.math-result {
            padding: 15px;
            background-color: white;
            border-radius: 4px;
            border: 1px solid #eee;
            font-size: 1.5rem;
            font-family: 'Cambria Math', 'Latin Modern Math', STIXGeneral, serif;
            margin: 10px 0;
            text-align: center;
        }
        .math-equation {
            font-size: 1.3rem;
            padding: 15px;
            background-color: rgba(70, 130, 180, 0.05);
            border-left: 4px solid var(--primary-color);
            border-radius: 4px;
            margin: 15px 0;
        }
        .subsection-title {
            font-weight: 600;
            margin-top: 2rem;
            margin-bottom: 1rem;
            color: var(--accent-color);
            font-size: 1.2rem;
        }
        .math-box {
            background-color: rgba(70, 130, 180, 0.05);
            border-left: 3px solid var(--primary-color);
            padding: 1rem;
            border-radius: 0 4px 4px 0;
            margin: 1.5rem 0;
        }
        .function-examples {
            display: flex;
            flex-wrap: wrap;
            gap: 0.5rem;
            margin: 1rem 0;
        }
        .example-btn {
            background-color: rgba(70, 130, 180, 0.1);
            border: 1px solid rgba(70, 130, 180, 0.2);
            border-radius: 4px;
            padding: 0.5rem 0.75rem;
            font-size: 0.9rem;
            color: var(--primary-color);
            cursor: pointer;
            transition: all 0.2s;
            font-family: 'Courier New', monospace;
        }
        .example-btn:hover {
            background-color: rgba(70, 130, 180, 0.2);
            transform: translateY(-2px);
        }
        .math-notation {
            font-family: 'Cambria Math', 'Latin Modern Math', STIXGeneral, serif;
            font-size: 1.1rem;
        }
        .property-table {
            width: 100%;
            border-collapse: collapse;
            margin: 1.5rem 0;
        }
        .property-table th,
        .property-table td {
            padding: 0.75rem;
            text-align: left;
            border: 1px solid var(--border-color);
        }
        .property-table th {
            background-color: var(--light-gray);
            font-weight: 600;
        }
        .property-table tr:nth-child(even) {
            background-color: rgba(70, 130, 180, 0.05);
        }
        .authority-note {
            font-size: 0.85rem;
            color: var(--text-muted);
            border-top: 1px solid var(--border-color);
            padding-top: 1rem;
            margin-top: 1rem;
            text-align: right;
        }
        .case-study {
            background-color: #f0f7fa;
            border-radius: 8px;
            padding: 1.5rem;
            margin: 1.5rem 0;
            border-left: 5px solid var(--primary-color);
        }
        .key-point {
            font-weight: 500;
            color: var(--accent-color);
        }
        .input-group-custom {
            margin-bottom: 1rem;
        }
        .result-row {
            font-size: 1.2rem;
            margin: 0.5rem 0;
        }
        .result-value {
            font-weight: 600;
            color: var(--primary-color);
            font-size: 2rem;
        }
        .author-bio {
            background-color: #f8f9fa;
            border-left: 4px solid var(--primary-color);
            padding: 1.2rem;
            margin: 2rem 0;
            border-radius: 0 8px 8px 0;
        }
        .privacy-note {
            font-size: 0.9rem;
            background-color: #e7f3ff;
            border: 1px solid #b8daff;
            color: #004085;
            padding: 0.5rem 1rem;
            border-radius: 4px;
            margin: 1rem 0;
        }
        .warning-note {
            background-color: #fff3cd;
            border: 1px solid #ffeeba;
            color: #856404;
            padding: 0.5rem 1rem;
            border-radius: 4px;
            margin: 1rem 0;
        }
        .info-note {
            background-color: #d1ecf1;
            border: 1px solid #bee5eb;
            color: #0c5460;
            padding: 0.5rem 1rem;
            border-radius: 4px;
            margin: 0.5rem 0;
            display: none;
        }
        .deep-dive {
            margin: 1.8rem 0;
        }
        .deep-dive p {
            text-align: justify;
        }
        .unit-note {
            font-size: 0.9rem;
            color: #6c757d;
        }
        .coord-input {
            margin-bottom: 0.5rem;
        }
        .geometry-canvas {
            width: 100%;
            height: auto;
            background-color: #f9f9f9;
            border: 1px solid #ddd;
            border-radius: 8px;
            margin-top: 1.5rem;
            display: block;
        }
        .canvas-container {
            text-align: center;
            margin-top: 1rem;
        }
        .legend {
            display: flex;
            justify-content: center;
            gap: 2rem;
            margin: 0.5rem 0;
            font-size: 0.9rem;
            flex-wrap: wrap;
        }
        .legend-item {
            display: flex;
            align-items: center;
            gap: 0.3rem;
        }
        .legend-color {
            width: 16px;
            height: 16px;
            border-radius: 50%;
            display: inline-block;
        }
        .legend-color.red {
            background-color: #dc3545;
        }
        .legend-color.blue {
            background-color: #0d6efd;
        }
        .legend-color.gray {
            background-color: #6c757d;
        }
        .legend-color.green {
            background-color: #28a745;
        }
        .legend-color.orange {
            background-color: #fd7e14;
        }
        .legend-line {
            width: 24px;
            height: 2px;
            display: inline-block;
        }
        .legend-line.dashed {
            border-top: 2px dashed #6c757d;
        }
        .legend-line.solid {
            border-top: 2px solid #28a745;
        }
        /* added for info toast */
        .info-toast {
            position: fixed;
            top: 20px;
            right: 20px;
            z-index: 9999;
            max-width: 350px;
        }