2d:null 2e:["$","title",null,{"children":"📑 ThebeCell Embedding | Olga Belitskaya | Observable"}] 33:T47e,html`

Cell #1

    sage: var('t'); n=3; d={2*i+1:[2*i+2] for i in [0..6]}
    sage: c=[colormaps.ocean(24*k)[:3] for k in [0..10]]
    sage: p=polar_plot([(t+k/n)*log(t/n) for k in [0..10]],
    sage:              0,n*pi,color=c,fill=d,fillcolor=c)
    sage: ti=r'$f=(t+k/%d)'%n+' \cdot \log(t/%d)'%n+', k \in \{0,1,...,10\}$'
    sage: p.show(title=ti,fontsize=12,figsize=5)

Cell #2

    sage: @interact
    sage: def _(a=[7,9,..,17],b=[10,12,..,20]):
    sage:     x(t)=cos(t)+cos(a*t)/2+sin((a+b)*t)/3
    sage:     y(t)=sin(t)+sin(a*t)/2+cos((a+b)*t)/3
    sage:     def col(c): return colormaps.hsv(5*c)[:3]
    sage:     p=sum([parametric_plot((x,y),(t,(i-1)*pi/24,i*pi/24),
    sage:                            color=col(i)) for i in [1..48]])
    sage:     p.show(aspect_ratio=1,figsize=7,gridlines=True)

Cell #3

    sage: %%r
    sage: elements<-c('☜','☞','☝︎','☟')
    sage: n<-length(elements)
    sage: S<-unique(t(sapply(1:10^3,function(x) sample(elements,n)))) 
    sage: S<-apply(S,1,function(x) paste0(x,collapse=''))
    sage: print(length(S)==factorial(4)); S

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✒️ Cell Styling

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":15,"value":"html`\n\n \n \n \n \n `","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":73,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":47,"value":"html`

✒️ Code Importing

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":21,"value":"import_js=function(src,module_name) {\n /*if (!$('head').find(`script[src='${src}']`)) {\n $('head').append(``);\n }*/\n return new Promise(function(resolve,reject) {\n function waiting(){\n if (typeof module_name=='undefined') resolve();\n if (eval(module_name)) resolve(eval(module_name));\n setTimeout(waiting,30);};\n require(src).then(function() {waiting();})\n .catch(function() {waiting();}); }); }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"thebecell=import_js('https://unpkg.com/thebe@latest/lib/index.js','window.thebecell')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":88,"value":"html`

Unlock the next command for live Python coding in Thebe cells

(remove symbols <!-- and --!>)

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