Within each other.\nThe logarithmic spiral

Page 98

{"slip": { "id": 96, "advice": "Don't give to others advice which you wouldn't follow."}}

{"slip": { "id": 101, "advice": "Alway do anything for love, but don't do that."}}

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{"slip": { "id": 162, "advice": "Stop using the term \"busy\" as an excuse."}}

{"slip": { "id": 217, "advice": "Identify sources of happiness."}}

{"type":"standard","title":"Tait–Kneser theorem","displaytitle":"Tait–Kneser theorem","namespace":{"id":0,"text":""},"wikibase_item":"Q85804930","titles":{"canonical":"Tait–Kneser_theorem","normalized":"Tait–Kneser theorem","display":"Tait–Kneser theorem"},"pageid":62530331,"thumbnail":{"source":"https://upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Osculating_circles_of_the_Archimedean_spiral.svg/330px-Osculating_circles_of_the_Archimedean_spiral.svg.png","width":320,"height":320},"originalimage":{"source":"https://upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Osculating_circles_of_the_Archimedean_spiral.svg/1000px-Osculating_circles_of_the_Archimedean_spiral.svg.png","width":1000,"height":1000},"lang":"en","dir":"ltr","revision":"1131428223","tid":"7e860724-8be0-11ed-8437-5d076030eae0","timestamp":"2023-01-04T03:33:03Z","description":"If a smooth plane curve has monotonic curvature, then its osculating circles are nested","description_source":"local","content_urls":{"desktop":{"page":"https://en.wikipedia.org/wiki/Tait%E2%80%93Kneser_theorem","revisions":"https://en.wikipedia.org/wiki/Tait%E2%80%93Kneser_theorem?action=history","edit":"https://en.wikipedia.org/wiki/Tait%E2%80%93Kneser_theorem?action=edit","talk":"https://en.wikipedia.org/wiki/Talk:Tait%E2%80%93Kneser_theorem"},"mobile":{"page":"https://en.m.wikipedia.org/wiki/Tait%E2%80%93Kneser_theorem","revisions":"https://en.m.wikipedia.org/wiki/Special:History/Tait%E2%80%93Kneser_theorem","edit":"https://en.m.wikipedia.org/wiki/Tait%E2%80%93Kneser_theorem?action=edit","talk":"https://en.m.wikipedia.org/wiki/Talk:Tait%E2%80%93Kneser_theorem"}},"extract":"In differential geometry, the Tait–Kneser theorem states that, if a smooth plane curve has monotonic curvature, then the osculating circles of the curve are disjoint and nested within each other.\nThe logarithmic spiral or the pictured Archimedean spiral provide examples of curves whose curvature is monotonic for the entire curve. This monotonicity cannot happen for a simple closed curve but for such curves the theorem can be applied to the arcs of the curves between its vertices.","extract_html":"

In differential geometry, the Tait–Kneser theorem states that, if a smooth plane curve has monotonic curvature, then the osculating circles of the curve are disjoint and nested within each other.\nThe logarithmic spiral or the pictured Archimedean spiral provide examples of curves whose curvature is monotonic for the entire curve. This monotonicity cannot happen for a simple closed curve but for such curves the theorem can be applied to the arcs of the curves between its vertices.

"}

{"slip": { "id": 15, "advice": "If it ain't broke don't fix it."}}

{"fact":"A cat can jump 5 times as high as it is tall.","length":45}

{"type":"standard","title":"Here Comes Louis Smith","displaytitle":"Here Comes Louis Smith","namespace":{"id":0,"text":""},"wikibase_item":"Q16995228","titles":{"canonical":"Here_Comes_Louis_Smith","normalized":"Here Comes Louis Smith","display":"Here Comes Louis Smith"},"pageid":29268148,"thumbnail":{"source":"https://upload.wikimedia.org/wikipedia/en/8/8c/Here_Comes_Louis_Smith.jpg","width":200,"height":200},"originalimage":{"source":"https://upload.wikimedia.org/wikipedia/en/8/8c/Here_Comes_Louis_Smith.jpg","width":200,"height":200},"lang":"en","dir":"ltr","revision":"1267367857","tid":"9567db6e-cadc-11ef-8999-1a990085e208","timestamp":"2025-01-04T20:43:42Z","description":"1958 studio album by Louis Smith","description_source":"local","content_urls":{"desktop":{"page":"https://en.wikipedia.org/wiki/Here_Comes_Louis_Smith","revisions":"https://en.wikipedia.org/wiki/Here_Comes_Louis_Smith?action=history","edit":"https://en.wikipedia.org/wiki/Here_Comes_Louis_Smith?action=edit","talk":"https://en.wikipedia.org/wiki/Talk:Here_Comes_Louis_Smith"},"mobile":{"page":"https://en.m.wikipedia.org/wiki/Here_Comes_Louis_Smith","revisions":"https://en.m.wikipedia.org/wiki/Special:History/Here_Comes_Louis_Smith","edit":"https://en.m.wikipedia.org/wiki/Here_Comes_Louis_Smith?action=edit","talk":"https://en.m.wikipedia.org/wiki/Talk:Here_Comes_Louis_Smith"}},"extract":"Here Comes Louis Smith is the debut album by American trumpeter Louis Smith recorded on February 4 & 9, 1958 for Transition, but the company went out of business before release; the album masters were acquired by Blue Note's Alfred Lion and released shortly after on Blue Note that same year.","extract_html":"

Here Comes Louis Smith is the debut album by American trumpeter Louis Smith recorded on February 4 & 9, 1958 for Transition, but the company went out of business before release; the album masters were acquired by Blue Note's Alfred Lion and released shortly after on Blue Note that same year.

"}