2b:null 2c:["$","title",null,{"children":"Circular Segment | Mike Bostock | Observable"}] 31:T614,svg``32:[] 2f:{"id":"6677a35f869df266","slug":"circular-segment","title":"Circular Segment","thumbnail":"232827db8df6425c644ff47565b9a004c00a28c7bbfef1bde74dac0be47b81ed","access_level":"public","create_time":"$D2019-12-06T21:41:05.306Z","update_time":"$D2019-12-09T00:01:04.513Z","view_time":null,"first_public_time":"$D2019-12-06T22:03:37.942Z","fork":false,"stars":18,"starred":false,"owner":{"type":"team","id":"8c2e47252fd4995c","login":"mbostock","name":"Mike Bostock","avatar_url":"https://avatars-next.observableusercontent.com/7dbba99ced40bd5ab8013c99b1a11da61231bce321ba1148a9d16ad0f121550a","tier":"starter_2024"},"version":100,"publish_version":100,"role":null,"authored":false,"authors":[{"type":"individual","id":"074c414ad1d825f5","login":"mbostock","name":"Mike Bostock","avatar_url":"https://avatars-next.observableusercontent.com/7dbba99ced40bd5ab8013c99b1a11da61231bce321ba1148a9d16ad0f121550a","tier":null}],"members":[{"type":"individual","id":"074c414ad1d825f5","login":"mbostock","name":"Mike Bostock","avatar_url":"https://avatars-next.observableusercontent.com/7dbba99ced40bd5ab8013c99b1a11da61231bce321ba1148a9d16ad0f121550a","tier":null,"role":"editor"}],"comments":[{"id":"106206b111d125dc","reply_to_id":null,"content":"See also a plot, https://observablehq.com/@harrystevens/circular-segment-with-chart-of-h-k-relationship\n\nAnd cf. https://observablehq.com/@fil/chord-area-inverse","create_time":"$D2021-01-27T22:08:58.180Z","update_time":null,"resolved":false,"user":{"type":"individual","id":"ddd7235babc79ce0","login":"jrus","name":"Jacob Rus","avatar_url":"https://avatars-next.observableusercontent.com/c33dbeed76527c50e64208b0e005e0b6e54a3bef2a14ea6a823f1c7de4867662","tier":null}}],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":12,"collection":{"id":"6d94bdd16890def0","slug":"geometry","title":"Geometry","owner":{"id":"8c2e47252fd4995c","login":"mbostock","name":"Mike Bostock"}},"type":"notebook","body":{"title":"Circular Segment","cells":[{"id":0,"value":"md`# Circular Segment\n\nThis notebook [computes](http://mathforum.org/dr.math/faq/faq.circle.segment.html) via [Newton’s method](http://en.wikipedia.org/wiki/Newton's_method) the height ${tex`h`} of a [circular segment](http://mathworld.wolfram.com/CircularSegment.html) given the fraction ${tex`k`} of the circle’s area that is covered by the segment. For example, ${tex`h = k`} for ${tex`k \\in \\{0, 0.5, 1\\}`}.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":6,"value":"viewof k = {\n const form = html``;\n form.i.oninput = () => {\n form.value = form.i.valueAsNumber;\n form.o.value = form.i.valueAsNumber.toFixed(3);\n };\n form.i.oninput();\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":13,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":16,"value":"h = {\n let h = k;\n if (h > 0 && h < 1) {\n let t0, t1 = Math.pow(12 * h * Math.PI, 1 / 3);\n for (let i = 0; i < 10; ++i) {\n t0 = t1;\n t1 = (Math.sin(t0) - t0 * Math.cos(t0) + 2 * h * Math.PI) / (1 - Math.cos(t0));\n }\n h = (1 - Math.cos(t1 / 2)) / 2;\n }\n return h;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W32","stdlib":"1","titling":"auto"}} 30:"$2f:body"