor="middle">r</text>

    
    <line x1="165" y1="65" x2="165" y2="215" stroke="#1e2945" stroke-width="1.4" />
    <line x1="160" y1="65" x2="170" y2="65" stroke="#1e2945" stroke-width="1.4" />
    <line x1="160" y1="215" x2="170" y2="215" stroke="#1e2945" stroke-width="1.4" />
    
    <path d="M 165,205 L 175,205 L 175,215" fill="none" stroke="#1e2945" stroke-width="1.2" />
    <text x="156" y="144" font-size="14" font-weight="700" fill="#1e2945" text-anchor="end">h</text>

    
    <text x="296" y="136" font-size="12" font-style="italic" font-weight="600" fill="#64748b" text-anchor="start">Slant ℓ</text>

    
    <text x="250" y="245" font-size="13" font-weight="700" fill="#1e2945" text-anchor="middle">Oblique Cylinder</text>
    <text x="250" y="263" font-size="12" font-weight="600" fill="#475569" text-anchor="middle">Base B = πr²</text>
  </svg>

  <div class="callout">
    <span>Equal Volumes:</span> V = B · h = πr²h
  </div>

</body>
</html>

Understanding Cavalieri's Principle for 2D and 3D Figures

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Volume by Slicing</title>
  <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.8/dist/katex.min.css">
  <script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.8/dist/katex.min.js"></script>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      -webkit-font-smoothing: antialiased;
    }

    body {
      width: 100%;
      min-height: 100%;
      background: #ffffff;
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
      color: #0f172a;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      padding: 14px 16px;
      overflow-x: hidden;
      user-select: none;
    }

    .container {
      width: 100%;
      max-width: 380px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 10px;
    }

    .toggle-group {
      display: flex;
      background: #f1f5f9;
      padding: 3px;
      border-radius: 8px;
      gap: 4px;
      width: 100%;
      max-width: 320px;
      border: 1px solid #e2e8f0;
    }

    .toggle-btn {
      flex: 1;
      border: none;
      background: transparent;
      padding: 7px 10px;
      font-size: 13px;
      font-weight: 600;
      color: #475569;
      border-radius: 6px;
      cursor: pointer;
      transition: background 0.15s ease, color 0.15s ease, box-shadow 0.15s ease;
      text-align: center;
      touch-action: manipulation;
    }

    .toggle-btn:hover {
      color: #0f172a;
    }

    .toggle-btn.active {
      background: #ffffff;
      color: #0369a1;
      box-shadow: 0 1px 3px rgba(0, 0, 0, 0.1);
      font-weight: 700;
    }

    .svg-container {
      width: 100%;
      display: flex;
      align-items: center;
      justify-content: center;
      min-height: 220px;
      max-height: 250px;
    }

    svg {
      width: 100%;
      height: 100%;
      max-height: 250px;
      overflow: visible;
    }

    .slab-top {
      fill: #e0f2fe;
      stroke: #38bdf8;
      stroke-width: 0.75;
    }

    .slab-front {
      fill: #bae6fd;
      stroke: #0284c7;
      stroke-width: 0.75;
    }

    .slab-side {
      fill: #7dd3fc;
      stroke: #0369a1;
      stroke-width: 0.75;
    }

    .slab-highlight-top {
      fill: #38bdf8;
      stroke: #0284c7;
      stroke-width: 1.2;
    }

    .slab-highlight-front {
      fill: #0284c7;
      stroke: #0369a1;
      stroke-width: 1.2;
    }

    .slab-highlight-side {
      fill: #0369a1;
      stroke: #0c4a6e;
      stroke-width: 1.2;
    }

    .math-card {
      width: 100%;
      max-width: 340px;
      background: #f8fafc;
      border: 1px solid #cbd5e1;
      border-radius: 8px;
      padding: 10px 12px;
      display: flex;
      justify-content: space-around;
      align-items: center;
      gap: 8px;
    }

    .math-col {
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 3px;
      flex: 1;
    }

    .math-title {
      font-size: 11px;
      font-weight: 700;
      color: #334155;
      text-transform: uppercase;
      letter-spacing: 0.6px;
    }

    .math-formula {
      font-size: 14px;
      color: #0f172a;
      font-weight: 600;
      min-height: 24px;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    .divider {
      width: 1px;
      height: 32px;
      background: #cbd5e1;
    }
  </style>
</head>
<body>
  <div class="container">
    <div class="toggle-group" role="tablist">
      <button id="btn5" class="toggle-btn active" role="tab" aria-selected="true">n = 5 Thick Slabs</button>
      <button id="btn30" class="toggle-btn" role="tab" aria-selected="false">n = 30 Thin Slabs</button>
    </div>

    <div class="svg-container">
      <svg id="diagram" viewBox="0 0 320 230" aria-label="3D visualization of solid slicing"></svg>
    </div>

    <div class="math-card">
      <div class="math-col">
        <div class="math-title" id="slabLabel">Slab Volume</div>
        <div id="slabEq" class="math-formula"></div>
      </div>
      <div class="divider"></div>
      <div class="math-col">
        <div class="math-title" id="totalLabel">Total Volume</div>
        <div id="totalEq" class="math-formula"></div>
      </div>
    </div>
  </div>

  <script>
    const $ = (selector) => document.querySelector(selector);
    let currentN = 5;

    function project(x, y, z) {
      // Oblique isometric projection
      const ox = 115;
      const oy = 195;
      const cosA = 0.866;
      const sinA = 0.48;
      const px = ox + (x * cosA) - (z * 0.68);
      const py = oy + (x * sinA * 0.48) + (z * 0.34) - y;
      return [px, py];
    }

    function renderMath(targetEl, tex, fallbackHtml) {
      if (window.katex && typeof katex.render === 'function') {
        try {
          katex.render(tex, targetEl, { throwOnError: false, displayMode: false });
          return;
        } catch (e) {
          // fallback below
        }
      }
      targetEl.innerHTML = fallbackHtml;
    }

    function updateFormulas(n) {
      const slabEq = $('#slabEq');
      const totalEq = $('#totalEq');
      const slabLabel = $('#slabLabel');
      const totalLabel = $('#totalLabel');

      if (n === 5) {
        slabLabel.textContent = "Slab Volume";
        totalLabel.textContent = "Total Volume (approx.)";
        renderMath(
          slabEq,
          "\\Delta V = A(y) \\cdot \\Delta h",
          "&Delta;V = A(y) &middot; &Delta;h"
        );
        renderMath(
          totalEq,
          "V \\approx \\sum A(y) \\cdot \\Delta h",
          "V &asymp; &sum; A(y) &middot; &Delta;h"
        );
      } else {
        slabLabel.textContent = "Differential Volume";
        totalLabel.textContent = "Total Volume (exact)";
        renderMath(
          slabEq,
          "dV = A(y) \\, dy",
          "dV = A(y) &middot; dy"
        );
        renderMath(
          totalEq,
          "V = \\int_0^H A(y) \\, dy",
          "V = &int;<sub>0</sub><sup>H</sup> A(y) dy"
        );
      }
    }

    function renderDiagram(n) {
      const svg = $('#diagram');
      svg.innerHTML = '';

      const W = 82;
      const D = 66;
      const H = 135;
      const shearTotal = 56;
      const dh = H / n;

      const highlightIdx = Math.floor(n * 0.52);

      // Create defs for marker/arrow
      const defs = document.createElementNS("http://www.w3.org/2000/svg", "defs");
      defs.innerHTML = `
        <marker id="arrow" viewBox="0 0 10 10" refX="5" refY="5" markerWidth="4.5" markerHeight="4.5" orient="auto-start-reverse">
          <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#0369a1"/>
        </marker>
      `;
      svg.appendChild(defs);

      // Draw slabs from bottom (0) to top (n-1)
      for (let i = 0; i < n; i++) {
        const y1 = i * dh;
        const y2 = (i + 1) * dh;
        const shear = (i / (n - 1 || 1)) * shearTotal;

        const isHi = (i === highlightIdx);
        const g = document.createElementNS("http://www.w3.org/2000/svg", "g");

        // Coordinates for slab i
        const p0 = project(shear, y1, 0);
        const p1 = project(shear + W, y1, 0);
        const p2 = project(shear + W, y1, D);
        
        const t0 = project(shear, y2, 0);
        const t1 = project(shear + W, y2, 0);
        const t2 = project(shear + W, y2, D);
        const t3 = project(shear, y2, D);

        // Front face
        const front = document.createElementNS("http://www.w3.org/2000/svg", "polygon");
        front.setAttribute("points", `${p0[0]},${p0[1]} ${p1[0]},${p1[1]} ${t1[0]},${t1[1]} ${t0[0]},${t0[1]}`);
        front.setAttribute("class", isHi ? "slab-highlight-front" : "slab-front");
        g.appendChild(front);

        // Side face
        const side = document.createElementNS("http://www.w3.org/2000/svg", "polygon");
        side.setAttribute("points", `${p1[0]},${p1[1]} ${p2[0]},${p2[1]} ${t2[0]},${t2[1]} ${t1[0]},${t1[1]}`);
        side.setAttribute("class", isHi ? "slab-highlight-side" : "slab-side");
        g.appendChild(side);

        // Top face
        const top = document.createElementNS("http://www.w3.org/2000/svg", "polygon");
        top.setAttribute("points", `${t0[0]},${t0[1]} ${t1[0]},${t1[1]} ${t2[0]},${t2[1]} ${t3[0]},${t3[1]}`);
        top.setAttribute("class", isHi ? "slab-highlight-top" : "slab-top");
        g.appendChild(top);

        svg.appendChild(g);
      }

      // Annotations for Highlighted Slab
      const hiY1 = highlightIdx * dh;
      const hiY2 = (highlightIdx + 1) * dh;
      const hiShear = (highlightIdx / (n - 1 || 1)) * shearTotal;

      const hiTopCenter = project(hiShear + W * 0.48, hiY2, D * 0.48);
      const hiEdgeRight1 = project(hiShear + W, hiY1, 0);
      const hiEdgeRight2 = project(hiShear + W, hiY2, 0);

      // Area label on top face
      const textA = document.createElementNS("http://www.w3.org/2000/svg", "text");
      textA.setAttribute("x", hiTopCenter[0]);
      textA.setAttribute("y", hiTopCenter[1] + 3.5);
      textA.setAttribute("text-anchor", "middle");
      textA.setAttribute("fill", "#0f172a");
      textA.setAttribute("font-size", n === 5 ? "12px" : "11px");
      textA.setAttribute("font-weight", "800");
      textA.textContent = "A(y)";
      svg.appendChild(textA);

      // Height dimension Δh / dh bracket on the right
      const dimX = hiEdgeRight1[0] + 16;
      const dhGroup = document.createElementNS("http://www.w3.org/2000/svg", "g");

      const labelText = n === 5 ? 'Δh' : 'dh';

      dhGroup.innerHTML = `
        <line x1="${hiEdgeRight1[0] + 3}" y1="${hiEdgeRight1[1]}" x2="${dimX}" y2="${hiEdgeRight1[1]}" stroke="#64748b" stroke-dasharray="2,2" stroke-width="1"/>
        <line x1="${hiEdgeRight2[0] + 3}" y1="${hiEdgeRight2[1]}" x2="${dimX}" y2="${hiEdgeRight2[1]}" stroke="#64748b" stroke-dasharray="2,2" stroke-width="1"/>
        <line x1="${dimX}" y1="${hiEdgeRight1[1]}" x2="${dimX}" y2="${hiEdgeRight2[1]}" stroke="#0369a1" stroke-width="1.5" marker-start="url(#arrow)" marker-end="url(#arrow)"/>
        <text x="${dimX + 6}" y="${(hiEdgeRight1[1] + hiEdgeRight2[1]) / 2 + 4}" fill="#0369a1" font-size="12px" font-weight="700">${labelText}</text>
      `;
      svg.appendChild(dhGroup);

      updateFormulas(n);
    }

    function setN(n) {
      currentN = n;
      const btn5 = $('#btn5');
      const btn30 = $('#btn30');
      
      btn5.classList.toggle('active', n === 5);
      btn5.setAttribute('aria-selected', n === 5 ? 'true' : 'false');

      btn30.classList.toggle('active', n === 30);
      btn30.setAttribute('aria-selected', n === 30 ? 'true' : 'false');

      renderDiagram(n);
    }

    $('#btn5').addEventListener('click', () => setN(5));
    $('#btn30').addEventListener('click', () => setN(30));

    // Wait for Katex script to load or execute immediately
    if (document.readyState === 'loading') {
      document.addEventListener('DOMContentLoaded', () => {
        renderDiagram(5);
      });
    } else {
      renderDiagram(5);
    }

    window.addEventListener('load', () => {
      updateFormulas(currentN);
    });
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      width: 100%;
      height: 100%;
      background: #f8f9fa;
      font-family: system-ui, -apple-system, sans-serif;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      padding: 12px;
      user-select: none;
    }
    .header {
      display: flex;
      justify-content: space-between;
      width: 100%;
      max-width: 326px;
      font-size: 13px;
      font-weight: 700;
      padding: 0 4px;
    }
    .stack-title {
      display: flex;
      align-items: center;
      gap: 6px;
    }
    .badge {
      background: #e2e8f0;
      color: #1e2945;
      padding: 2px 8px;
      border-radius: 12px;
      font-size: 11px;
    }
    .svg-container {
      width: 100%;
      max-width: 326px;
      aspect-ratio: 326 / 240;
      position: relative;
    }
    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
    }
    .controls {
      display: flex;
      align-items: center;
      gap: 10px;
      width: 100%;
      max-width: 326px;
      background: #ffffff;
      padding: 6px 12px;
      border-radius: 20px;
      border: 1px solid #e2e8f0;
    }
    .btn-play {
      background: #22b7ff;
      border: none;
      color: white;
      width: 28px;
      height: 28px;
      border-radius: 50%;
      font-size: 11px;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      flex-shrink: 0;
    }
    input[type=range] {
      flex: 1;
      accent-color: #22b7ff;
      cursor: pointer;
      height: 4px;
    }
    .formula-tag {
      font-size: 12px;
      font-weight: 700;
      color: #0284c7;
      background: #e0f2fe;
      padding: 3px 8px;
      border-radius: 6px;
      white-space: nowrap;
    }
  </style>
</head>
<body>

  <div class="header">
    <div class="stack-title">Stack A <span class="badge">Vertical</span></div>
    <div class="stack-title">Stack B <span class="badge">Oblique</span></div>
  </div>

  <div class="svg-container">
    <svg viewBox="0 0 326 240">
      <defs>
        
        <linearGradient id="coinGrad" x1="0" y1="0" x2="0" y2="1">
          <stop offset="0%" stop-color="#f1f5f9" />
          <stop offset="100%" stop-color="#cbd5e1" />
        </linearGradient>
        <linearGradient id="coinSideGrad" x1="0" y1="0" x2="1" y2="0">
          <stop offset="0%" stop-color="#94a3b8" />
          <stop offset="50%" stop-color="#cbd5e1" />
          <stop offset="100%" stop-color="#64748b" />
        </linearGradient>
        <linearGradient id="planeGrad" x1="0" y1="0" x2="1" y2="0">
          <stop offset="0%" stop-color="rgba(34, 183, 255, 0.05)" />
          <stop offset="50%" stop-color="rgba(34, 183, 255, 0.25)" />
          <stop offset="100%" stop-color="rgba(34, 183, 255, 0.05)" />
        </linearGradient>
      </defs>

      
      <line x1="16" y1="216" x2="310" y2="216" stroke="#cbd5e1" stroke-width="1.5" stroke-dasharray="4 4" />

      
      <g id="coinsGroup"></g>

      
      <g id="cuttingPlane">
        
        <polygon id="planePoly" points="12,120 300,120 314,106 26,106" fill="url(#planeGrad)" stroke="#22b7ff" stroke-width="1.5" stroke-dasharray="3 2" />
        
        <line id="heightLine" x1="6" y1="216" x2="6" y2="120" stroke="#0284c7" stroke-width="1.5" />
        <line x1="3" y1="216" x2="9" y2="216" stroke="#0284c7" stroke-width="1.5" />
        <line id="heightTick" x1="3" y1="120" x2="9" y2="120" stroke="#0284c7" stroke-width="1.5" />
        <text id="heightLabel" x="10" y="116" font-size="10" font-weight="700" fill="#0284c7">y</text>
      </g>
    </svg>
  </div>

  <div class="controls">
    <button class="btn-play" id="playBtn" aria-label="Toggle Animation">⏸</button>
    <input type="range" id="heightSlider" min="0" max="14" step="0.05" value="7">
    <div class="formula-tag">Area = πr²</div>
  </div>

  <script>
    const TOTAL_COINS = 15;
    const RX = 36;
    const RY = 9;
    const THICKNESS = 9;
    const BASE_Y = 205;
    const STACK_A_X = 82;
    const STACK_B_BASE_X = 204;
    const SHEAR_PER_COIN = 3.2;

    const coinsGroup = document.getElementById('coinsGroup');
    const planePoly = document.getElementById('planePoly');
    const heightLine = document.getElementById('heightLine');
    const heightTick = document.getElementById('heightTick');
    const heightLabel = document.getElementById('heightLabel');
    const slider = document.getElementById('heightSlider');
    const playBtn = document.getElementById('playBtn');

    // Build static SVG structure for coins
    const coinElementsA = [];
    const coinElementsB = [];

    for (let i = 0; i < TOTAL_COINS; i++) {
      const cy = BASE_Y - i * THICKNESS;
      const xA = STACK_A_X;
      const xB = STACK_B_BASE_X + i * SHEAR_PER_COIN;

      // Group for Coin A
      const gA = document.createElementNS('http://www.w3.org/2000/svg', 'g');
      gA.innerHTML = `
        <path d="M ${xA - RX} ${cy} v ${THICKNESS} a ${RX} ${RY} 0 0 0 ${2 * RX} 0 v -${THICKNESS} Z" fill="url(#coinSideGrad)" stroke="#94a3b8" stroke-width="0.75" />
        <ellipse cx="${xA}" cy="${cy}" rx="${RX}" ry="${RY}" class="coin-top" fill="url(#coinGrad)" stroke="#94a3b8" stroke-width="1" />
      `;
      coinsGroup.appendChild(gA);
      coinElementsA.push(gA.querySelector('.coin-top'));

      // Group for Coin B
      const gB = document.createElementNS('http://www.w3.org/2000/svg', 'g');
      gB.innerHTML = `
        <path d="M ${xB - RX} ${cy} v ${THICKNESS} a ${RX} ${RY} 0 0 0 ${2 * RX} 0 v -${THICKNESS} Z" fill="url(#coinSideGrad)" stroke="#94a3b8" stroke-width="0.75" />
        <ellipse cx="${xB}" cy="${cy}" rx="${RX}" ry="${RY}" class="coin-top" fill="url(#coinGrad)" stroke="#94a3b8" stroke-width="1" />
      `;
      coinsGroup.appendChild(gB);
      coinElementsB.push(gB.querySelector('.coin-top'));
    }

    function update(val) {
      const activeIdx = Math.min(TOTAL_COINS - 1, Math.floor(val));
      const py = BASE_Y - val * THICKNESS;

      // Update cutting plane
      planePoly.setAttribute('points', `8,${py + 7} 302,${py + 7} 318,${py - 7} 24,${py - 7}`);
      heightLine.setAttribute('y2', py);
      heightTick.setAttribute('y1', py);
      heightTick.setAttribute('y2', py);
      heightLabel.setAttribute('y', py - 3);

      // Highlight corresponding cross-sections
      for (let i = 0; i < TOTAL_COINS; i++) {
        const topA = coinElementsA[i];
        const topB = coinElementsB[i];
        if (i === activeIdx) {
          topA.setAttribute('fill', '#22b7ff');
          topA.setAttribute('stroke', '#0284c7');
          topA.setAttribute('stroke-width', '2');
          topB.setAttribute('fill', '#22b7ff');
          topB.setAttribute('stroke', '#0284c7');
          topB.setAttribute('stroke-width', '2');
        } else {
          topA.setAttribute('fill', 'url(#coinGrad)');
          topA.setAttribute('stroke', '#94a3b8');
          topA.setAttribute('stroke-width', '1');
          topB.setAttribute('fill', 'url(#coinGrad)');
          topB.setAttribute('stroke', '#94a3b8');
          topB.setAttribute('stroke-width', '1');
        }
      }
    }

    let isPlaying = true;
    let animDir = 1;
    let currentVal = 7;

    slider.addEventListener('input', (e) => {
      currentVal = parseFloat(e.target.value);
      update(currentVal);
    });

    playBtn.addEventListener('click', () => {
      isPlaying = !isPlaying;
      playBtn.textContent = isPlaying ? '⏸' : '▶';
    });

    function loop() {
      if (isPlaying) {
        currentVal += 0.04 * animDir;
        if (currentVal >= TOTAL_COINS - 0.05) {
          currentVal = TOTAL_COINS - 0.05;
          animDir = -1;
        } else if (currentVal <= 0.05) {
          currentVal = 0.05;
          animDir = 1;
        }
        slider.value = currentVal;
        update(currentVal);
      }
      requestAnimationFrame(loop);
    }

    update(currentVal);
    requestAnimationFrame(loop);
  </script>
</body>
</html>

面積（広さ）の概念と直接比較

図形の要素から面積を考える

面積の単位 1cm² の意味と表し方

方眼上の図形のマス目を数えて面積を求める

半分のマス目を組み合わせて求める面積

図形の形が変わっても面積が変わらない性質（面積の保存性）

math

平面図形の面積の基礎と1cm²の単位

長方形と正方形の面積の公式 — たて×横、一辺×一辺

正方形の面積の求め方 — 一辺×一辺

長方形の面積の計算練習と小数の辺を含む応用

面積の公式を使った逆算 — たての長さ＝面積÷横の長さ

正方形の1辺の長さと面積の変化 — ○＝□×□

周りの長さと面積の違い — 同じ周長で異なる面積

長方形と正方形の面積の公式と応用

L字形図形を縦または横に2つに分けて足す方法

大きな長方形から足りない部分を引く方法

複合図形の隠れた辺の長さを計算して求める

道や枠がある図形の面積の工夫した求め方

複数の求め方の比較と最も効率的な解法の検討

L字形や複合図形の面積と計算の工夫

Finding the Central Angle from Arc Length or Sector Area

Calculating the Area of Circular Segments

Perimeter of Sectors and Composite Circular Regions

Mixed Arc Length and Sector Area Problems

Circle Metrics: Arc Length, Sectors, and Circular Segments

1m²の広さと1cm²との関係（1m²＝10000cm²）

アール（a）とヘクタール（ha）を知る

1km²の広さと1m²やhaとの関係（1km²＝1000000m²＝100ha）

面積の単位換算 — cm², m², a, ha, km²（2乗の倍率）

場面に合わせた面積単位の適切な使い分け

面積の広い単位の総合マスター

面積の大きな単位（m², a, ha, km²）と単位換算

Volume and Surface Area of Right and Oblique Prisms

Volume and Surface Area of Right and Oblique Cylinders

Deriving Pyramid Volume Through Cube Decomposition

Deriving the Curved Surface Area of a Cone Using a Sector

Surface Area of Pyramids and Cones

Deriving the Volume and Surface Area of a Sphere Using Cavalieri's Principle

Comparing Volumes of Cylinders, Cones, and Spheres

Volume and Surface Area of Frustums

Word Problems: Surface Areas and Volumes of Combined Solids

Cavalieri's Principle and Spatial Measurement of 3D Solids

身の回りのものの面積の見当づけとおよその計算

複雑な形を長方形や正方形とみなして面積を見積もる

面積と材料の必要量 — ペンキ塗りやタイル貼りの計算

第4学年 面積の学習の総まとめと第5学年（平行四辺形・三角形）への展望

OGM.10.TRG.2

Aligned learning resources

Related diagrams