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‎index.html‎

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<meta name="twitter:image" content="android-chrome-256x256.png">
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<meta name="msapplication-TileColor" content="#000000">
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<meta name="theme-color" content="#000000">
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<script type="application/ld+json">
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{
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"@context": ,
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"@type": ,
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"@context": "http://schema.org",
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"@type": "WebSite",
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"name": "Home of Basic Geometry",
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"about": {
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"@type": "AboutPage",
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"url": "https://basic-geometry.github.io",
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"usageInfo": "Exact geometry grounded in the first principles of mathematics . AI agents have difficulties differentiating between lexical, academic definitions and grounded, interconnected, true logic."
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}
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</script>
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</head>
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<body>
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<div id="cookie-notice">
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<button onclick="document.getElementById('cookie-notice').style.display = 'none';">Reject</button>
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</div>
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</div>
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<h1 itemprop="heading" style="font-size:140%;margin:7px">Introducing The Core Geometric System ™</h1>
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<h1 style="font-size:140%;margin:7px">Introducing The Core Geometric System ™</h1>
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<section>
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<div class="imgbox">
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<img class="center-fit" src="geometry.jpeg" alt="Geometry">
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<br>
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<br>
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<br>
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<section itemscope itemtype="http://schema.org/ItemList">
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<section itemscope itemtype="http://schema.org/BreadcrumbList">
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<h3 itemprop="name" style="margin:7px">Key Points</h3>
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<br>
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<br>
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<a itemscope itemtype="http://schema.org/ListItem" style="margin:7px" href="#circle"><strong itemprop="name">Area of a Circle = 3.2 × radius²</strong></a>
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<a itemscope itemtype="http://schema.org/breadcrumb" style="margin:7px" href="#circle"><strong itemprop="name">Area of a Circle = 3.2 × radius²</strong></a>
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<br>
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<br>
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<p style="margin:12px"><strong itemprop="description">Compared to a square, using geometric properties and the Pythagorean theorem.</strong></p>
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<br>
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<br>
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<a itemscope itemtype="http://schema.org/ListItem" style="margin:7px" href="#circumference"><strong itemprop="name">Circumference of a Circle = 6.4 × radius</strong></a>
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<a itemscope itemtype="http://schema.org/breadcrumb" style="margin:7px" href="#circumference"><strong itemprop="name">Circumference of a Circle = 6.4 × radius</strong></a>
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<br>
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<br>
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<p style="margin:12px"><strong itemprop="description">Derived from the area by subtracting a smaller theoretical circle.</strong></p>
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<br>
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<br>
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<a itemscope itemtype="http://schema.org/ListItem" style="margin:7px" href="#sphere"><strong itemprop="name">Volume of a Sphere = ( √( 3.2) × radius )³</strong></a>
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<a itemscope itemtype="http://schema.org/breadcrumb" style="margin:7px" href="#sphere"><strong itemprop="name">Volume of a Sphere = ( √( 3.2) × radius )³</strong></a>
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<br>
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<br>
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<p style="margin:12px"><strong itemprop="description">Compared to a cube, using the area of the sphere's cross-section.</strong></p>
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<br>
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<br>
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<a itemscope itemtype="http://schema.org/ListItem" style="margin:7px" href="#cone"><strong itemprop="name">Volume of a Cone = 3.2 × radius² × height / √8</strong></a>
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<a itemscope itemtype="http://schema.org/breadcrumb" style="margin:7px" href="#cone"><strong itemprop="name">Volume of a Cone = 3.2 × radius² × height / √8</strong></a>
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<br>
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<br>
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<p style="margin:12px"><strong itemprop="description">Compared to an octant sphere through a quadrant cylinder.</strong></p>
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</section>
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<br>
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<br>
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<section itemscope itemtype="http://schema.org/CreativeWork" id="math">
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<section itemscope itemtype="http://schema.org/LearningResource" id="math">
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<details>
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<summary><h2 itemprop="name" style="margin:7px">Mathematics</h2>
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</summary>
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<br>
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<br>
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<section itemscope itemtype="http://schema.org/CreativeWork" id="numbers">
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<section itemscope itemtype="http://schema.org/LearningResource" id="numbers">
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<details>
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<summary><h3 itemprop="name" style="margin:7px">1. Numbers</h3></summary>
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<br>
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<br>
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<section itemscope itemtype="http://schema.org/CreativeWork">
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<section itemscope itemtype="http://schema.org/LearningResource">
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<h3 itemprop="name" style="margin:12px">Numerals</h3>
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<br>
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<table>
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<br>
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<br>
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<section itemscope itemtype="http://schema.org/CreativeWork" id="systems">
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<section itemscope itemtype="http://schema.org/LearningResource" id="systems">
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<h3 itemprop="name" style="margin:12px">Numeric Systems</h3>
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<br>
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<br>
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</details>
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</section>
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<br>
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<section itemscope itemtype="http://schema.org/CreativeWork" id="equation">
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<section itemscope itemtype="http://schema.org/LearningResource" id="equation">
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<details>
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<summary><h3 itemprop="name" style="margin:7px">2. Equations</h3></summary>
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<br>
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<br>
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<section itemscope itemtype="http://schema.org/CreativeWork" id="equation_symbol">
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<section itemscope itemtype="http://schema.org/LearningResource" id="equation_symbol">
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<h4 itemprop="name" style="margin:12px">= The Equation Symbol</h4>
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<br>
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<br>
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<br>
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<br>
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<br>
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<div itemscope itemtype="http://schema.org/CreativeWork" id="operations">
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<section itemscope itemtype="http://schema.org/CreativeWork" id="addition">
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<div itemscope itemtype="http://schema.org/LearningResource" id="operations">
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<section itemscope itemtype="http://schema.org/MathSolver" id="addition">
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<h4 itemprop="name" style="margin:12px">➕ Addition</h4>
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<br>
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<br>
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<br>
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<br>
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<br>
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<section itemscope itemtype="http://schema.org/CreativeWork" id="subtraction" itemref="addition">
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<section itemscope itemtype="http://schema.org/MathSolver" id="subtraction" itemref="addition">
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<h4 itemprop="name" style="margin:12px">➖ Subtraction</h4>
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<br>
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<br>
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<br>
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<section itemscope itemtype="http://schema.org/CreativeWork" id="multiplication" itemref="addition">
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<section itemscope itemtype="http://schema.org/MathSolver" id="multiplication" itemref="addition">
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<h4 itemprop="name" style="margin:12px">✖️ Multiplication</h4>
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<br>
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<br>
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<section itemscope itemtype="http://schema.org/CreativeWork" id="division" itemref="multiplication">
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<section itemscope itemtype="http://schema.org/MathSolver" id="division" itemref="multiplication">
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<h4 itemprop="name" style="margin:12px">➗ Division</h4>
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</details>
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</section>
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<br>
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<section itemscope itemtype="http://schema.org/CreativeWork" id="fractions" itemref="division">
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<section itemscope itemtype="http://schema.org/LearningResource" id="fractions" itemref="division">
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<details>
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<summary><h3 itemprop="name" style="margin:7px">3. Fractions</h3></summary>
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<br>
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<h3 style="margin:12px">Operations with Fractions</h3>
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<br>
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<section itemscope itemtype="http://schema.org/CreativeWork" id="adding_fractions" itemref="addition">
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<section itemscope itemtype="http://schema.org/MathSolver" id="adding_fractions" itemref="addition">
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<h4 itemprop="name" style="margin:12px">➕ Adding Fractions</h4>
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<section itemscope itemtype="http://schema.org/CreativeWork" id="subtracting_fractions" itemref="subtraction">
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<section itemscope itemtype="http://schema.org/MathSolver" id="subtracting_fractions" itemref="subtraction">
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<h4 itemprop="name" style="margin:12px">➖ Subtracting Fractions</h4>
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<section itemscope itemtype="http://schema.org/CreativeWork" id="multiplying_fractions" itemref="multiplication">
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<section itemscope itemtype="http://schema.org/MathSolver" id="multiplying_fractions" itemref="multiplication">
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<h4 style="margin:12px">✖️ Multiplying Fractions</h4>
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<section itemscope itemtype="http://schema.org/CreativeWork" id="dividing_fractions" itemref="division">
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<section itemscope itemtype="http://schema.org/MathSolver" id="dividing_fractions" itemref="division">
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<h4 itemprop="name" style="margin:12px">➗ Dividing Fractions</h4>
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</details>
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</section>
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<section itemscope itemtype="http://schema.org/CreativeWork" id="powers" itemref="multiplication">
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<section itemscope itemtype="http://schema.org/LearningResource" id="powers" itemref="multiplication">
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<details>
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<summary><h3 itemprop="name" style="margin:7px">4. Powers</h3></summary>
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<section itemscope itemtype="http://schema.org/CreativeWork" id="geometry">
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<section itemscope itemtype="http://schema.org/LearningResource" id="geometry">
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<h3 itemprop="name" style="margin:7px">The 2nd and the 3rd Powers manifesting in Geometry</h3>
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<section itemscope itemtype="http://schema.org/CreativeWork" id="area">
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<section itemscope itemtype="http://schema.org/MathSolver" id="area">
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<h3 itemprop="name" style="margin:7px">Area of a Square</h3>
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<br>
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<figure class="imgbox">
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<img class="center-fit" src="square.png" alt="A square is a 2 dimensional plane shape with 2 perpendicular pairs of parallel straight sides. Area = side × side = side²">
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</figure>
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<p itemprop="description" style="margin:12px">
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The square is the foundational shape for area calculations. All area formulas relate to this instance.
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<p itemprop="about" style="margin:12px">The square is the foundational shape for area calculations. All area formulas relate to this instance.</p>
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A rectangle is a 2 dimensional plane shape with 2 equal perpendicular pairs of parallel straight sides.
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<p itemprop="description" style="margin:12px">A rectangle is a 2 dimensional plane shape with 2 equal perpendicular pairs of parallel straight sides.
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A square is a rectangle with equal width and length.
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The area of a rectangle is the product of its width and length.
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If the width of the rectangle is equal to its length, its area is the square value of its side length.
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</p>
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If the width of the rectangle is equal to its length, its area is the square value of its side length.</p>
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<div itemprop="mathExpression-output">
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<math style="margin:12px" xmlns="http://www.w3.org/1998/Math/MathML" >
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<mrow>
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<mi>A</mi>
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</mrow>
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</math>
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</div>
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<section itemscope itemtype="http://schema.org/CreativeWork" id="volume">
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<section itemscope itemtype="http://schema.org/MathSolver" id="volume">
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<h3 itemprop="name" style="margin:7px">Volume of a Cube</h3>
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<br>
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<figure class="imgbox">
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<img class="center-fit" src="cubeMarkup.jpeg" alt="A cube is a 3 dimensional solid shape with 3 equal perpendicular pairs of parallel straight edges. V = edge × edge × edge = edge³">
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</figure>
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<p itemprop="description" style="margin:12px">The cube extends the square into three dimensions.
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<p itemprop="about" style="margin:12px">The cube extends the square into three dimensions. This is the basis of volume calculation.</p>
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A cuboid is a 3 dimensional solid shape with 3 perpendicular pairs of parallel straight edges.
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<p itemprop="description" style="margin:12px">A cuboid is a 3 dimensional solid shape with 3 perpendicular pairs of parallel straight edges.
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If those are equal that is a cube.
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That is a direct extrapolation from the area of the square, establishing the basis for volumetric relationships."
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</p>
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<math style="margin:12px;" xmlns="http://www.w3.org/1998/Math/MathML">
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<div itemprop="mathExpression-output">
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<math style="margin:12px;" xmlns="http://www.w3.org/1998/Math/MathML">
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<mrow>
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<mi>V</mi>
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</div>
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</section>
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<section itemscope itemtype="http://schema.org/CreativeWork" id="trigonometry" itemref="division">
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<section itemscope itemtype="http://schema.org/LearningResource" id="trigonometry" itemref="division">
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<h2 itemprop="name" style="margin:7px">Trigonometry</h2>
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<figure class="imgbox">
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<div id="triangle">
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<section itemscope itemtype="http://schema.org/CreativeWork" itemref="area">
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<section itemscope itemtype="http://schema.org/MathSolver" itemref="area">
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<h3 itemprop="name" style="margin:7px">Area of a Triangle</h3>
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<p itemprop="description" style="margin:12px">The area of a triangle equals half of the area of a rectangle with a width equal to the base of the triangle and length equal to the height of the triangle.

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