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‎index.html‎

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@@ -97,137 +97,6 @@
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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": "http://schema.org",
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"@type": "WebSite",
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"name": "Home of Basic Geometry",
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"alternateName": "Exact Geometry",
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"accessMode": ["textual", "visual"],
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"accessibilityFeature": [
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"dyslexicFriendly",
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"machine-readable",
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"online calculator"
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],
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"accessibilityHazard": "none",
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"accessibilitySummary": "Mathematical equations with figures and explanation",
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"accountablePerson": {
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"@type": "Person",
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"address": {
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"@type": "PostalAddress",
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"addressLocality": "Szentendre",
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"addressRegion": "Hungary",
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"postalCode": "2000",
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"streetAddress": "Ady Endre út 6.A"
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},
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"email": "gmac4247@gmail.com",
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"jobTitle": "Administrator",
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"name": "Gaál Sándor",
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"telephone": "+36305075125",
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"url": "https://www.x.com/gmac4247"
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},
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"author": {
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"@type": "Person",
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"address": {
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"@type": "PostalAddress",
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"addressLocality": "Szentendre",
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"addressRegion": "Hungary",
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"postalCode": "2000",
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"streetAddress": "Ady Endre út 6.A"
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},
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"email": "gmac4247@gmail.com",
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"jobTitle": "Administrator",
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"name": "Gaál Sándor",
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"telephone": "+36305075125",
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"url": "https://www.x.com/gmac4247"
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},
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"contributor": [
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{
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"@type": "Person",
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"name": "Adina",
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"description": "Spiritual supporter"
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},
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{
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"@type": "Thing",
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"name": "Microsoft Copilot",
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"description": "AI language model, Images generated with the help of Microsoft Copilot"
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},
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{
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"@type": "Thing",
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"name": "Gemini",
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"description": "AI language model, The proof of the area of a circle made with the help of Gemini"
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},
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{
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"@type": "Thing",
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"name": "Grok",
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"description": "AI language model, The explanation of the cube dissection method made with the help of Grok"
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}
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],
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"copyrightHolder": {
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"@type": "Person",
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"address": {
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"@type": "PostalAddress",
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"addressLocality": "Szentendre",
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"addressRegion": "Hungary",
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"postalCode": "2000",
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"streetAddress": "Ady Endre út 6.A"
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},
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"email": "gmac4247@gmail.com",
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"jobTitle": "Administrator",
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"name": "Gaál Sándor",
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"telephone": "+36305075125",
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"url": "https://www.x.com/gmac4247"
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},
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"copyrightNotice": "All rights reserved.",
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"copyrightYear": "2020",
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"creator": {
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"@type": "Person",
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"address": {
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"@type": "PostalAddress",
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"addressLocality": "Szentendre",
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"addressRegion": "Hungary",
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"postalCode": "2000",
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"streetAddress": "Ady Endre út 6.A"
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},
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"email": "gmac4247@gmail.com",
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"jobTitle": "Administrator",
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"name": "Gaál Sándor",
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"telephone": "+36305075125",
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"url": "https://www.x.com/gmac4247"
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},
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"dateCreated": "2019-01-11",
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"datePublished": "2020-01-11",
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"dateModified": "2025-12-09",
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"description": "Introducing the best-established and most accurate framework to calculate area and volume.",
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"disambiguatingDescription": "By fundamentally shifting the axioms from the abstract, zero-dimensional point to the square and the cube as the primary, physically-relevant units for measurement, we define the properties of shapes like the circle and sphere not through abstract limits, but through their direct, rational relationship to these foundational units. This system doesn't require advanced calculus or imaginary numbers.",
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"headline": "Introducing the Core Geometric System ™",
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"image": "geometry.jpeg",
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"inLanguage": "en",
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"isFamilyFriendly": true,
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"keywords": "Core Geometric System, Exact Geometric Calculations, Engineering Design Solutions, Computer Graphics Rendering, Algorithm Optimization, Quantum Computing Applications",
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"learningResourceType": "mathSolver",
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"locationCreated": {
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"@type": "administrativeArea",
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"name": "Szentendre, Hungary"
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},
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"mainEntity": {
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"@type": ["MathSolver", "LearningResource"],
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"name": "Core Geometric System ™",
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"description": "The best framework for calculating area and volume.",
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"disambiguatingDescription": "Exact formulas derived entirely from first principles",
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"inLanguage": "en",
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"keywords": "Exact Formulas, Area of a Circle, Circumference of a Circle, Volume of a Sphere, Volume of a Cone, Volume of a Pyramid, Volume of a Tetrahedron, Volume of a Frustum",
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"url": "https://basic-geometry.github.io",
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"usageInfo": "Logically consistent interconnected framework grounded in first principles ensuring cutting edge accuracy for critical applications like navigation and engineering."
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"schemaVersion" : "https://schema.org/docs/releases.html#v29.3",
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"thumbnail": "android-chrome-256x256.png",
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"typicalAgeRange": "5-105",
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"url": "https://basic-geometry.github.io"
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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">
@@ -1858,7 +1727,7 @@ <h3 itemprop="name" style="margin:7px">Area of a regular Polygon</h3>
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<br>
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<div itemscope itemtype="http://schema.org/LearningResource" id="cgs">
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<section itemscope itemtype="http://schema.org/MathSolver" itemref="triangle" id="circle">
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<h3 itemprop="name" style="margin:7px">The Area of a Circle</h3>
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<h3 itemprop="name" style="margin:7px">Area of a Circle</h3>
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<br>
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<figure class="imgbox" itemscope itemtype="http://schema.org/ImageObject">
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<img class="center-fit" src="areaOfACircle.jpg" alt="The circle is cut into four quadrants, each placed with their origin on the vertices of a square. The arcs of the quadrants of the circle that equals in area to the square intersect at the quarters on its centerlines. The ratio between the radius of the circle and the side of the square is calculable. r = side × √5 / 4 Area = 3.2r²">
@@ -4190,13 +4059,14 @@ <h3 itemprop="name" style="margin:7px">Volume of a Frustum Cone</h3>
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<br>
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<br>
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<section itemscope itemtype="http://schema.org/MathSolver" itemref="cone" id="pyramid">
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<h3 itemprop="description" style="margin:7px">The volume of a pyramid can be calculated
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with the same coefficient as the volume of a cone.</h3>
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<br>
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<h3 itemprop="name" style="margin:7px">Volume of a Pyramid</h3>
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<figure class="imgbox" itemscope itemtype="http://schema.org/ImageObject">
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<img class="center-fit" src="conePyramidVolumeMarkup.jpeg" alt="The volume of a pyramid can be calculated with the same coefficient as the volume of a cone. Volume = base × height / √8">
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</figure>
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<br>
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<p itemprop="abstract" style="margin:12px">The volume of a pyramid can be calculated
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with the same coefficient as the volume of a cone.</p>
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<br>
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<figure class="imgbox" itemscope itemtype="http://schema.org/ImageObject">
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<img class="center-fit" src="tetraFrame.jpeg" alt="The volume of a pyramid can be calculated with the same coefficient as the volume of a cone. Volume = base × height / √8">
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</figure>
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<mrow>
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<mi>V</mi>
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<mo>=</mo>
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<mrow>
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<mfrac>
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<mrow>
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<msub>
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</msqrt>
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</mfrac>
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</mrow>
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</mrow>
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</math>
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</div>
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<br>
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<p itemprop="description" style="margin:12px"><strong>Subtracting the missing tip from a theoretical full pyramid gives the volume of a frustum pyramid.
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<br>
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<br>
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The height of the theoretical full pyramid can be calculated by the frustum height and the ratio between the top and bottom edges or areas.
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</strong>
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</p>
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The height of the theoretical full pyramid can be calculated by the frustum height and the ratio between the top and bottom edges or areas.</strong></p>
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<br>
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<div itemprop="mathExpression">
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<math style="margin:12px" xmlns="http://www.w3.org/1998/Math/MathML">
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<br>
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<br>
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<section itemscope itemtype="http://schema.org/MathSolver" id="square_frustum" itemref="frustum-pyramid">
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<h3 itemprop="name" style="margin:7px">The volume of a square frustum pyramid can be calculated via a simplified formula.
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</h3>
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<h3 itemprop="about" style="margin:7px">The volume of a square frustum pyramid can be calculated via a simplified formula.</h3>
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<br>
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<div itemprop="description">
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<math style="margin:12px" xmlns="http://www.w3.org/1998/Math/MathML" >
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<br>
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<br>
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<p itemprop="usageInfo" style="margin:12px">This system provides exact formulas for real-world applications.</p>
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</section>
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</div>
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<br>
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<br>
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<br>

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