2b:null 2c:["$","title",null,{"children":"Multiplication circles, packed primes | Forrest O. | Observable"}] 31:T4b4,// https://en.wikipedia.org/wiki/Circle_packing_in_a_circle // Approximate packings = { const regularTransform = n => (outerRadius, radius, i) => `rotate(${(360 / n) * i}) translate(0, ${radius - outerRadius})`; const transform7 = (outerRadius, radius, i) => i < 6 ? regularTransform(6)(outerRadius, radius, i) : `translate(0, 0)`; // Not exact const transform11 = (outerRadius, radius, i) => i < 8 ? `rotate(${(360 / 9) * i - (360 / 9) * 3.5}) translate(0, ${radius - outerRadius})` : `translate(0, ${radius * 0.4}) rotate(${(360 / 3) * i - 180}) translate(0, ${0 - radius * 1.155})`; return [ { count: 1, r: 1, transforms: regularTransform(1) }, { count: 2, r: 2, transforms: regularTransform(2) }, { count: 3, r: 2.154, transforms: regularTransform(3) }, { count: 4, primes: [2, 2] }, { count: 5, r: 2.701, transforms: regularTransform(5) }, { count: 6, primes: [3, 2] }, { count: 7, r: 3, transforms: transform7 }, { count: 8, primes: [2, 2, 2] }, { count: 9, primes: [3, 3] }, { count: 10, primes: [5, 2] }, { count: 11, r: 3.923, transforms: transform11 }, { count: 12, primes: [3, 2, 2] } ]; }32:[] 2f:{"id":"13080a6fd2059c87","slug":"multiplication-circles-packed-primes","title":"Multiplication circles, packed primes","thumbnail":"d5b277fcab09cb0c5996e9c24d52362b95601312a989326bea2ff7a6c8fe881e","access_level":"public","create_time":"$D2019-12-12T05:17:55.548Z","update_time":"$D2020-01-02T22:30:41.323Z","view_time":null,"first_public_time":"$D2019-12-13T13:51:32.437Z","fork":false,"stars":36,"starred":false,"owner":{"type":"team","id":"f9abb147dc0e6dcd","login":"forresto","name":"Forrest O.","avatar_url":"https://avatars-next.observableusercontent.com/c22671040121cb9b9d22913e2eb0ffc4d65d3e535cda1133d6655f1d63b32e3f","tier":"starter_2024"},"version":551,"publish_version":551,"role":null,"authored":false,"authors":[{"type":"individual","id":"b16dd1586d4d1422","login":"forresto","name":"Forrest O.","avatar_url":"https://avatars-next.observableusercontent.com/c22671040121cb9b9d22913e2eb0ffc4d65d3e535cda1133d6655f1d63b32e3f","tier":null}],"members":[{"type":"individual","id":"b16dd1586d4d1422","login":"forresto","name":"Forrest O.","avatar_url":"https://avatars-next.observableusercontent.com/c22671040121cb9b9d22913e2eb0ffc4d65d3e535cda1133d6655f1d63b32e3f","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":8,"collection":{"id":"cee7f229da905180","slug":"plotter","title":"plotter","owner":{"id":"f9abb147dc0e6dcd","login":"forresto","name":"Forrest O."}},"type":"notebook","body":{"title":"Multiplication circles, packed primes","cells":[{"id":0,"value":"md`# Multiplication circles, packed primes\n\nContent Warning: [Trypophobia](https://en.wikipedia.org/wiki/Trypophobia)-triggering images: many circles in circles.\n\nOnly implemented up to 12. Primes are [circle-packed](https://en.wikipedia.org/wiki/Circle_packing_in_a_circle), non-primes are broken down to primes.\n\nInspiration: how my seven-year-old is explaining multiplication, and https://twitter.com/FogleBird/status/1203875808806424576\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":437,"value":"md`## Multiplication table, 1 to 12`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":6,"value":"html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":284,"value":"timesTable = Array(cols * cols)\n .fill()\n .map((_, i) => {\n const a = (i % cols) + 1;\n const b = Math.floor(i / cols) + 1;\n return [a, b];\n // return x === 1 ? [y] : [b, a];\n })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":222,"value":"size = cols * 96 * 2","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":245,"value":"cols = 12","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":429,"value":"md`## 7 x 7 x 7 x 7\n> As I was going to St. Ives, I met a man with seven wives, \nEvery wife had seven sacks, \nEvery sack had seven cats, \nEvery cat had seven kits.\nKits, cats, sacks, and wives, How many were going to St. Ives?\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":258,"value":"fromStIves = html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":461,"value":"md`## 2 x 3 x 5 x 7\nPrime multiplication, with different sorting`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":444,"value":"primes = html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":537,"value":"md`## 3^8`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":525,"value":"sierp = html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":468,"value":"md`## Recursive draw function`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":4,"value":"function draw(arr, radius, transform) {\n const cloned = arr.slice();\n const n = cloned.shift();\n let packing;\n if (n) {\n packing = packings[n - 1];\n if (packing.primes) {\n const primesClone = [...packing.primes, ...cloned];\n return draw(primesClone, radius, transform);\n }\n }\n return svg`\n \n \n ${\n n && packing\n ? Array(n)\n .fill(0)\n .map((_, i) => {\n const nextRadius = radius / packing.r;\n return draw(\n cloned,\n nextRadius,\n packing.transforms(radius, nextRadius, i)\n );\n })\n : ''\n }\n `;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":178,"value":"$31","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":491,"value":"elevens = html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W32","stdlib":"1","titling":"auto"}} 30:"$2f:body"