30:T614,svg``31:[] 2e:{"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"},{"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"},{"id":13,"value":"$30","pinned":false,"hidden":false,"mode":"ojs"},{"id":16,"value":"h = {\n let h = k;\n if (h > 0 && h < 1) {\n let t0, t1 = Math.pow(12 * h * Math.PI, 1 / 3);\n for (let i = 0; i < 10; ++i) {\n t0 = t1;\n t1 = (Math.sin(t0) - t0 * Math.cos(t0) + 2 * h * Math.PI) / (1 - Math.cos(t0));\n }\n h = (1 - Math.cos(t1 / 2)) / 2;\n }\n return h;\n}","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}