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"https://registry.npmjs.org/tiny-invariant/-/tiny-invariant-1.3.3.tgz", @@ -6961,6 +7602,36 @@ "node": ">=8.0" } }, + "node_modules/troika-three-text": { + "version": "0.52.4", + "resolved": "https://registry.npmjs.org/troika-three-text/-/troika-three-text-0.52.4.tgz", + "integrity": "sha512-V50EwcYGruV5rUZ9F4aNsrytGdKcXKALjEtQXIOBfhVoZU9VAqZNIoGQ3TMiooVqFAbR1w15T+f+8gkzoFzawg==", + "license": "MIT", + "dependencies": { + "bidi-js": "^1.0.2", + "troika-three-utils": "^0.52.4", + "troika-worker-utils": "^0.52.0", + "webgl-sdf-generator": "1.1.1" + }, + "peerDependencies": { + "three": ">=0.125.0" + } + }, + "node_modules/troika-three-utils": { + "version": "0.52.4", + "resolved": "https://registry.npmjs.org/troika-three-utils/-/troika-three-utils-0.52.4.tgz", + "integrity": "sha512-NORAStSVa/BDiG52Mfudk4j1FG4jC4ILutB3foPnfGbOeIs9+G5vZLa0pnmnaftZUGm4UwSoqEpWdqvC7zms3A==", + "license": "MIT", + "peerDependencies": { + "three": ">=0.125.0" + } + }, + "node_modules/troika-worker-utils": { + "version": "0.52.0", + "resolved": "https://registry.npmjs.org/troika-worker-utils/-/troika-worker-utils-0.52.0.tgz", + "integrity": "sha512-W1CpvTHykaPH5brv5VHLfQo9D1OYuo0cSBEUQFFT/nBUzM8iD6Lq2/tgG/f1OelbAS1WtaTPQzE5uM49egnngw==", + "license": "MIT" + }, "node_modules/ts-api-utils": { "version": "1.3.0", "resolved": "https://registry.npmjs.org/ts-api-utils/-/ts-api-utils-1.3.0.tgz", @@ -6987,6 +7658,43 @@ "integrity": "sha512-jWVzBLplnCmoaTr13V9dYbiQ99wvZRd0vNWaDRg+aVYRcjDF3nDksxFDE/+fkXnKhpnUUkmx5pK/v8mCtLVqZA==", "license": "0BSD" }, + "node_modules/tunnel-rat": { + "version": "0.1.2", + "resolved": "https://registry.npmjs.org/tunnel-rat/-/tunnel-rat-0.1.2.tgz", + "integrity": "sha512-lR5VHmkPhzdhrM092lI2nACsLO4QubF0/yoOhzX7c+wIpbN1GjHNzCc91QlpxBi+cnx8vVJ+Ur6vL5cEoQPFpQ==", + "license": "MIT", + "dependencies": { + "zustand": "^4.3.2" + } + }, + "node_modules/tunnel-rat/node_modules/zustand": { + "version": "4.5.7", + "resolved": "https://registry.npmjs.org/zustand/-/zustand-4.5.7.tgz", + "integrity": "sha512-CHOUy7mu3lbD6o6LJLfllpjkzhHXSBlX8B9+qPddUsIfeF5S/UZ5q0kmCsnRqT1UHFQZchNFDDzMbQsuesHWlw==", + "license": "MIT", + "dependencies": { + "use-sync-external-store": "^1.2.2" + }, + "engines": { + "node": ">=12.7.0" + }, + "peerDependencies": { + "@types/react": ">=16.8", + "immer": ">=9.0.6", + "react": ">=16.8" + }, + "peerDependenciesMeta": { + "@types/react": { + "optional": true + }, + "immer": { + "optional": true + }, + "react": { + "optional": true + } + } + }, "node_modules/type-check": { "version": "0.4.0", "resolved": "https://registry.npmjs.org/type-check/-/type-check-0.4.0.tgz", @@ -7128,6 +7836,15 @@ } } }, + "node_modules/use-sync-external-store": { + "version": "1.6.0", + "resolved": "https://registry.npmjs.org/use-sync-external-store/-/use-sync-external-store-1.6.0.tgz", + "integrity": "sha512-Pp6GSwGP/NrPIrxVFAIkOQeyw8lFenOHijQWkUTrDvrF4ALqylP2C/KCkeS9dpUM3KvYRQhna5vt7IL95+ZQ9w==", + "license": "MIT", + "peerDependencies": { + "react": "^16.8.0 || ^17.0.0 || ^18.0.0 || ^19.0.0" + } + }, "node_modules/util-deprecate": { "version": "1.0.2", "resolved": "https://registry.npmjs.org/util-deprecate/-/util-deprecate-1.0.2.tgz", @@ -7135,6 +7852,15 @@ "dev": true, "license": "MIT" }, + "node_modules/utility-types": { + "version": "3.11.0", + "resolved": "https://registry.npmjs.org/utility-types/-/utility-types-3.11.0.tgz", + "integrity": "sha512-6Z7Ma2aVEWisaL6TvBCy7P8rm2LQoPv6dJ7ecIaIixHcwfbJ0x7mWdbcwlIM5IGQxPZSFYeqRCqlOOeKoJYMkw==", + "license": "MIT", + "engines": { + "node": ">= 4" + } + }, "node_modules/vaul": { "version": "0.9.9", "resolved": "https://registry.npmjs.org/vaul/-/vaul-0.9.9.tgz", @@ -7230,11 +7956,21 @@ } } }, + "node_modules/webgl-constants": { + "version": "1.1.1", + "resolved": "https://registry.npmjs.org/webgl-constants/-/webgl-constants-1.1.1.tgz", + "integrity": "sha512-LkBXKjU5r9vAW7Gcu3T5u+5cvSvh5WwINdr0C+9jpzVB41cjQAP5ePArDtk/WHYdVj0GefCgM73BA7FlIiNtdg==" + }, + "node_modules/webgl-sdf-generator": { + "version": "1.1.1", + "resolved": "https://registry.npmjs.org/webgl-sdf-generator/-/webgl-sdf-generator-1.1.1.tgz", + "integrity": "sha512-9Z0JcMTFxeE+b2x1LJTdnaT8rT8aEp7MVxkNwoycNmJWwPdzoXzMh0BjJSh/AEFP+KPYZUli814h8bJZFIZ2jA==", + "license": "MIT" + }, "node_modules/which": { "version": "2.0.2", "resolved": "https://registry.npmjs.org/which/-/which-2.0.2.tgz", "integrity": "sha512-BLI3Tl1TW3Pvl70l3yq3Y64i+awpwXqsGBYWkkqMtnbXgrMD+yj7rhW0kuEDxzJaYXGjEW5ogapKNMEKNMjibA==", - "dev": true, "license": "ISC", "dependencies": { "isexe": "^2.0.0" @@ -7525,6 +8261,23 @@ "funding": { "url": "https://github.com/sponsors/colinhacks" } + }, + "node_modules/zustand": { + "version": "3.7.2", + "resolved": "https://registry.npmjs.org/zustand/-/zustand-3.7.2.tgz", + "integrity": "sha512-PIJDIZKtokhof+9+60cpockVOq05sJzHCriyvaLBmEJixseQ1a5Kdov6fWZfWOu5SK9c+FhH1jU0tntLxRJYMA==", + "license": "MIT", + "engines": { + "node": ">=12.7.0" + }, + "peerDependencies": { + "react": ">=16.8" + }, + "peerDependenciesMeta": { + "react": { + "optional": true + } + } } } } diff --git a/package.json b/package.json index 47d0209..538fcb9 100644 --- a/package.json +++ b/package.json @@ -39,6 +39,8 @@ "@radix-ui/react-toggle": "^1.1.0", "@radix-ui/react-toggle-group": "^1.1.0", "@radix-ui/react-tooltip": "^1.1.4", + "@react-three/drei": "^9.122.0", + "@react-three/fiber": "^8.18.0", "@tanstack/react-query": "^5.56.2", "@types/qrcode": "^1.5.5", "canvas-confetti": "^1.9.3", @@ -61,6 +63,7 @@ "sonner": "^1.5.0", "tailwind-merge": "^2.5.2", "tailwindcss-animate": "^1.0.7", + "three": "^0.160.1", "vaul": "^0.9.3", "zod": "^3.23.8" }, diff --git a/src/App.tsx b/src/App.tsx index 7d2f5fb..d73976c 100644 --- a/src/App.tsx +++ b/src/App.tsx @@ -58,6 +58,7 @@ import ParityBitsGamePage from './pages/ParityBitsGamePage'; import CrapsGamePage from './pages/CrapsGamePage'; import NeighborSumAvoidancePage from './pages/NeighborSumAvoidancePage'; import BurnsidesLemmaPage from './pages/BurnsidesLemmaPage'; +import CubeColoringPage from './pages/CubeColoringPage'; const queryClient = new QueryClient(); @@ -83,8 +84,9 @@ const App = () => ( } /> } /> } /> - } /> - } /> + } /> + } /> + } /> } /> } /> } /> diff --git a/src/components/CubeColoring.tsx b/src/components/CubeColoring.tsx new file mode 100644 index 0000000..06c468a --- /dev/null +++ b/src/components/CubeColoring.tsx @@ -0,0 +1,345 @@ +import { useState, useRef } from 'react'; +import { Canvas, useFrame } from '@react-three/fiber'; +import { OrbitControls } from '@react-three/drei'; +import { Card, CardContent, CardDescription, CardHeader, CardTitle } from '@/components/ui/card'; +import { Button } from '@/components/ui/button'; +import { Select, SelectContent, SelectItem, SelectTrigger, SelectValue } from '@/components/ui/select'; +import { Badge } from '@/components/ui/badge'; +import SocialShare from './SocialShare'; +import { Box, RotateCw, ArrowRightLeft } from 'lucide-react'; +import * as THREE from 'three'; + +interface CubeColoringProps { + showSocialShare?: boolean; + shareUrl?: string; +} + +const colorPalette = [ + '#ef4444', // red + '#3b82f6', // blue + '#22c55e', // green + '#eab308', // yellow + '#a855f7', // purple +]; + +// Face indices: 0=top, 1=bottom, 2=front, 3=back, 4=right, 5=left +const faceNames = ['Top', 'Bottom', 'Front', 'Back', 'Right', 'Left']; + +// Rotation definitions: each rotation maps face indices [0,1,2,3,4,5] to new positions +const rotations = [ + { name: 'Identity', permutation: [0, 1, 2, 3, 4, 5], description: 'No rotation' }, + { name: 'Y-90° (vertical)', permutation: [0, 1, 4, 5, 3, 2], description: 'Front→Right→Back→Left' }, + { name: 'Y-180°', permutation: [0, 1, 3, 2, 5, 4], description: 'Front↔Back, Right↔Left' }, + { name: 'Y-270°', permutation: [0, 1, 5, 4, 2, 3], description: 'Front→Left→Back→Right' }, + { name: 'X-90° (horizontal)', permutation: [2, 3, 1, 0, 4, 5], description: 'Top→Front→Bottom→Back' }, + { name: 'X-180°', permutation: [1, 0, 3, 2, 4, 5], description: 'Top↔Bottom, Front↔Back' }, + { name: 'X-270°', permutation: [3, 2, 0, 1, 4, 5], description: 'Top→Back→Bottom→Front' }, + { name: 'Z-90° (front-back)', permutation: [4, 5, 2, 3, 1, 0], description: 'Top→Right→Bottom→Left' }, + { name: 'Z-180°', permutation: [1, 0, 2, 3, 5, 4], description: 'Top↔Bottom, Right↔Left' }, + { name: 'Z-270°', permutation: [5, 4, 2, 3, 0, 1], description: 'Top→Left→Bottom→Right' }, +]; + +interface PaintableCubeProps { + colors: string[]; + onFaceClick: (faceIndex: number) => void; +} + +function PaintableCube({ colors, onFaceClick }: PaintableCubeProps) { + const meshRef = useRef(null); + + useFrame(() => { + if (meshRef.current) { + meshRef.current.rotation.y += 0.005; + } + }); + + return ( + + + {colors.map((color, i) => ( + + ))} + + ); +} + +function PermutationCube({ permutation }: { permutation: number[] }) { + const meshRef = useRef(null); + + useFrame(() => { + if (meshRef.current) { + meshRef.current.rotation.y += 0.005; + } + }); + + // Create materials based on permutation + const baseMaterials = [ + new THREE.MeshStandardMaterial({ color: '#ef4444' }), // red - top + new THREE.MeshStandardMaterial({ color: '#3b82f6' }), // blue - bottom + new THREE.MeshStandardMaterial({ color: '#22c55e' }), // green - front + new THREE.MeshStandardMaterial({ color: '#eab308' }), // yellow - back + new THREE.MeshStandardMaterial({ color: '#a855f7' }), // purple - right + new THREE.MeshStandardMaterial({ color: '#f97316' }), // orange - left + ]; + + // Apply permutation: materials[i] shows the color that should be at position i + const permutedMaterials = permutation.map(originalIndex => baseMaterials[originalIndex]); + + return ( + + + {permutedMaterials.map((material, i) => ( + + ))} + + ); +} + +const CubeColoring = ({ showSocialShare = false, shareUrl }: CubeColoringProps) => { + const [faceColors, setFaceColors] = useState(Array(6).fill(colorPalette[0])); + const [selectedColor, setSelectedColor] = useState(colorPalette[0]); + const [selectedPermutation, setSelectedPermutation] = useState([0, 1, 2, 3, 4, 5]); + const [selectedRotation, setSelectedRotation] = useState(0); + + const handleFaceClick = (faceIndex: number) => { + const newColors = [...faceColors]; + newColors[faceIndex] = selectedColor; + setFaceColors(newColors); + }; + + const handlePermutationChange = (position: number, value: string) => { + const newPerm = [...selectedPermutation]; + newPerm[position] = parseInt(value); + setSelectedPermutation(newPerm); + }; + + const permutationToRotation = () => { + const match = rotations.findIndex(r => + r.permutation.every((val, idx) => val === selectedPermutation[idx]) + ); + return match >= 0 ? rotations[match] : null; + }; + + return ( +
+ + + + + Burnside's Lemma: Cube Coloring + + + How many distinct cubes can you make by painting each face in one of 5 colors? + Two cubes are the same if one can be rotated to look like the other. + + + + {/* 3D Cube Arena */} +
+

Paint Your Cube

+
+
+ + + + + + +
+ +
+
+ +
+ {colorPalette.map((color) => ( +
+
+ +
+ +
+ {faceNames.map((name, idx) => ( +
+
+ {name} +
+ ))} +
+
+
+
+
+ + {/* Permutation to Rotation */} +
+

+ + Permutation → Rotation +

+
+ + + Pick a Permutation + + Choose where each face (0-5) goes + + + + {selectedPermutation.map((value, idx) => ( +
+ + Face {idx} + + → + + ({faceNames[idx]}) +
+ ))} + + + + + + Corresponding Rotation + + Visualize the rotation + + + + {permutationToRotation() ? ( + <> +
+ + {permutationToRotation()!.name} + +

+ {permutationToRotation()!.description} +

+
+
+ + + + + + +
+ + ) : ( +
+

Invalid permutation

+

Each number 0-5 must appear exactly once

+
+ )} + + +
+
+ + {/* Rotation to Permutation */} +
+

+ + Rotation → Permutation +

+
+ + + Corresponding Permutation + + How faces move with this rotation + + + + {rotations[selectedRotation].permutation.map((target, source) => ( +
+ + Face {source} + + → + Face {target} + + {faceNames[source]} → {faceNames[target]} + +
+ ))} + + + + + + Pick a Rotation + + Select a cube rotation + + + + + +
+ + + + + + +
+ + +
+
+ + + + {showSocialShare && ( + + )} +
+ ); +}; + +export default CubeColoring; diff --git a/src/components/InteractiveIndex.tsx b/src/components/InteractiveIndex.tsx index b25fd91..7e75219 100644 --- a/src/components/InteractiveIndex.tsx +++ b/src/components/InteractiveIndex.tsx @@ -261,6 +261,15 @@ const allInteractives: Interactive[] = [ path: '/themes/discrete-math/structures/burnsides-lemma', theme: 'Discrete Math', dateAdded: '2025-01-22' + }, + { + id: 'cube-coloring', + title: "Burnside's Lemma: Cube Coloring", + description: 'Explore cube rotations and their correspondence with permutations. Paint a 3D cube and understand the rotational symmetry group.', + tags: ['group-theory', 'symmetry', 'cube', 'rotations', 'permutations', 'algebra', '3d'], + path: '/themes/discrete-math/structures/cube-coloring', + theme: 'Discrete Math', + dateAdded: '2025-01-22' } ]; diff --git a/src/pages/CubeColoringPage.tsx b/src/pages/CubeColoringPage.tsx new file mode 100644 index 0000000..30ddb00 --- /dev/null +++ b/src/pages/CubeColoringPage.tsx @@ -0,0 +1,17 @@ +import Layout from '@/components/Layout'; +import CubeColoring from '@/components/CubeColoring'; + +const CubeColoringPage = () => { + return ( + +
+ +
+ + ); +}; + +export default CubeColoringPage; diff --git a/src/pages/theme-pages/discrete-math/Structures.tsx b/src/pages/theme-pages/discrete-math/Structures.tsx index be94b99..ac39aa3 100644 --- a/src/pages/theme-pages/discrete-math/Structures.tsx +++ b/src/pages/theme-pages/discrete-math/Structures.tsx @@ -5,6 +5,7 @@ import { Badge } from '@/components/ui/badge'; import Layout from '@/components/Layout'; import { useState } from 'react'; import BurnsidesLemma from '@/components/BurnsidesLemma'; +import CubeColoring from '@/components/CubeColoring'; interface Interactive { id: string; @@ -24,6 +25,14 @@ const interactives: Interactive[] = [ path: '/themes/discrete-math/structures/burnsides-lemma', component: BurnsidesLemma }, + { + id: 'cube-coloring', + title: "Burnside's Lemma: Cube Coloring", + description: 'Explore cube rotations and their correspondence with permutations. Paint a 3D cube and understand the rotational symmetry group.', + tags: ['group-theory', 'symmetry', 'cube', 'rotations', 'permutations', 'algebra', '3d'], + path: '/themes/discrete-math/structures/cube-coloring', + component: CubeColoring + }, ]; const Structures = () => {