{"version":9,"randomSeed":"2dcd184d38ce53997aa035bf324426eb","graph":{"viewport":{"xmin":-0.5546224690394472,"ymin":-0.07852700743978702,"xmax":1.567934047822994,"ymax":1.1460782914179803}},"expressions":{"list":[{"type":"text","id":"219","text":"fractions here are represented as points (num, den)"},{"type":"text","id":"216","text":"mediant: (a/b), (c/d) => (a + b) / (c + d)"},{"type":"text","id":"223","text":"in this case, that's just the sum of points"},{"type":"folder","id":"213","title":"data","collapsed":true},{"type":"text","id":"233","folderId":"213","text":"generated sequence"},{"type":"expression","id":"214","folderId":"213","color":"#388c46","latex":"F=\\left[\\left(0,1\\right),\\left(1,1\\right)\\right]","hidden":true},{"type":"expression","id":"249","folderId":"213","color":"#000000","latex":"\\operatorname{length}\\left(F\\right)"},{"type":"text","id":"236","folderId":"213","text":"insert position"},{"type":"expression","id":"237","folderId":"213","color":"#2d70b3","latex":"p=2","slider":{"hardMin":true,"hardMax":true,"min":"0","max":"1000","step":"2"}},{"type":"text","id":"227","text":"insert into list L, replacing index i with n, shifting the rest further (return new list)"},{"type":"expression","id":"228","color":"#c74440","latex":"I\\left(L,i,n\\right)=\\operatorname{join}\\left(L\\left[1...\\left(i-1\\right)\\right],n,L\\left[i...\\right]\\right)"},{"type":"folder","id":"242","title":"actions","collapsed":true},{"type":"text","id":"239","folderId":"242","text":"insert new Farey entry and increment position (normal step)"},{"type":"expression","id":"240","folderId":"242","color":"#6042a6","latex":"S_{n}=F\\to I\\left(F,p,F\\left[p-1\\right]+F\\left[p\\right]\\right),p\\to p+2"},{"type":"text","id":"247","folderId":"242","text":"general step"},{"type":"expression","id":"248","folderId":"242","color":"#6042a6","latex":"S_{g}=\\left\\{p>\\operatorname{length}\\left(F\\right):p\\to2,S_{n}\\right\\}"},{"type":"text","id":"244","folderId":"242","text":"reset"},{"type":"expression","id":"245","folderId":"242","color":"#2d70b3","latex":"F\\to\\left[\\left(0,1\\right),\\left(1,1\\right)\\right],p\\to2"},{"type":"folder","id":"252","title":"Ford circles","collapsed":true},{"type":"expression","id":"253","folderId":"252","color":"#388c46","latex":"\\left(x-\\frac{F.x}{F.y}\\right)^{2}+\\left(y-\\frac{1}{2F.y^{2}}\\right)^{2}=\\left(\\frac{1}{2F.y^{2}}\\right)^{2}"}],"ticker":{"handlerLatex":"S_{g}","minStepLatex":"100","open":true}}}