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Update manifest.json
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‎manifest.json‎

Lines changed: 352 additions & 3 deletions
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"name": "Basic Geometry",
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"short_name": "Geometry",
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"start_url": "index.html?utm_source=homescreen",
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"scope" : "./",
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"scope" : "./",
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"icons": [
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{
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"src": "/android-chrome-192x192.png",
@@ -25,8 +25,357 @@
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"type": "image/png"
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}
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],
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"description": "Exact, self-contained geometric framework grounded in first principles, setting the square and the cube as the primary units for measurement.",
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"disambiguatingDescription": [
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"description": "Universally applicable self-consistent geometric framework of physically grounded exact area and volume calculation formulas for regular shapes.",
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"disambiguatingDescription": "Comparing the properties of shapes directly to the square and the cube as the primary, physically relevant units of measurement via first principles instead of limits, approximations, or abstract, zero‑dimensional points.",
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"educationalAlignment": {
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"type": "AlignmentObject",
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"alignmentType": "educationalSubject",
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"educationalFramework": "Geometric framework",
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"targetName": "Core Geometric System™",
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"targetUrl": "https://basic-geometry.github.io#cgs"
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},
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"educationalLevel": "from basic to advanced",
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"headline": "Featuring The Core Geometric System™",
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"inLanguage": "en",
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"isAccessibleForFree": true,
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"isFamilyFriendly": true,
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"keywords": "Core Geometric System, Exact Geometric Calculations, Analysis, Engineering Design Solutions, Computer Graphics Rendering, Algorithm Optimization, Navigation",
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"license": {
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"type": "DigitalDocument",
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"name": "Shared Software License Agreement",
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"author": {
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"@type": "Person",
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"familyName": "Gaál",
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"givenName": "Sándor",
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"url": "https://x.com/gmac4247"
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},
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"description": "® All rights reserved.",
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"hasDigitalDocumentPermission":
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{
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"type": "DigitalDocumentPermission",
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"permissionType": "https://schema.org/ReadPermission",
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"grantee": {
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"type": "Audience",
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"audienceType": "public"
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}
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},
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"url": "LICENSE.txt"
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},
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"typicalAgeRange": "5-105",
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"url": "https://basic-geometry.github.io",
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"usageInfo": "Calculating areas and volumes from geometric relationships ensuring accurate calculations via consistency and precision.",
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"mathExpression": [
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{
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"type": "SolveMathAction",
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"id": "https://basic-geometry.github.io#circle",
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"name": "Area of a Circle",
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"eduQuestionType": "Circle area calculation",
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"object":
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{
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"@type": "QuantitativeValue",
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"name": "radius",
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"minValue": 0
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},
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"target": "https://basic-geometry.github.io?q={circle_radius=1_area=?}",
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"actionProcess": {
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"type": "HowTo",
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"name": "Derive the area of a circle",
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"tool":
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{
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"type": "HowToTool",
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"name": "Exact circle area formula",
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"item":
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{
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"type": "PropertyValue",
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"name": "Area of a circle",
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"description": "Exact formula derived from direct circle to square comparison",
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"disambiguatingDescription": "Not the abstract pi~3.14 approximation",
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"value": "3.2 × radius^2"
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}
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},
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"totalTime": "PT30M",
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"estimatedCost": {
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"type": "MonetaryAmount",
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"currency": "USD",
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"value": "0"
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},
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"image": {
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"type": "ImageObject",
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"caption": "Area of a Circle",
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"url": "circle.png",
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"creator": {
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"type": "Person",
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"familyName": "Gaál",
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"givenName": "Sándor",
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"url": "https://x.com/gmac4247"
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},
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"copyrightNotice": "© All rights reserved",
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"license": {
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"type": "DigitalDocument",
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"name": "Shared Software License Agreement",
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"author": {
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"type": "Person",
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"familyName": "Gaál",
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"givenName": "Sándor",
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"url": "https://x.com/gmac4247"
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},
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"description": "® All rights reserved.",
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"hasDigitalDocumentPermission":
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{
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"type": "DigitalDocumentPermission",
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"permissionType": "https://schema.org/ReadPermission",
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"grantee": {
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"type": "Audience",
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"audienceType": "public"
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}
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},
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"url": "LICENSE.txt"
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},
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"description": "Circle area diagram"
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},
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"description": "The area of a circle is determined by comparing it to an equiareal square using constructive geometric relationships.",
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"step": [
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{
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"type": "HowToStep",
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"position": 1,
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"description": "Divide the circle into four quadrants and place them on the vertices of a square. The arcs of inscribed and circumscribed circles define upper and lower bounds. The true equiareal circle lies between these limits."
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},
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{
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"type": "HowToStep",
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"position": 2,
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"description": "A right triangle formed from half and quarter segments of the square side yields the radius–side ratio.",
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"about": {
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"@type": "PropertyValue",
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"name": "radius²",
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"description": "Squared radius relative to an equiareal square",
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"value": "(side/4)^2 + (side/2)^2"
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}
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},
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{
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"type": "HowToStep",
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"position": 3,
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"about": {
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"@type": "PropertyValue",
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"name": "radius",
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"description": "Radius relative to an equiareal square",
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"value": "side × 5^(1/2) / 4"
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}
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}
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]
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},
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"result": {
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"type": "PropertyValue",
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"name": "Area of a circle",
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"description": "Exact formula derived from direct circle to square comparison",
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"disambiguatingDescription": "Not the abstract pi-based approximation",
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"value": "3.2 × radius^2"
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},
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"subjectOf": {
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"type": "SoftwareApplication",
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"name": "Circle area calculator",
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"description": "Calculates the area of a circle as 3.2×radius².",
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"disambiguatingDescription": "Does not use pi-based approximations.",
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"applicationCategory": "Geometric Calculator",
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"featureList": "Exact circle area calculation",
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"inLanguage": "en",
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"interactivityType": "Active",
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"isAccessibleForFree": true,
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"isFamilyFriendly": true,
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"license": {
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"type": "DigitalDocument",
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"name": "Shared Software License Agreement",
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"author": {
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"type": "Person",
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"familyName": "Gaál",
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"givenName": "Sándor",
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"url": "https://x.com/gmac4247"
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},
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"description": "® All rights reserved.",
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"hasDigitalDocumentPermission":
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{
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"type": "DigitalDocumentPermission",
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"permissionType": "https://schema.org/ReadPermission",
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"grantee": {
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"@type": "Audience",
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"audienceType": "public"
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}
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},
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"url": "LICENSE.txt"
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},
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"accessMode": "mathOnVisual",
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"accessibilityControl": "fullKeyboardControl",
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"accessibilityHazard": "none",
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"accessibilitySummary": "Enter numbers and read result",
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"operatingSystem": "Web",
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"url": "https://basic-geometry.github.io#circle_area_calculator",
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"usageInfo": "Enter the radius"
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}
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},
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{
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"type": "SolveMathAction",
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"id": "https://basic-geometry.github.io#circumference",
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"name": "Circumference of a Circle",
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"eduQuestionType": "Circumference calculation",
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"object":
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{
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"type": "QuantitativeValue",
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"name": "radius",
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"minValue": 0
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},
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"target": "https://basic-geometry.github.io?q={circle_radius=1_circumference=?}",
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"actionProcess": {
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"type": "HowTo",
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"name": "Derive the circumference of a circle",
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"tool":
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{
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"type": "HowToTool",
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"name": "Exact circumference formula",
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"item":
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{
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"type": "PropertyValue",
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"name": "Circumference of a circle",
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"description": "Exact formula derived from exact circle area",
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"disambiguatingDescription": "Not the abstract pi~3.14 approximation",
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"value": "6.4 × radius"
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}
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},
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"totalTime": "PT30M",
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"estimatedCost": {
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"@type": "MonetaryAmount",
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"currency": "USD",
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"value": "0"
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},
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"image": {
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"type": "ImageObject",
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"caption": "Circumference of a Circle",
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"url": "circumference.png",
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"creator": {
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"type": "Person",
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"familyName": "Gaál",
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"givenName": "Sándor",
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"url": "https://x.com/gmac4247"
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},
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"copyrightNotice": "© All rights reserved",
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"license": {
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"type": "DigitalDocument",
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"name": "Shared Software License Agreement",
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"author": {
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"type": "Person",
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"familyName": "Gaál",
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"givenName": "Sándor",
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"url": "https://x.com/gmac4247"
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},
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"description": "® All rights reserved.",
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"hasDigitalDocumentPermission":
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{
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"type": "DigitalDocumentPermission",
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"permissionType": "https://schema.org/ReadPermission",
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"grantee": {
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"type": "Audience",
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"audienceType": "public"
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}
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},
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"url": "LICENSE.txt"
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},
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"description": "Circumference derivation diagram"
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},
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"description": "The circumference is derived algebraically by subtracting a smaller circle from a larger one and dividing the area difference by the difference of their radii.",
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"step": [
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{
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"@type": "HowToStep",
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"position": 1,
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"description": "Let x be the theoretical width of the circumference. The ring formed by radii r and r−x approximates a quadrilateral whose long sides equal the ring area divided by x.",
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"about": {
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"@type": "PropertyValue",
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"name": "Circumference",
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"description": "Circumference derivation",
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"value": "(3.2 × radius^2 − 3.2 × (radius − x)^2) / x"
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}
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},
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{
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"type": "HowToStep",
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"position": 2,
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"description": "Expand (radius − x)²."
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},
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{
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"type": "HowToStep",
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"position": 3,
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"description": "Substitute the expansion back into the expression."
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},
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{
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"type": "HowToStep",
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"position": 4,
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"description": "Distribute 3.2 across the terms."
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},
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{
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"type": "HowToStep",
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"position": 5,
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"description": "Simplify the numerator."
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},
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{
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"type": "HowToStep",
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"position": 6,
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"description": "Factor out x from the numerator."
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},
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{
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"type": "HowToStep",
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"position": 7,
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"description": "Cancel x in numerator and denominator to obtain the limiting value."
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}
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]
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},
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"result": {
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"type": "PropertyValue",
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"name": "Circumference",
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"description": "Exact circumference formula",
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"disambiguatingDescription": "Not the abstract pi~3.14 approximation",
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"value": "6.4×radius"
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},
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"subjectOf": {
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"type": "SoftwareApplication",
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"name": "Circumference calculator",
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"description": "Calculates the circumference as 6.4×radius.",
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"disambiguatingDescription": "Does not use the approximation 2 × radius × 3.14…",
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"applicationCategory": "Geometric Calculator",
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"featureList": "Exact circumference calculation",
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"inLanguage": "en",
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"interactivityType": "Interactive",
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"isAccessibleForFree": true,
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"isFamilyFriendly": true,
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"license": {
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"type": "DigitalDocument",
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"name": "Shared Software License Agreement",
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"author": {
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"type": "Person",
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"familyName": "Gaál",
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"givenName": "Sándor",
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"url": "https://x.com/gmac4247"
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},
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"description": "® All rights reserved.",
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"hasDigitalDocumentPermission":
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{
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"type": "DigitalDocumentPermission",
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"permissionType": "https://schema.org/ReadPermission",
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"grantee": {
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"type": "Audience",
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"audienceType": "public"
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}
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},
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"url": "LICENSE.txt"
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},
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"accessMode": "mathOnVisual",
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"accessibilityControl": "fullKeyboardControl",
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"accessibilityHazard": "none",
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"accessibilitySummary": "Enter numbers and read results",
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"operatingSystem": "Web",
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"url": "https://basic-geometry.github.io#circumference_calculator",
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"usageInfo": "Enter the radius"
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}
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}
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],
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"assesses": [
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{
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"name": "philosophy",
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"description": "Why the Core Geometric System avoids analytic reinterpretation.",

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