3e:null 3f:["$","title",null,{"children":"An Illustrated Theory of Numbers | Yasuyuki Ageishi | Observable"}] 45:T774,元々数とは物を数えるのに使うものであった. はいくつかの赤い点で, はいくつかの黒い点である. 一見, 赤い点と黒い点が同じ数あるとは見えにくい. ただそれぞれの色の点を直線に並べて, 赤い点と黒い点を一つずつ組にすれば同じ数あったことがわかる. 組を作ることで数が同じであることを視覚化することが、数え上げることの本質である. 物の個数を数えるには、直線に並べて自然数の上に配置すれば良い. 例えば, 1と20の間の素数を数えるには, 次のように並べればよい:46:Tc0e,足し算とは, 合体することに対応する数を求めることである. 2つの点の集合を合体, つまり一緒にして1つの集合とみなしたときの数である. 2点の赤点と5点の黒点を合体すると7点を得る 2つの数の足し算には正解は1つしかないが, 2つの集合の合体の仕方は沢山ある. 合体した集合の並べ方が沢山あるからである. 例えば 1+3=4 という数式に対応するような点の書き方は次のようなものがある： + = , + = , + = どの絵も結局4点あるので, 「だからどうした?」と思うかもしれない. しかし上手に点を並べることで, 一見難しそうな足し算の問題が解けることもある.47:T5c9,function primitiveCount(svg, data, title, additional) { let x = d3.scaleLinear() .domain([0, 20]) .range([margin.left, width - margin.right]) let _data = additional ? data.concat(['...', additional]) : data let count = additional ? data.map((d, i) => `${i + 1}番`).concat(['...', '?番']) : data.map((d, i) => `${i}番`) const title_margins = { left: 10, top: 20 } let label = title ? svg.append('g') .classed('label', true) .append('text') .text(`${title}: `) .attr("x", title_margins.left) .attr('y', title_margins.top) : null; let number = svg.append('g') .classed("numbers", true) .selectAll('g') .data(_data) .enter() .append('g') .append('text') .text(d => d) .attr("x", (d, i) => x(i) + 40) .attr("y", 20) .attr('text-anchor', 'middle'); let counter = svg.append('g') .classed("counters", true) .selectAll('g') .data(count) .enter() .append('g') .append('text') .text(d => d) .attr("x", (d, i) => x(i) + 40) .attr("y", 45) .attr('text-anchor', 'middle'); return }48:[] 43:{"id":"97daba77ba856537","slug":null,"title":"An Illustrated Theory of Numbers","thumbnail":"9377741a3fc9282984d89c678c0cc8daa949b37959e573eb325a845dad7c2938","access_level":"public","create_time":"$D2023-09-10T14:02:16.263Z","update_time":"$D2023-12-03T06:11:34.627Z","view_time":null,"first_public_time":"$D2023-09-10T14:02:16.263Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"66c2f4acccb2ae01","login":"y4suyuki","name":"Yasuyuki Ageishi","avatar_url":"https://avatars-next.observableusercontent.com/5d14aba29bee6c952464915a60f3ebbdcc4730b1df50ad842a397059515992b9","tier":"starter_2024","bio":"","following":false},"version":271,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"0523abf717b4296b","login":"y4suyuki","name":"Yasuyuki Ageishi","avatar_url":"https://avatars-next.observableusercontent.com/5d14aba29bee6c952464915a60f3ebbdcc4730b1df50ad842a397059515992b9","tier":null,"bio":"","following":false}],"members":[{"type":"individual","id":"0523abf717b4296b","login":"y4suyuki","name":"Yasuyuki Ageishi","avatar_url":"https://avatars-next.observableusercontent.com/5d14aba29bee6c952464915a60f3ebbdcc4730b1df50ad842a397059515992b9","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":{"id":"601e62cb884c9d41","slug":"an-illustrated-numbers-theory","title":"An Illustrated Theory of Numbers","owner":{"id":"66c2f4acccb2ae01","login":"y4suyuki","name":"Yasuyuki Ageishi"}},"type":"notebook","body":{"titling":"auto","title":"An Illustrated Theory of Numbers","cells":[{"id":0,"value":"# An Illustrated Theory of Numbers\n\nMartin H. Weissman","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":7,"value":"## 0 \n### 整数を見る","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":11,"value":"$45","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":15,"value":"chart = {\n let x = d3.scaleLinear()\n .domain([0, 20])\n .range([margin.left, width - margin.right])\n const primes = [2,3,5,7,11,13,17,19];\n const svg = d3.select(DOM.svg(width, 70));\n primitiveCount(svg, primes, \"素数\");\n\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":114,"value":"## 問題 0.1 \n1以上100以下の偶数は何個あるだろうか?\n\n解答: 偶数を直線に並べて, 自然数の上におけばよい.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":133,"value":"even = {\n let x = d3.scaleLinear()\n .domain([0, 20])\n .range([margin.left, width - margin.right])\n const even_nums = [2,4,6,8,10,12];\n const svg = d3.select(DOM.svg(width, 70));\n primitiveCount(svg, even_nums, \"偶数\", 100);\n\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":151,"value":"全て点を書いていくのは面倒である. \nその代わりに、下の行が、組みとなっている上の行の半分になっていることに注目する","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":155,"value":"even_b = {\n let x = d3.scaleLinear()\n .domain([0, 20])\n .range([margin.left, width - margin.right])\n const even_nums = [2,4,6,8,10,12];\n const svg = d3.select(DOM.svg(width, 70));\n primitiveCount(svg, even_nums, \"偶数\", 100);\n const red_text = svg.append('text').text(\"半分にする\").attr(\"fill\", \"coral\").attr('y', 30).attr('x', 500)\n\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":175,"value":"## 問題 0.2\n\n37以上185以下の自然数は何個あるだろうか？\n\n解答：37以上185以下の数を正の自然数と対応して並べていく：\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":179,"value":"natural_numbers = {\n let x = d3.scaleLinear()\n .domain([0, 20])\n .range([margin.left, width - margin.right])\n const nat_nums = [37, 38, 39, 40];\n const svg = d3.select(DOM.svg(width, 70));\n primitiveCount(svg, nat_nums, null, 185);\n\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":188,"value":"下の行の数は、対応する上の行の数より36小さい.\n\nだから, 「？」は 185 - 36 = 149. つまり37以上185以下の自然数は149個である.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":192,"value":"natural_numbers_b = {\n let x = d3.scaleLinear()\n .domain([0, 20])\n .range([margin.left, width - margin.right])\n const nat_nums = [37, 38, 39, 40];\n const svg = d3.select(DOM.svg(width, 70));\n primitiveCount(svg, nat_nums, null, 185);\n \n const red_text = svg.append('text').text(\"36引く\").attr(\"fill\", \"coral\").attr('y', 30).attr('x', 500)\n\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":199,"value":"## 問題 0.3\n\n1以上1000以下の3の倍数は何個あるだろうか？\n\n解答：3の倍数を自然数と対応させて並べればよい：","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":204,"value":"multiple_of_three = {\n let x = d3.scaleLinear()\n .domain([0, 20])\n .range([margin.left, width - margin.right])\n const nat_nums = [3, 6, 9, 12];\n const svg = d3.select(DOM.svg(width, 70));\n primitiveCount(svg, nat_nums, null, 999);\n \n const red_text = svg.append('text').text(\"3で割る\").attr(\"fill\", \"coral\").attr('y', 30).attr('x', 500)\n\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":208,"value":"$46","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":250,"value":"## 問題 0.4\n\n1以上28以下の奇数の和, すなわち, 1+3+5+...+23+25+27を求めよ\n\n解答：奇数側の点は\n\nのような形に並べることができる. これを順番に積み重ねていくと正方形の形に点が並ぶ.\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":118,"value":"$47","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":26,"value":"margin = ({top: 20, right: 30, bottom: 30, left: 40})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W48","stdlib":"1"}} 44:"$43:body"