<!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">
  <link rel="stylesheet" href="{{VENDOR_CDN}}/katex.min.css">
  <script src="{{VENDOR_CDN}}/katex.min.js"></script>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #ffffff;
      color: #1e2945;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
    }

    .header-bar {
      width: 100%;
      display: flex;
      justify-content: space-between;
      align-items: center;
      padding: 4px 8px 8px;
      border-bottom: 1px solid #e2e8f0;
    }
    .header-title {
      font-size: 15px;
      font-weight: 700;
      color: #0f172a;
      display: flex;
      align-items: center;
      gap: 6px;
    }
    .badge-n {
      background: #eff6ff;
      color: #2563eb;
      font-size: 13px;
      font-weight: 700;
      padding: 2px 8px;
      border-radius: 6px;
      border: 1px solid #bfdbfe;
    }

    /* Strips Container */
    .strips-container {
      width: 100%;
      display: flex;
      flex-direction: column;
      gap: 8px;
      margin: 8px 0;
    }

    .strip {
      display: flex;
      align-items: center;
      justify-content: space-between;
      background: #f8fafc;
      border: 1.5px solid #e2e8f0;
      border-radius: 8px;
      padding: 8px 12px;
      opacity: 0.4;
      transition: all 0.3s ease;
      cursor: pointer;
    }
    .strip.active {
      opacity: 1;
      background: #ffffff;
      border-color: #2563eb;
      box-shadow: 0 2px 8px rgba(37, 99, 235, 0.12);
    }
    .strip-label {
      font-size: 12px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      color: #64748b;
      min-width: 72px;
    }
    .strip.active .strip-label {
      color: #2563eb;
    }
    .strip-calc {
      font-size: 14px;
      flex: 1;
      text-align: center;
      padding: 0 4px;
    }
    .strip-res {
      font-size: 15px;
      font-weight: 700;
      min-width: 60px;
      text-align: right;
    }
    .neg { color: #dc2626; }
    .pos { color: #16a34a; }

    /* Result Panel */
    .result-box {
      width: 100%;
      background: #f1f5f9;
      border: 1.5px solid #cbd5e1;
      border-radius: 10px;
      padding: 10px 14px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 6px;
      transition: border-color 0.3s ease;
    }
    .result-box.highlight {
      border-color: #2563eb;
      background: #f8fafc;
    }
    .result-math {
      font-size: 17px;
      font-weight: 600;
      letter-spacing: 0.5px;
    }
    .sign-badge {
      display: inline-block;
      font-weight: 800;
      padding: 1px 4px;
      border-radius: 4px;
      margin: 0 2px;
    }
    .sign-neg { background: #fee2e2; color: #dc2626; }
    .sign-pos { background: #dcfce7; color: #16a34a; }

    /* Controls */
    .controls {
      width: 100%;
      display: flex;
      align-items: center;
      justify-content: space-between;
      padding-top: 6px;
    }
    .btn-play {
      background: #2563eb;
      color: #ffffff;
      border: none;
      border-radius: 6px;
      padding: 6px 12px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      display: flex;
      align-items: center;
      gap: 4px;
    }
    .btn-play:hover { background: #1d4ed8; }
    .nav-dots {
      display: flex;
      gap: 6px;
      align-items: center;
    }
    .dot-btn {
      width: 10px;
      height: 10px;
      border-radius: 50%;
      background: #cbd5e1;
      border: none;
      cursor: pointer;
      padding: 0;
      transition: background 0.2s, transform 0.2s;
    }
    .dot-btn.active {
      background: #2563eb;
      transform: scale(1.25);
    }
    .step-tag {
      font-size: 12px;
      font-weight: 600;
      color: #64748b;
    }
  </style>
</head>
<body>

  <div class="header-bar">
    <div class="header-title">
      <span id="tex-target"></span>
    </div>
    <div class="badge-n">n = -2</div>
  </div>

  <div class="strips-container">
    
    <div class="strip active" id="strip-0" onclick="goToStep(0)">
      <span class="strip-label">Linear</span>
      <span class="strip-calc" id="calc-0"></span>
      <span class="strip-res neg" id="res-0"></span>
    </div>

    
    <div class="strip" id="strip-1" onclick="goToStep(1)">
      <span class="strip-label">Quadratic</span>
      <span class="strip-calc" id="calc-1"></span>
      <span class="strip-res pos" id="res-1"></span>
    </div>

    
    <div class="strip" id="strip-2" onclick="goToStep(2)">
      <span class="strip-label">Cubic</span>
      <span class="strip-calc" id="calc-2"></span>
      <span class="strip-res neg" id="res-2"></span>
    </div>
  </div>

  
  <div class="result-box" id="res-box" onclick="goToStep(3)">
    <div class="result-math" id="final-math"></div>
  </div>

  
  <div class="controls">
    <button class="btn-play" id="play-btn" onclick="togglePlay()">
      <span id="play-icon">⏸</span> <span id="play-text">Pause</span>
    </button>
    <div class="nav-dots">
      <button class="dot-btn active" onclick="goToStep(0)" title="Step 1"></button>
      <button class="dot-btn" onclick="goToStep(1)" title="Step 2"></button>
      <button class="dot-btn" onclick="goToStep(2)" title="Step 3"></button>
      <button class="dot-btn" onclick="goToStep(3)" title="All Steps"></button>
    </div>
    <div class="step-tag" id="step-desc">Step 1 of 4</div>
  </div>

  <script>
    const stepsData = [
      {
        target: "(1+x)^{-2}",
        calcs: [
          { id: "calc-0", tex: "\\frac{-2}{1!} x" },
          { id: "res-0", tex: "-2x" },
          { id: "calc-1", tex: "\\frac{(-2)(-3)}{2!} x^2" },
          { id: "res-1", tex: "+3x^2" },
          { id: "calc-2", tex: "\\frac{(-2)(-3)(-4)}{3!} x^3" },
          { id: "res-2", tex: "-4x^3" }
        ]
      }
    ];

    function renderMath() {
      if (window.katex) {
        katex.render("(1 + x)^{-2}", document.getElementById("tex-target"), { throwOnError: false });
        katex.render("\\frac{-2}{1} x", document.getElementById("calc-0"), { throwOnError: false });
        katex.render("-2x", document.getElementById("res-0"), { throwOnError: false });

        katex.render("\\frac{(-2)(-3)}{2} x^2", document.getElementById("calc-1"), { throwOnError: false });
        katex.render("+3x^2", document.getElementById("res-1"), { throwOnError: false });

        katex.render("\\frac{(-2)(-3)(-4)}{6} x^3", document.getElementById("calc-2"), { throwOnError: false });
        katex.render("-4x^3", document.getElementById("res-2"), { throwOnError: false });

        document.getElementById("final-math").innerHTML = 
          '1 <span class="sign-badge sign-neg">- 2x</span> ' +
          '<span class="sign-badge sign-pos">+ 3x²</span> ' +
          '<span class="sign-badge sign-neg">- 4x³</span> + ...';
      } else {
        document.getElementById("tex-target").textContent = "(1 + x)⁻²";
        document.getElementById("calc-0").textContent = "(-2/1) · x";
        document.getElementById("res-0").textContent = "-2x";
        document.getElementById("calc-1").textContent = "(-2)(-3)/2 · x²";
        document.getElementById("res-1").textContent = "+3x²";
        document.getElementById("calc-2").textContent = "(-2)(-3)(-4)/6 · x³";
        document.getElementById("res-2").textContent = "-4x³";
        document.getElementById("final-math").textContent = "1 - 2x + 3x² - 4x³ + ...";
      }
    }

    let currentStep = 0;
    let isPlaying = true;
    let timer = null;

    const strips = [
      document.getElementById('strip-0'),
      document.getElementById('strip-1'),
      document.getElementById('strip-2')
    ];
    const resBox = document.getElementById('res-box');
    const dots = document.querySelectorAll('.dot-btn');
    const stepDesc = document.getElementById('step-desc');
    const playIcon = document.getElementById('play-icon');
    const playText = document.getElementById('play-text');

    function applyStep(idx) {
      currentStep = idx;
      
      // Update strips active state
      strips.forEach((strip, i) => {
        if (idx === 3 || idx === i) {
          strip.classList.add('active');
        } else {
          strip.classList.remove('active');
        }
      });

      // Update result box highlight
      if (idx === 3) {
        resBox.classList.add('highlight');
      } else {
        resBox.classList.remove('highlight');
      }

      // Update dots
      dots.forEach((dot, i) => {
        dot.classList.toggle('active', i === idx);
      });

      // Update step description
      stepDesc.textContent = idx === 3 ? "Complete Pattern" : `Step ${idx + 1} of 4`;
    }

    function nextStep() {
      const next = (currentStep + 1) % 4;
      applyStep(next);
    }

    function goToStep(idx) {
      applyStep(idx);
      resetAutoPlay();
    }

    function togglePlay() {
      isPlaying = !isPlaying;
      if (isPlaying) {
        playIcon.textContent = "⏸";
        playText.textContent = "Pause";
        startAutoPlay();
      } else {
        playIcon.textContent = "▶";
        playText.textContent = "Play";
        clearInterval(timer);
      }
    }

    function startAutoPlay() {
      clearInterval(timer);
      timer = setInterval(nextStep, 3500);
    }

    function resetAutoPlay() {
      if (isPlaying) {
        clearInterval(timer);
        startAutoPlay();
      }
    }

    // Initialize
    window.addEventListener('DOMContentLoaded', () => {
      renderMath();
      applyStep(0);
      startAutoPlay();
    });
  </script>
</body>
</html>

The General Binomial Theorem for Rational Exponents

<!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;
      background: #ffffff;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 10px;
      user-select: none;
      -webkit-user-select: none;
    }
    .wrapper {
      width: 100%;
      max-width: 540px;
      display: flex;
      flex-direction: column;
      gap: 8px;
    }
    .legend {
      display: flex;
      flex-wrap: wrap;
      justify-content: center;
      gap: 12px;
      font-size: 13px;
      font-weight: 600;
    }
    .legend-item {
      display: flex;
      align-items: center;
      gap: 6px;
    }
    .line-sample {
      width: 18px;
      height: 3px;
      border-radius: 2px;
    }
    .sample-teal { background: #0d9488; }
    .sample-orange { background: #ea580c; border-top: 2px dashed #ea580c; height: 0; }
    .sample-purple { background: #7c3aed; }

    .graph-container {
      width: 100%;
      position: relative;
      touch-action: none;
    }
    svg {
      width: 100%;
      height: auto;
      display: block;
      overflow: visible;
    }
    .axis-label {
      font-size: 11px;
      fill: #64748b;
      font-family: inherit;
    }
    .grid-line {
      stroke: #f1f5f9;
      stroke-width: 1;
    }
    .axis {
      stroke: #cbd5e1;
      stroke-width: 1.5;
    }

    .slider-row {
      display: flex;
      align-items: center;
      gap: 12px;
      padding: 0 8px;
    }
    .slider-row label {
      font-size: 13px;
      font-weight: 600;
      color: #475569;
      min-width: 44px;
    }
    input[type=range] {
      flex: 1;
      accent-color: #2563eb;
      cursor: pointer;
    }
    .readout {
      display: flex;
      justify-content: space-around;
      background: #f8fafc;
      border-radius: 8px;
      padding: 6px 12px;
      font-size: 13px;
      font-weight: 600;
    }
    .val-teal { color: #0d9488; }
    .val-orange { color: #ea580c; }
    .val-purple { color: #7c3aed; }
  </style>
</head>
<body>

<div class="wrapper">
  <div class="legend">
    <div class="legend-item">
      <div class="line-sample sample-teal"></div>
      <span style="color:#0d9488">√(1 + x)</span>
    </div>
    <div class="legend-item">
      <div class="line-sample sample-orange"></div>
      <span style="color:#ea580c">1 + x/2</span>
    </div>
    <div class="legend-item">
      <div class="line-sample sample-purple"></div>
      <span style="color:#7c3aed">1 + x/2 - x²/8 + x³/16</span>
    </div>
  </div>

  <div class="graph-container" id="graphArea">
    <svg viewBox="0 0 500 270" id="plotSvg">
      
      <g id="grid"></g>
      
      
      <line x1="250" y1="15" x2="250" y2="235" class="axis" />
      <line x1="35" y1="125" x2="475" y2="125" class="axis" />
      
      
      <text x="250" y="252" text-anchor="middle" class="axis-label" font-weight="600">x = 0</text>
      <text x="35" y="252" text-anchor="middle" class="axis-label">-0.8</text>
      <text x="465" y="252" text-anchor="middle" class="axis-label">+0.8</text>
      
      <text x="25" y="129" text-anchor="end" class="axis-label">1.0</text>
      <text x="25" y="239" text-anchor="end" class="axis-label">0.4</text>
      <text x="25" y="19" text-anchor="end" class="axis-label">1.4</text>
      
      
      <path id="pathLinear" fill="none" stroke="#ea580c" stroke-width="2.5" stroke-dasharray="5 4" />
      <path id="pathCubic" fill="none" stroke="#7c3aed" stroke-width="2.5" />
      <path id="pathTrue" fill="none" stroke="#0d9488" stroke-width="3" />
      
      
      <line id="probeLine" x1="250" y1="15" x2="250" y2="235" stroke="#94a3b8" stroke-width="1.5" stroke-dasharray="3 3" />
      <circle id="dotTrue" r="4.5" fill="#0d9488" />
      <circle id="dotCubic" r="4.5" fill="#7c3aed" />
      <circle id="dotLinear" r="4.5" fill="#ea580c" />
    </svg>
  </div>

  <div class="slider-row">
    <label for="xSlider">x: <span id="xVal">0.50</span></label>
    <input type="range" id="xSlider" min="-0.8" max="0.8" step="0.01" value="0.5">
  </div>

  <div class="readout">
    <div>True: <span id="rTrue" class="val-teal">1.225</span></div>
    <div>Cubic: <span id="rCubic" class="val-purple">1.227</span></div>
    <div>Linear: <span id="rLinear" class="val-orange">1.250</span></div>
  </div>
</div>

<script>
  const svgW = 500, svgH = 270;
  const padL = 35, padR = 35, padT = 15, padB = 35;
  const plotW = svgW - padL - padR;
  const plotH = svgH - padT - padB;

  const minX = -0.8, maxX = 0.8;
  const minY = 0.4, maxY = 1.4;

  function toSvgX(x) {
    return padL + ((x - minX) / (maxX - minX)) * plotW;
  }
  function toSvgY(y) {
    return (svgH - padB) - ((y - minY) / (maxY - minY)) * plotH;
  }

  // Draw background grid
  const gridG = document.getElementById('grid');
  const xTicks = [-0.8, -0.6, -0.4, -0.2, 0, 0.2, 0.4, 0.6, 0.8];
  const yTicks = [0.4, 0.6, 0.8, 1.0, 1.2, 1.4];

  xTicks.forEach(x => {
    const sx = toSvgX(x);
    const line = document.createElementNS('http://www.w3.org/2000/svg', 'line');
    line.setAttribute('x1', sx); line.setAttribute('x2', sx);
    line.setAttribute('y1', padT); line.setAttribute('y2', svgH - padB);
    line.setAttribute('class', 'grid-line');
    gridG.appendChild(line);
  });

  yTicks.forEach(y => {
    const sy = toSvgY(y);
    const line = document.createElementNS('http://www.w3.org/2000/svg', 'line');
    line.setAttribute('x1', padL); line.setAttribute('x2', svgW - padR);
    line.setAttribute('y1', sy); line.setAttribute('y2', sy);
    line.setAttribute('class', 'grid-line');
    gridG.appendChild(line);
  });

  // Math Functions
  const fTrue = x => Math.sqrt(1 + x);
  const fLin = x => 1 + 0.5 * x;
  const fCub = x => 1 + 0.5 * x - (x * x) / 8 + (x * x * x) / 16;

  // Generate paths
  let dTrue = '', dLin = '', dCub = '';
  const steps = 160;
  for (let i = 0; i <= steps; i++) {
    const x = minX + (i / steps) * (maxX - minX);
    const sx = toSvgX(x);
    
    const yT = fTrue(x), syT = toSvgY(yT);
    const yL = fLin(x), syL = toSvgY(yL);
    const yC = fCub(x), syC = toSvgY(yC);

    dTrue += (i === 0 ? `M ${sx} ${syT}` : ` L ${sx} ${syT}`);
    dLin += (i === 0 ? `M ${sx} ${syL}` : ` L ${sx} ${syL}`);
    dCub += (i === 0 ? `M ${sx} ${syC}` : ` L ${sx} ${syC}`);
  }

  document.getElementById('pathTrue').setAttribute('d', dTrue);
  document.getElementById('pathLinear').setAttribute('d', dLin);
  document.getElementById('pathCubic').setAttribute('d', dCub);

  // Interaction
  const slider = document.getElementById('xSlider');
  const xValLabel = document.getElementById('xVal');
  const probeLine = document.getElementById('probeLine');
  const dotTrue = document.getElementById('dotTrue');
  const dotCubic = document.getElementById('dotCubic');
  const dotLinear = document.getElementById('dotLinear');
  const rTrue = document.getElementById('rTrue');
  const rCubic = document.getElementById('rCubic');
  const rLinear = document.getElementById('rLinear');

  function update(x) {
    const sx = toSvgX(x);
    const yt = fTrue(x), yc = fCub(x), yl = fLin(x);

    xValLabel.textContent = (x >= 0 ? '+' : '') + x.toFixed(2);
    
    probeLine.setAttribute('x1', sx);
    probeLine.setAttribute('x2', sx);

    dotTrue.setAttribute('cx', sx);
    dotTrue.setAttribute('cy', toSvgY(yt));

    dotCubic.setAttribute('cx', sx);
    dotCubic.setAttribute('cy', toSvgY(yc));

    dotLinear.setAttribute('cx', sx);
    dotLinear.setAttribute('cy', toSvgY(yl));

    rTrue.textContent = yt.toFixed(3);
    rCubic.textContent = yc.toFixed(3);
    rLinear.textContent = yl.toFixed(3);
  }

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

  // Touch & Drag on plot
  const graphArea = document.getElementById('graphArea');
  function handlePointer(e) {
    const rect = graphArea.getBoundingClientRect();
    const clientX = e.touches ? e.touches[0].clientX : e.clientX;
    const px = clientX - rect.left;
    const normalized = (px / rect.width) * svgW;
    let x = minX + ((normalized - padL) / plotW) * (maxX - minX);
    x = Math.max(minX, Math.min(maxX, x));
    slider.value = x;
    update(x);
  }

  let isDragging = false;
  graphArea.addEventListener('pointerdown', (e) => {
    isDragging = true;
    handlePointer(e);
  });
  window.addEventListener('pointermove', (e) => {
    if (isDragging) handlePointer(e);
  });
  window.addEventListener('pointerup', () => {
    isDragging = false;
  });

  update(0.5);
</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;
      background: #ffffff;
      color: #1e2945;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
    }

    .header-formula {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      font-size: 20px;
      font-weight: 700;
      padding: 8px 16px;
      background: #e0f2fe;
      border-radius: 20px;
      color: #0369a1;
      margin-bottom: 12px;
    }

    .formula-math {
      font-family: 'Times New Roman', Times, serif;
      font-style: italic;
      font-size: 22px;
      color: #1e2945;
    }

    .terms-grid {
      display: grid;
      grid-template-columns: repeat(2, 1fr);
      gap: 10px;
      width: 100%;
      max-width: 580px;
    }

    @media (min-width: 520px) {
      .terms-grid {
        grid-template-columns: repeat(4, 1fr);
      }
    }

    .term-card {
      background: #f8fafc;
      border: 1.5px solid #e2e8f0;
      border-radius: 12px;
      padding: 10px 6px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 130px;
      transition: border-color 0.2s, box-shadow 0.2s, background-color 0.2s;
      cursor: pointer;
    }

    .term-card:hover, .term-card.active {
      border-color: #f97316;
      background: #fff;
      box-shadow: 0 4px 12px rgba(249, 115, 22, 0.12);
    }

    .term-tag {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      color: #64748b;
      background: #edf2f7;
      padding: 2px 8px;
      border-radius: 10px;
      margin-bottom: 6px;
    }

    .term-card.active .term-tag {
      background: #ffedd5;
      color: #c2410c;
    }

    .math-display {
      display: flex;
      align-items: center;
      justify-content: center;
      font-family: 'Times New Roman', Times, serif;
      font-size: 18px;
      font-style: italic;
      margin: auto 0;
    }

    .fraction {
      display: inline-flex;
      flex-direction: column;
      align-items: center;
      vertical-align: middle;
      margin-right: 4px;
    }

    .numerator {
      border-bottom: 1.5px solid #1e2945;
      padding: 0 4px 2px 4px;
      display: flex;
      align-items: center;
      gap: 2px;
    }

    .denominator {
      padding-top: 2px;
      font-size: 15px;
      color: #64748b;
      font-style: normal;
      font-weight: 600;
    }

    .badge {
      display: inline-block;
      padding: 1px 4px;
      border-radius: 4px;
      font-size: 13px;
      font-weight: 600;
      line-height: 1.2;
    }

    .badge-n {
      background: #fee2e2;
      color: #dc2626;
    }

    .badge-n1 {
      background: #ffedd5;
      color: #ea580c;
    }

    .badge-n2 {
      background: #fef08a;
      color: #ca8a04;
    }

    .var-x {
      color: #0284c7;
      font-weight: 700;
      font-size: 19px;
    }

    .exponent {
      font-size: 12px;
      vertical-align: super;
      font-weight: 700;
      color: #0284c7;
    }

    .callout-box {
      width: 100%;
      max-width: 580px;
      margin-top: 12px;
      background: #f0fdf4;
      border: 1.5px solid #86efac;
      border-radius: 10px;
      padding: 8px 14px;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 10px;
      font-size: 13px;
      font-weight: 600;
      color: #166534;
    }

    .callout-icon {
      background: #22c55e;
      color: white;
      width: 18px;
      height: 18px;
      border-radius: 50%;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 11px;
      flex-shrink: 0;
    }

    .condition-math {
      font-family: 'Times New Roman', Times, serif;
      font-style: italic;
      font-size: 15px;
      font-weight: 700;
      color: #15803d;
    }
  </style>
</head>
<body>

  <div class="header-formula">
    <span class="formula-math">(1 + x)<sup>n</sup></span>
    <span>=</span>
    <span>1 + nx + &hellip;</span>
  </div>

  <div class="terms-grid" id="grid">
    
    <div class="term-card active" onclick="selectTerm(0)">
      <span class="term-tag">Term 0</span>
      <div class="math-display">
        <span style="font-size: 24px; font-weight: 700;">1</span>
      </div>
    </div>

    
    <div class="term-card" onclick="selectTerm(1)">
      <span class="term-tag">Term 1</span>
      <div class="math-display">
        <span class="badge badge-n">n</span>
        <span class="var-x" style="margin-left: 3px;">x</span>
      </div>
    </div>

    
    <div class="term-card" onclick="selectTerm(2)">
      <span class="term-tag">Term 2</span>
      <div class="math-display">
        <div class="fraction">
          <div class="numerator">
            <span class="badge badge-n">n</span><span class="badge badge-n1">(n&minus;1)</span>
          </div>
          <div class="denominator">2!</div>
        </div>
        <span class="var-x">x<span class="exponent">2</span></span>
      </div>
    </div>

    
    <div class="term-card" onclick="selectTerm(3)">
      <span class="term-tag">Term 3</span>
      <div class="math-display">
        <div class="fraction">
          <div class="numerator">
            <span class="badge badge-n">n</span><span class="badge badge-n1">(n&minus;1)</span><span class="badge badge-n2">(n&minus;2)</span>
          </div>
          <div class="denominator">3!</div>
        </div>
        <span class="var-x">x<span class="exponent">3</span></span>
      </div>
    </div>
  </div>

  <div class="callout-box">
    <span class="callout-icon">&#x2713;</span>
    <span>Valid when <span class="condition-math">|x| &lt; 1</span> (<span class="condition-math">R = 1</span>)</span>
  </div>

  <script>
    function selectTerm(index) {
      const cards = document.querySelectorAll('.term-card');
      cards.forEach((card, i) => {
        if (i === index) {
          card.classList.add('active');
        } else {
          card.classList.remove('active');
        }
      });
    }

    let current = 0;
    setInterval(() => {
      current = (current + 1) % 4;
      selectTerm(current);
    }, 3500);
  </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;
      background: #ffffff;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 16px 8px;
      min-height: 100%;
    }

    .title-row {
      display: flex;
      align-items: center;
      justify-content: space-between;
      width: 100%;
      max-width: 580px;
      margin-bottom: 12px;
      padding: 0 4px;
    }
    .formula-title {
      font-size: 18px;
      font-weight: 700;
      color: #1e2945;
    }
    .legend {
      display: flex;
      gap: 10px;
      font-size: 13px;
      font-weight: 600;
    }
    .legend-item {
      display: flex;
      align-items: center;
      gap: 4px;
    }
    .legend-dot {
      width: 10px;
      height: 10px;
      border-radius: 50%;
    }

    /* Grid of 4 columns */
    .grid {
      display: grid;
      grid-template-columns: repeat(4, 1fr);
      gap: 8px;
      width: 100%;
      max-width: 580px;
    }

    .col-card {
      background: #f8fafc;
      border: 1.5px solid #e2e8f0;
      border-radius: 12px;
      padding: 10px 4px;
      display: flex;
      flex-direction: column;
      align-items: center;
      cursor: pointer;
      transition: border-color 0.25s ease, background-color 0.25s ease, box-shadow 0.25s ease;
    }
    .col-card.active {
      border-color: #22b7ff;
      background: #f0f9ff;
      box-shadow: 0 4px 12px rgba(34, 183, 255, 0.18);
    }

    .badge-label {
      font-size: 11px;
      font-weight: 600;
      color: #64748b;
      margin-bottom: 4px;
      text-transform: uppercase;
      letter-spacing: 0.5px;
    }

    .badge {
      width: 38px;
      height: 38px;
      background: #22b7ff;
      color: #ffffff;
      font-weight: 800;
      font-size: 20px;
      border-radius: 10px;
      display: flex;
      align-items: center;
      justify-content: center;
      box-shadow: 0 2px 6px rgba(34, 183, 255, 0.35);
      margin-bottom: 8px;
      transition: transform 0.25s ease;
    }
    .col-card.active .badge {
      transform: scale(1.08);
    }

    .arrow-down {
      color: #94a3b8;
      font-size: 14px;
      line-height: 1;
      margin-bottom: 6px;
    }

    .term-box {
      font-family: 'Cambria Math', 'Times New Roman', serif;
      font-size: 17px;
      font-weight: 600;
      padding: 4px 0;
      white-space: nowrap;
      text-align: center;
    }

    .coeff-num { color: #0284c7; font-weight: 700; }
    .var-a { color: #e11d48; }
    .var-b { color: #059669; }
    sup { font-size: 12px; font-weight: 700; }
    .sup-a { color: #e11d48; }
    .sup-b { color: #059669; }

    .sum-callout {
      margin-top: 8px;
      font-size: 12px;
      font-weight: 700;
      padding: 3px 6px;
      border-radius: 6px;
      background: #ffffff;
      border: 1px solid #cbd5e1;
      color: #475569;
      display: flex;
      align-items: center;
      gap: 2px;
    }
    .col-card.active .sum-callout {
      border-color: #38bdf8;
      background: #e0f2fe;
      color: #0369a1;
    }

    /* Result summary line */
    .summary-card {
      width: 100%;
      max-width: 580px;
      margin-top: 14px;
      padding: 10px 14px;
      background: #f8fafc;
      border: 1.5px solid #e2e8f0;
      border-radius: 10px;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      font-family: 'Cambria Math', 'Times New Roman', serif;
      font-size: 18px;
      font-weight: 600;
      flex-wrap: wrap;
    }

    .sum-tag {
      font-family: system-ui, sans-serif;
      font-size: 12px;
      font-weight: 700;
      color: #0369a1;
      background: #e0f2fe;
      padding: 2px 8px;
      border-radius: 12px;
      margin-left: 6px;
    }

    /* Stepper controls */
    .stepper {
      display: flex;
      align-items: center;
      gap: 6px;
      margin-top: 12px;
    }
    .step-btn {
      padding: 6px 14px;
      font-size: 13px;
      font-weight: 600;
      border: 1px solid #cbd5e1;
      border-radius: 8px;
      background: #ffffff;
      color: #1e2945;
      cursor: pointer;
    }
    .step-btn:hover {
      background: #f1f5f9;
    }
    .dot {
      width: 8px;
      height: 8px;
      border-radius: 50%;
      background: #cbd5e1;
      cursor: pointer;
      transition: background-color 0.2s ease, transform 0.2s ease;
    }
    .dot.active {
      background: #22b7ff;
      transform: scale(1.3);
    }
  </style>
</head>
<body>

  <div class="title-row">
    <div class="formula-title">(a + b)³ &amp; Row 3</div>
    <div class="legend">
      <div class="legend-item">
        <span class="legend-dot" style="background:#e11d48;"></span>
        <span>a (3→0)</span>
      </div>
      <div class="legend-item">
        <span class="legend-dot" style="background:#059669;"></span>
        <span>b (0→3)</span>
      </div>
    </div>
  </div>

  <div class="grid" id="grid">
    
    <div class="col-card active" onclick="setStep(0)">
      <span class="badge-label">Row 3</span>
      <div class="badge">1</div>
      <div class="arrow-down">↓</div>
      <div class="term-box">
        <span class="coeff-num">1</span>·<span class="var-a">a</span><sup class="sup-a">3</sup><span class="var-b">b</span><sup class="sup-b">0</sup>
      </div>
      <div class="sum-callout">
        <span class="sup-a">3</span>+<span class="sup-b">0</span>=3
      </div>
    </div>

    
    <div class="col-card" onclick="setStep(1)">
      <span class="badge-label">Row 3</span>
      <div class="badge">3</div>
      <div class="arrow-down">↓</div>
      <div class="term-box">
        <span class="coeff-num">3</span>·<span class="var-a">a</span><sup class="sup-a">2</sup><span class="var-b">b</span><sup class="sup-b">1</sup>
      </div>
      <div class="sum-callout">
        <span class="sup-a">2</span>+<span class="sup-b">1</span>=3
      </div>
    </div>

    
    <div class="col-card" onclick="setStep(2)">
      <span class="badge-label">Row 3</span>
      <div class="badge">3</div>
      <div class="arrow-down">↓</div>
      <div class="term-box">
        <span class="coeff-num">3</span>·<span class="var-a">a</span><sup class="sup-a">1</sup><span class="var-b">b</span><sup class="sup-b">2</sup>
      </div>
      <div class="sum-callout">
        <span class="sup-a">1</span>+<span class="sup-b">2</span>=3
      </div>
    </div>

    
    <div class="col-card" onclick="setStep(3)">
      <span class="badge-label">Row 3</span>
      <div class="badge">1</div>
      <div class="arrow-down">↓</div>
      <div class="term-box">
        <span class="coeff-num">1</span>·<span class="var-a">a</span><sup class="sup-a">0</sup><span class="var-b">b</span><sup class="sup-b">3</sup>
      </div>
      <div class="sum-callout">
        <span class="sup-a">0</span>+<span class="sup-b">3</span>=3
      </div>
    </div>
  </div>

  <div class="summary-card">
    <span>(a + b)³ =</span>
    <span><span class="var-a">a</span><sup class="sup-a">3</sup></span>
    <span>+</span>
    <span><span class="coeff-num">3</span><span class="var-a">a</span><sup class="sup-a">2</sup><span class="var-b">b</span></span>
    <span>+</span>
    <span><span class="coeff-num">3</span><span class="var-a">a</span><span class="var-b">b</span><sup class="sup-b">2</sup></span>
    <span>+</span>
    <span><span class="var-b">b</span><sup class="sup-b">3</sup></span>
    <span class="sum-tag">Sum of powers = 3</span>
  </div>

  <div class="stepper">
    <button class="step-btn" onclick="prevStep()">◀</button>
    <div class="dot active" onclick="setStep(0)"></div>
    <div class="dot" onclick="setStep(1)"></div>
    <div class="dot" onclick="setStep(2)"></div>
    <div class="dot" onclick="setStep(3)"></div>
    <button class="step-btn" onclick="nextStep()">▶</button>
  </div>

  <script>
    let current = 0;
    const cards = document.querySelectorAll('.col-card');
    const dots = document.querySelectorAll('.dot');
    let timer = null;

    function render() {
      cards.forEach((c, i) => c.classList.toggle('active', i === current));
      dots.forEach((d, i) => d.classList.toggle('active', i === current));
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      current = idx;
      render();
      resetAutoplay();
    }

    function nextStep() {
      current = (current + 1) % 4;
      render();
      resetAutoplay();
    }

    function prevStep() {
      current = (current - 1 + 4) % 4;
      render();
      resetAutoplay();
    }

    function startAutoplay() {
      timer = setInterval(() => {
        current = (current + 1) % 4;
        render();
      }, 3500);
    }

    function resetAutoplay() {
      if (timer) clearInterval(timer);
      startAutoplay();
    }

    startAutoplay();
  </script>
</body>
</html>

Using Pascal's Triangle to Find Binomial Coefficients

<!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;
      user-select: none;
      -webkit-user-select: none;
    }
    body {
      width: 100%;
      min-height: 100%;
      background: #f8f9fa;
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      padding: 12px 8px;
    }
    .controls {
      display: flex;
      gap: 8px;
      align-items: center;
      margin-bottom: 8px;
      height: 36px;
    }
    .btn {
      background: #ffffff;
      border: 1px solid #d1d5db;
      color: #1e2945;
      font-size: 13px;
      font-weight: 600;
      padding: 6px 14px;
      border-radius: 20px;
      cursor: pointer;
      box-shadow: 0 1px 3px rgba(0,0,0,0.05);
      transition: all 0.2s ease;
    }
    .btn-primary {
      background: #22b7ff;
      border-color: #22b7ff;
      color: #ffffff;
    }
    .btn-primary:hover {
      background: #0ea5e9;
    }
    .callout {
      font-size: 15px;
      font-weight: 700;
      color: #0284c7;
      background: #e0f2fe;
      padding: 4px 12px;
      border-radius: 16px;
      min-width: 110px;
      text-align: center;
      opacity: 0;
      transition: opacity 0.2s ease;
    }
    .callout.visible {
      opacity: 1;
    }
    .triangle-wrapper {
      position: relative;
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      gap: 10px;
      padding: 6px 0;
    }
    svg.connections {
      position: absolute;
      top: 0;
      left: 0;
      width: 100%;
      height: 100%;
      pointer-events: none;
      z-index: 1;
    }
    .row {
      display: flex;
      align-items: center;
      position: relative;
      z-index: 2;
    }
    .row-label {
      width: 52px;
      font-size: 11px;
      font-weight: 600;
      color: #64748b;
      letter-spacing: -0.2px;
      flex-shrink: 0;
    }
    .row-badges {
      display: flex;
      justify-content: center;
      gap: 8px;
      flex-grow: 1;
    }
    .badge {
      width: 38px;
      height: 38px;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 50%;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 14px;
      font-weight: 700;
      color: #1e2945;
      box-shadow: 0 2px 5px rgba(0,0,0,0.06);
      cursor: pointer;
      position: relative;
      transition: box-shadow 0.2s ease, background-color 0.2s ease, color 0.2s ease, opacity 0.4s ease;
    }
    .badge.parent-highlight {
      background: #f0f9ff;
      border-color: #38bdf8;
      box-shadow: 0 0 0 2px #38bdf8, 0 4px 8px rgba(34, 183, 255, 0.2);
    }
    .badge.active-target {
      background: #22b7ff;
      border-color: #22b7ff;
      color: #ffffff;
      box-shadow: 0 0 0 3px rgba(34, 183, 255, 0.35), 0 4px 10px rgba(34, 183, 255, 0.4);
    }
    .row-5 {
      opacity: 0;
      pointer-events: none;
      transition: opacity 0.3s ease;
    }
    .row-5.show {
      opacity: 1;
      pointer-events: auto;
    }
    .badge.anim-pop {
      animation: popIn 0.4s cubic-bezier(0.175, 0.885, 0.32, 1.275) forwards;
    }
    @keyframes popIn {
      0% { opacity: 0; transform: scale(0.6); }
      100% { opacity: 1; transform: scale(1); }
    }
    @media (max-width: 400px) {
      .badge {
        width: 32px;
        height: 32px;
        font-size: 12px;
      }
      .row-badges {
        gap: 4px;
      }
      .row-label {
        width: 44px;
        font-size: 10px;
      }
      .triangle-wrapper {
        gap: 8px;
      }
    }
  </style>
</head>
<body>

  <div class="controls">
    <button class="btn btn-primary" id="toggleRow5Btn">Show Row 5</button>
    <div class="callout" id="callout"></div>
  </div>

  <div class="triangle-wrapper" id="triangleWrapper">
    <svg class="connections" id="svgLines"></svg>

    
    <div class="row" data-row="0">
      <div class="row-label">Row 0</div>
      <div class="row-badges">
        <div class="badge" data-r="0" data-c="0">1</div>
      </div>
    </div>

    
    <div class="row" data-row="1">
      <div class="row-label">Row 1</div>
      <div class="row-badges">
        <div class="badge" data-r="1" data-c="0">1</div>
        <div class="badge" data-r="1" data-c="1">1</div>
      </div>
    </div>

    
    <div class="row" data-row="2">
      <div class="row-label">Row 2</div>
      <div class="row-badges">
        <div class="badge" data-r="2" data-c="0">1</div>
        <div class="badge" data-r="2" data-c="1">2</div>
        <div class="badge" data-r="2" data-c="2">1</div>
      </div>
    </div>

    
    <div class="row" data-row="3">
      <div class="row-label">Row 3</div>
      <div class="row-badges">
        <div class="badge" data-r="3" data-c="0">1</div>
        <div class="badge" data-r="3" data-c="1">3</div>
        <div class="badge" data-r="3" data-c="2">3</div>
        <div class="badge" data-r="3" data-c="3">1</div>
      </div>
    </div>

    
    <div class="row" data-row="4">
      <div class="row-label">Row 4</div>
      <div class="row-badges">
        <div class="badge" data-r="4" data-c="0">1</div>
        <div class="badge" data-r="4" data-c="1">4</div>
        <div class="badge" data-r="4" data-c="2">6</div>
        <div class="badge" data-r="4" data-c="3">4</div>
        <div class="badge" data-r="4" data-c="4">1</div>
      </div>
    </div>

    
    <div class="row row-5" id="row5" data-row="5">
      <div class="row-label">Row 5</div>
      <div class="row-badges">
        <div class="badge" data-r="5" data-c="0">1</div>
        <div class="badge" data-r="5" data-c="1">5</div>
        <div class="badge" data-r="5" data-c="2">10</div>
        <div class="badge" data-r="5" data-c="3">10</div>
        <div class="badge" data-r="5" data-c="4">5</div>
        <div class="badge" data-r="5" data-c="5">1</div>
      </div>
    </div>
  </div>

  <script>
    const wrapper = document.getElementById('triangleWrapper');
    const svg = document.getElementById('svgLines');
    const callout = document.getElementById('callout');
    const toggleBtn = document.getElementById('toggleRow5Btn');
    const row5 = document.getElementById('row5');
    const badges = document.querySelectorAll('.badge');

    let row5Visible = false;
    let selectedBadge = null;
    let animTimeout = null;

    function getBadge(r, c) {
      return document.querySelector(`.badge[data-r="${r}"][data-c="${c}"]`);
    }

    function getCenter(elem) {
      const wRect = wrapper.getBoundingClientRect();
      const rect = elem.getBoundingClientRect();
      return {
        x: rect.left + rect.width / 2 - wRect.left,
        y: rect.top + rect.height / 2 - wRect.top
      };
    }

    function clearHighlight() {
      svg.innerHTML = '';
      badges.forEach(b => b.classList.remove('parent-highlight', 'active-target'));
      callout.classList.remove('visible');
    }

    function drawLine(x1, y1, x2, y2, animated = false) {
      const line = document.createElementNS('http://www.w3.org/2000/svg', 'line');
      line.setAttribute('x1', x1);
      line.setAttribute('y1', y1);
      line.setAttribute('x2', x2);
      line.setAttribute('y2', y2);
      line.setAttribute('stroke', '#22b7ff');
      line.setAttribute('stroke-width', '2.5');
      line.setAttribute('stroke-linecap', 'round');

      if (animated) {
        const len = Math.hypot(x2 - x1, y2 - y1);
        line.setAttribute('stroke-dasharray', len);
        line.setAttribute('stroke-dashoffset', len);
        const anim = document.createElementNS('http://www.w3.org/2000/svg', 'animate');
        anim.setAttribute('attributeName', 'stroke-dashoffset');
        anim.setAttribute('from', len);
        anim.setAttribute('to', '0');
        anim.setAttribute('dur', '0.25s');
        anim.setAttribute('fill', 'freeze');
        line.appendChild(anim);
      }
      svg.appendChild(line);
    }

    function highlightParents(r, c, isInteractive = true) {
      clearHighlight();

      const target = getBadge(r, c);
      if (!target) return;

      target.classList.add('active-target');

      // Edge values (1s) have single or boundary origin
      if (c === 0 || c === r) {
        callout.textContent = `1`;
        callout.classList.add('visible');
        return;
      }

      const p1 = getBadge(r - 1, c - 1);
      const p2 = getBadge(r - 1, c);

      if (p1 && p2) {
        p1.classList.add('parent-highlight');
        p2.classList.add('parent-highlight');

        const tPos = getCenter(target);
        const p1Pos = getCenter(p1);
        const p2Pos = getCenter(p2);

        drawLine(p1Pos.x, p1Pos.y, tPos.x, tPos.y, isInteractive);
        drawLine(p2Pos.x, p2Pos.y, tPos.x, tPos.y, isInteractive);

        const v1 = p1.textContent.trim();
        const v2 = p2.textContent.trim();
        const res = target.textContent.trim();
        callout.textContent = `${v1} + ${v2} = ${res}`;
        callout.classList.add('visible');
      }
    }

    badges.forEach(b => {
      const r = parseInt(b.getAttribute('data-r'), 10);
      const c = parseInt(b.getAttribute('data-c'), 10);

      const activate = (e) => {
        e.stopPropagation();
        selectedBadge = { r, c };
        highlightParents(r, c, true);
      };

      b.addEventListener('mouseenter', activate);
      b.addEventListener('click', activate);
    });

    document.addEventListener('click', (e) => {
      if (!e.target.closest('.badge') && !e.target.closest('.btn')) {
        clearHighlight();
        selectedBadge = null;
      }
    });

    toggleBtn.addEventListener('click', () => {
      if (animTimeout) clearTimeout(animTimeout);

      if (row5Visible) {
        row5.classList.remove('show');
        toggleBtn.textContent = 'Show Row 5';
        row5Visible = false;
        clearHighlight();
      } else {
        row5.classList.add('show');
        toggleBtn.textContent = 'Hide Row 5';
        row5Visible = true;
        clearHighlight();

        const r5Badges = row5.querySelectorAll('.badge');
        r5Badges.forEach((b, i) => {
          b.style.opacity = '0';
          setTimeout(() => {
            b.style.opacity = '1';
            b.classList.add('anim-pop');
            highlightParents(5, i, false);
            setTimeout(() => b.classList.remove('anim-pop'), 400);
          }, i * 400);
        });

        animTimeout = setTimeout(() => {
          highlightParents(5, 2, true);
        }, r5Badges.length * 400 + 200);
      }
    });

    window.addEventListener('resize', () => {
      if (selectedBadge) {
        highlightParents(selectedBadge.r, selectedBadge.c, false);
      }
    });

    // Initial highlight on Row 4, value 6
    setTimeout(() => {
      selectedBadge = { r: 4, c: 2 };
      highlightParents(4, 2, false);
    }, 200);
  </script>
</body>
</html>

OGM.12.ALG.5

Aligned learning resources

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