Fun_With_Math/experiments/basic/fourier.html at main · SimiaCryptus/Fun_With_Math · GitHub

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<!doctype html>
<html lang="en">
  <head>
    <meta charset="UTF-8" />
    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
    <meta
      name="description"
      content="Visualize Fourier series approximations with interactive spinning circles."
    />
    <title>Fourier Series – Fun With Math</title>
    <link rel="stylesheet" href="../../css/style.css" />
    <link rel="stylesheet" href="../../css/experiments-basic-fourier.css" />
  </head>
  <body>
    <nav>
      <a class="brand" href="../../index.html">∑ Fun With Math</a>
      <a href="../../index.html">← All Experiments</a>
    </nav>

    <div class="page-header">
      <h1>Fourier Series Visualizer</h1>
      <p>Sum of rotating circles that together draw any periodic waveform.</p>
    </div>

    <div class="experiment-layout">
      <div class="col2">
        <div class="canvas-wrapper">
          <canvas id="circleCanvas"></canvas>
        </div>
        <div class="canvas-wrapper">
          <canvas id="waveCanvas"></canvas>
        </div>
      </div>

      <aside class="controls">
        <h3>Controls</h3>

        <label>
          Harmonics: <span id="termLabel">7</span>
          <input type="range" id="termRange" min="1" max="41" step="2" value="7" />
        </label>

        <label>
          Speed: <span id="speedLabel">1.0×</span>
          <input type="range" id="speedRange" min="0.1" max="4" step="0.1" value="1" />
        </label>

        <label>
          Waveform
          <select id="waveform">
            <option value="square">Square Wave</option>
            <option value="sawtooth">Sawtooth Wave</option>
            <option value="triangle">Triangle Wave</option>
          </select>
        </label>

        <div style="display: flex; gap: 0.5rem; flex-wrap: wrap">
          <button class="btn btn-primary" id="toggleBtn">⏸ Pause</button>
          <button class="btn btn-secondary" id="clearBtn">Clear Trail</button>
        </div>

        <div class="info-box">
          <h4>Square Wave</h4>
          <p>
            <code>f(t) = (4/π) Σ sin((2k-1)t) / (2k-1)</code>
            for k = 1, 2, 3, …<br />
            Only odd harmonics contribute.
          </p>
        </div>

        <div class="info-box">
          <h4>What you're seeing</h4>
          Each circle spins at a harmonic frequency. Their combined tip traces the target wave on
          the right. Add more harmonics for a sharper approximation.
        </div>
      </aside>
    </div>

    <footer>
      <p><a href="../../index.html">← Back to all experiments</a></p>
    </footer>

    <script src="../../js/experiments-basic-fourier.js"></script>
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