Ggthjy

Writing π with the digits of π - using the verbatim environment.

documentclass{article}

linespread{0.7}

begin{document}

begin{verbatim}

     3.141592653589793238462643383279

   5028841971693993751058209749445923

  07816406286208998628034825342117067

  9821    48086         5132     

 823      06647        09384

46        09550        58223

17        25359        4081

          2848         1117

          4502         8410

          2701         9385

         21105        55964

         46229        48954

         9303         81964

         4288         10975

        66593         34461

       284756         48233

       78678          31652        71

      2019091         456485       66

     9234603           48610454326648

    2133936            0726024914127

    3724587             00660631558

    817488               152092096

end{verbatim}

end{document}

Based on ascii art drawing by Jorel - https://www.flickr.com/photos/jorel314/3352784321/

Some tessellated pi...

This one is done in plain Metapost, so compile with mpost.

prologues := 3;

outputtemplate := "%j%c.eps";

input colorbrewer-rgb;

beginfig(1);

    path pi; numeric t; t = 13;

    pi = (origin -- (5,0) -- (5,1) -- (4,1) -- (4,4) -- (3,4) -- (3,1) -- (2,1) -- (2,4) -- (1,4) -- (1,1) -- up -- cycle) scaled t;



    for i=1 upto 48:

        for j=1 upto 48:

            fill pi                              shifted (4t*i-2t*j, t*i+5t*j) withcolor Spectral[7][i mod 7 + 1];

            fill pi rotated 180 shifted (4t, 5t) shifted (4t*i-2t*j, t*i+5t*j) withcolor Spectral[7][(3+i) mod 7 + 1];

       endfor

    endfor

    clip currentpicture to unitsquare scaled 100t shifted (0, 32t);

endfig;

end.

You will need to load Metapost Colorbrewer for the colours...

For Pi day, the tikzlings decided to go on holidays. Unfortunately, the snowman could not come with them, so they sent him a postcard:

documentclass{standalone}

usepackage{tikz}

usepackage{tikzlings}



newcommand{palm}{%

    foreach x in {1.2,1.15,...,0} {

        pgfmathsetmacro{y}{0.2*x*(1-x)};

        pgfmathsetmacro{len}{0.3-0.11*x};

        pgfmathsetmacro{angup}{-50-30*x)};

        pgfmathsetmacro{angdown}{20+30*x)};

        fill[bottom color=green!80!black,top color=green!0!brown,shift={(x,y)},rotate=angup] (0,0) -- (0.05,0) -- (0.025+0.015*rnd,len+0.03*rnd) -- cycle;

        fill[top color=green!80!black,bottom color=green!0!brown,shift={(x,y)},rotate=angdown] (0,0) -- (0.05,0) -- (0.025+0.015*rnd,-len+0.03*rnd) -- cycle;

    }

}

newcommand{palmtree}{%

    foreach y in {0,0.05,...,2} {

        fill[inner color=brown!40!yellow,outer color=brown] (0.1*y*y,y) ellipse({0.2-0.015*y} and 0.1);

    }

    foreach angle in {-20,-10,0} {

        begin{scope}[shift={(0.3,2)},rotate=angle]

            palm

        end{scope}

        begin{scope}[shift={(0.5,2)},rotate=-angle,xscale=-1]

            palm

        end{scope}

    }

}



begin{document}



begin{tikzpicture}

    pgfmathsetseed{1}

    begin{scope}[shift={(0.7,0)}]

        palmtree

    end{scope}

    begin{scope}[shift={(-0.7,0)},xscale=-1]

        palmtree

    end{scope}

    bear[hat,xshift=-1.6cm,yshift=1.9cm,scale=0.25];

    coati[tophat,xshift=-1.2cm,yshift=1.9cm,scale=0.25];

    koala[beret,xshift=-0.8cm,yshift=1.9cm,scale=0.25];

    marmot[strawhat,xshift=-0.4cm,yshift=1.9cm,scale=0.25];

    moles[harlequin,xshift=-0.0cm,yshift=1.9cm,scale=0.25];

    mouse[strawhat=blue,xshift=0.4cm,yshift=1.9cm,scale=0.25];

    owl[beret=green!50!black,xshift=0.8cm,yshift=1.9cm,scale=0.25];

    penguin[tophat=red,xshift=1.2cm,yshift=1.9cm,scale=0.25];

    sloth[hat=brown!40!yellow,xshift=1.6cm,yshift=1.9cm,scale=0.25];

end{tikzpicture}



end{document}

We could extract the MetaPost paths for the glyph pi from the font and draw it using LuaTeX.

documentclass{article}



usepackage{fontspec}

setmainfont{latinmodern-math.otf}



usepackage{luacode}

begin{luacode*}

-- We need some utilities from ConTeXt

callbacks = callbacks or {}

callbacks.supported = callbacks.supported or {}

CONTEXTLMTXMODE = CONTEXTLMTXMODE or (status.obj_ptr == nil and 2 or 1)

dofile(kpse.find_file("util-fmt.lua"))

dofile(kpse.find_file("node-ini.lua"))

dofile(kpse.find_file("font-mps.lua"))

dofile(kpse.find_file("font-shp.lua"))



-- That's a simple reimplemetation of ConTeXt's showshape macro

function outlinepaths(character)

    local fontid      = font.current()

    local shapedata   = fonts.hashes.shapes[fontid] -- by index

    local chardata    = fonts.hashes.characters[fontid] -- by unicode

    local shapeglyphs = shapedata.glyphs or { }



    character = utf.byte(character)

    local c = chardata[character]

    if c then

        if not c.index then

            return {}

        end

        local glyph = shapeglyphs[c.index]

        if glyph and (glyph.segments or glyph.sequence) then

            local units  = shapedata.units or 1000

            local factor = 100/units

            local paths  = fonts.metapost.paths(glyph,factor)

            return paths

        end

    end

end

end{luacode*}



usepackage{luamplib}

everymplib{beginfig(0);}

everyendmplib{endfig;}



defmpdefineoutlines#1{directlua{

    local char = "luaescapestring{#1}"

    local outlines = outlinepaths("#1")

    for i, path in ipairs(outlines) do

        tex.print("fill " .. path .. ";")

    end

  }}



begin{document} 



begin{mplibcode}



  mpdefineoutlines{𝜋}



end{mplibcode}



end{document}

Instead of using luamplib, we could also simply print the path to the log file and copy it to a MetaPost file. With some additonal formatting we get:

prologues := 3;

outputformat := "pdf";



beginfig(1)

  fill (56.70,40.70)

    .. controls (56.70,43.10) and (54.60,43.10)

    .. (52.70,43.10)

    -- (19.20,43.10)

    .. controls (17,43.10) and (13.20,43.10)

    .. (8.80,38.40)

    .. controls (5.30,34.50) and (2.70,29.90)

    .. (2.70,29.40)

    .. controls (2.70,29.40) and (2.70,28.40)

    .. (3.90,28.40)

    .. controls (4.70,28.40) and (4.90,28.80)

    .. (5.50,29.60)

    .. controls (10.40,37.30) and (16.20,37.30)

    .. (18.20,37.30)

    -- (23.90,37.30)

    .. controls (20.70,25.20) and (15.30,13.10)

    .. (11.10,4)

    .. controls (10.30,2.50) and (10.30,2.30)

    .. (10.30,1.60)

    .. controls (10.30,-0.30) and (11.90,-1.10)

    .. (13.20,-1.10)

    .. controls (16.20,-1.10) and (17,1.70)

    .. (18.20,5.40)

    .. controls (19.60,10) and (19.60,10.20)

    .. (20.90,15.20)

    -- (26.50,37.30)

    -- (37.80,37.30)

    .. controls (34.50,22.50) and (33.60,18.20)

    .. (33.60,11.50)

    .. controls (33.60,10) and (33.60,7.30)

    .. (34.40,3.90)

    .. controls (35.40,-0.50) and (36.50,-1.10)

    .. (38,-1.10)

    .. controls (40,-1.10) and (42.10,0.70)

    .. (42.10,2.70)

    .. controls (42.10,3.30) and (42.10,3.50)

    .. (41.50,4.90)

    .. controls (38.60,12.10) and (38.60,18.60)

    .. (38.60,21.40)

    .. controls (38.60,26.70) and (39.30,32.10)

    .. (40.40,37.30)

    -- (51.80,37.30)

    .. controls (53.10,37.30) and (56.70,37.30)

    .. (56.70,40.70)

    -- cycle;

endfig;

end

Or you can even use the path with TikZ.

documentclass{article}



usepackage{tikz}



begin{document} 



begin{tikzpicture}[x=1pt,y=1pt]



  fill (56.70,40.70)

    .. controls (56.70,43.10) and (54.60,43.10)

    .. (52.70,43.10)

    -- (19.20,43.10)

    .. controls (17,43.10) and (13.20,43.10)

    .. (8.80,38.40)

    .. controls (5.30,34.50) and (2.70,29.90)

    .. (2.70,29.40)

    .. controls (2.70,29.40) and (2.70,28.40)

    .. (3.90,28.40)

    .. controls (4.70,28.40) and (4.90,28.80)

    .. (5.50,29.60)

    .. controls (10.40,37.30) and (16.20,37.30)

    .. (18.20,37.30)

    -- (23.90,37.30)

    .. controls (20.70,25.20) and (15.30,13.10)

    .. (11.10,4)

    .. controls (10.30,2.50) and (10.30,2.30)

    .. (10.30,1.60)

    .. controls (10.30,-0.30) and (11.90,-1.10)

    .. (13.20,-1.10)

    .. controls (16.20,-1.10) and (17,1.70)

    .. (18.20,5.40)

    .. controls (19.60,10) and (19.60,10.20)

    .. (20.90,15.20)

    -- (26.50,37.30)

    -- (37.80,37.30)

    .. controls (34.50,22.50) and (33.60,18.20)

    .. (33.60,11.50)

    .. controls (33.60,10) and (33.60,7.30)

    .. (34.40,3.90)

    .. controls (35.40,-0.50) and (36.50,-1.10)

    .. (38,-1.10)

    .. controls (40,-1.10) and (42.10,0.70)

    .. (42.10,2.70)

    .. controls (42.10,3.30) and (42.10,3.50)

    .. (41.50,4.90)

    .. controls (38.60,12.10) and (38.60,18.60)

    .. (38.60,21.40)

    .. controls (38.60,26.70) and (39.30,32.10)

    .. (40.40,37.30)

    -- (51.80,37.30)

    .. controls (53.10,37.30) and (56.70,37.30)

    .. (56.70,40.70)

    -- cycle;



end{tikzpicture}



end{document}

The output is rather unspectacular.

documentclass[serif]{beamer}



usepackage{pst-text,pst-eucl,pst-grad}

usepackage[active,tightpage]{preview}

PreviewBorder=0pt

PreviewEnvironment{pspicture}





DeclareFixedFont{ps}{U}{psy}{m}{n}{12cm}% the symbol font

DeclareFixedFont{PS}{T1}{ptm}{m}{n}{11cm}% the times font

DeclareFixedFont{RM}{T1}{ptm}{b}{n}{2cm}



defx{3.43}



psset

{

    PointName=none,

    PointSymbol=none,

    linestyle=none,

    fillstyle=gradient,

    gradlines=1500,

    gradangle=30,

    gradmidpoint=1,

}



newrgbcolor{TopBegin}{0.027 0.6 0.254}

newrgbcolor{TopEnd}{0.521 0.749 0.125}



newrgbcolor{LeftBegin}{0 0.368 0.549}

newrgbcolor{LeftEnd}{0 0.596 0.701}



newrgbcolor{BottomBegin}{0.905 0.223 0.050}

newrgbcolor{BottomEnd}{0.949 0.568 0.003}



newrgbcolor{RightBegin}{0.513 0.117 0.380}

newrgbcolor{RightEnd}{0.870 0.007 0.349}



begin{document}

begin{frame}

begin{pspicture}[showgrid=false](-x,x)(x,-x)

    pstGeonode(-x,x){TL}(-x,-x){BL}(x,-x){BR}(x,x){TR}

    pstGeonode

        (-2.4,1.7){A}

        (-1.2,1.7){B}

        (-1.5,-2.2){C}

        (0.7,-2.3){D}

        (1.0,1.7){E}

    only<6>{psclip{pscircle[linewidth=0,fillstyle=none]{x}}}

        only<1->{pspolygon[gradbegin=TopBegin,gradend=TopEnd](TL)(A)(E)(TR)}

        only<2->{pspolygon[gradbegin=LeftBegin,gradend=LeftEnd](TL)(A)(B)(C)(BL)}

        only<3->{pspolygon[gradbegin=BottomBegin,gradend=BottomEnd](BL)(C)(B)(E)(D)(BR)}

        only<4->{pspolygon[gradbegin=RightBegin,gradend=RightEnd](BR)(D)(E)(TR)}

        only<5->{rput(-0.2,-0.45){pscharpath[fillstyle=solid,fillcolor=white]{ps p}}}

    only<6>{endpsclip}

end{pspicture}

end{frame}

end{document}

Time for a bad joke...

documentclass[margin=1cm]{standalone}

usepackage{tikz}



begin{document}



begin{tikzpicture}[y=0.80pt, x=0.80pt, yscale=-3.000000, xscale=3.000000, inner sep=0pt, outer sep=0pt]

  path[scale=0.265,fill=black,nonzero rule,line width=0.175pt]

    (391.8613,471.7441) .. controls (391.0467,471.6791) and (390.9815,472.0037) ..

    (392.4473,472.7852) .. controls (393.4234,473.3051) and (394.2051,473.8288) ..

    (394.2051,473.8926) .. controls (394.2051,474.1541) and (390.1011,473.8291) ..

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    (366.8496,475.6523) .. controls (361.9658,475.9778) and (361.5745,476.1090) ..

    (363.5938,476.6289) -- (365.8750,477.2168) -- (363.9180,477.9980) .. controls

    (362.8749,478.4542) and (361.1186,478.9102) .. (360.0117,478.9102) --

    (358.0566,479.0410) -- (360.3340,479.8867) -- (362.6133,480.7324) --

    (359.0312,480.9922) .. controls (355.7105,481.2537) and (355.5810,481.3193) ..

    (357.5332,481.7754) .. controls (360.6593,482.5569) and (359.4882,483.4694) ..

    (355.2520,483.5332) .. controls (351.6696,483.5971) and (351.6064,483.5968) ..

    (353.6895,484.3145) -- (355.8379,484.9648) -- (353.3633,486.1387) .. controls

    (351.0825,487.2456) and (351.0829,487.3091) .. (352.8438,486.9199) .. controls

    (355.3829,486.4638) and (354.2754,487.7660) .. (351.6055,488.4199) .. controls

    (350.1062,488.7453) and (349.8471,488.6806) .. (350.2363,487.9629) .. controls

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    (206.7576,562.1390) and (206.4307,563.4438) .. (204.3477,567.2207) .. controls

    (201.0907,573.0168) and (195.1644,579.2050) .. (190.2168,581.8750) .. controls

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    (166.5153,570.3471) and (165.6705,570.0840) .. (162.6113,570.0840) --

    (158.9629,570.0840) -- (159.1562,572.9492) .. controls (159.2870,574.5123) and

    (159.2213,575.6861) .. (158.9629,575.4883) .. controls (158.6375,575.3575) and

    (158.4414,575.4885) .. (158.4414,575.8809) .. controls (158.4414,576.2063) and

    (158.7684,576.7260) .. (159.0938,576.9238) .. controls (159.4861,577.1854) and

    (159.6119,577.6414) .. (159.3535,577.9668) .. controls (159.1590,578.3560) and

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    (184.9512,614.4981) .. controls (185.1457,615.4742) and (184.6892,617.7561) ..

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    (394.2109,575.4817) .. (394.2109,575.2871) .. controls (394.2109,575.0925) and

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    (407.8887,560.3106) .. controls (407.8887,561.6121) and (408.0191,561.7425) ..

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    (415.8989,559.3355) and (417.0053,559.8551) .. (417.0723,561.8106) .. controls

    (417.1392,563.1120) and (417.2040,563.1114) .. (417.6602,561.6152) --

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    (455.3017,502.4160) .. (454.2617,500.7891) .. controls (453.2186,499.2260) and

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    (441.7525,481.1881) .. (438.5625,478.2598) .. controls (435.3726,475.2644) and

    (432.0492,473.4398) .. (428.7285,472.7891) -- (426.4473,472.3965) --

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    (429.9668,475.9121) -- (426.4473,474.2168) -- (428.0742,475.9746) --

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    (423.8395,474.3477) .. (422.9941,474.3477) .. controls (422.2126,474.3477) and

    (421.3657,473.8930) .. (421.1680,473.3730) .. controls (420.9064,472.8531) and

    (420.1917,472.3965) .. (419.4102,472.3965) .. controls (418.1724,472.3965) and

    (418.1085,472.4627) .. (419.2793,473.6973) .. controls (420.6478,475.2603) and

    (420.4505,475.2598) .. (417.5859,474.0859) .. controls (416.3482,473.6298) and

    (413.9400,473.0442) .. (412.2461,472.8496) -- (409.0566,472.5234) --

    (411.2695,474.4121) .. controls (413.8087,476.6259) and (413.5516,476.6926) ..

    (409.7715,475.0625) .. controls (406.9069,473.8248) and (400.2625,473.1071) ..

    (398.9609,473.8887) .. controls (398.6355,474.0833) and (397.2018,473.6936) ..

    (395.7695,473.0430) .. controls (394.2384,472.2630) and (392.6760,471.8091) ..

    (391.8613,471.7441) -- cycle(276.5215,566.2402) -- (279.3223,568.1973) ..

    controls (283.8807,571.3234) and (291.3057,574.5792) .. (296.1895,575.6191) ..

    controls (308.9556,578.2891) and (318.9856,577.3135) .. (328.5586,572.4297) ..

    controls (333.3786,569.9543) and (335.0047,569.4336) .. (338.0000,569.4336) ..

    controls (340.6062,569.4336) and (342.0383,569.7603) .. (343.2090,570.7363) ..

    controls (344.1213,571.4541) and (345.2300,572.0371) .. (345.6191,572.0371) ..

    controls (346.0083,572.0371) and (346.9867,572.5563) .. (347.8320,573.2070) ..

    controls (349.2643,574.3139) and (349.2652,574.4462) .. (348.2891,576.3984) ..

    controls (347.4437,578.0923) and (347.3126,581.0873) .. (347.4434,595.2188) ..

    controls (347.6379,611.4364) and (347.5729,612.2178) .. (346.1406,615.9277) --

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    (347.3125,623.4809) .. (347.3125,625.9531) .. controls (347.3125,628.2339) and

    (347.8319,630.3806) .. (348.8750,632.4668) .. controls (349.7203,634.1606) and

    (350.7639,636.5703) .. (351.1562,637.8750) .. controls (351.3326,638.4122) and

    (351.5011,638.8830) .. (351.6797,639.3027) .. controls (335.5248,639.5443) and

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    (306.2745,639.0478) .. (306.8691,638.5352) .. controls (307.7145,637.7536) and

    (308.9521,637.1660) .. (309.5391,637.1660) .. controls (310.1260,637.1660) and

    (310.7775,636.9719) .. (311.0391,636.7773) .. controls (311.6898,636.1266) and

    (308.3685,630.1331) .. (307.0000,629.3516) .. controls (305.0446,628.3755) and

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    (273.2643,604.0163) .. (274.6328,597.1133) .. controls (275.4144,593.2726) and

    (275.9331,586.9538) .. (276.1309,578.7461) -- (276.5215,566.2402) --

    cycle(243.8203,570.0820) .. controls (244.0149,570.0820) and

    (245.6453,573.7951) .. (247.3359,578.3535) .. controls (249.0298,582.9789) and

    (251.9611,589.6208) .. (253.7188,593.2031) -- (256.9785,599.7188) --

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    (227.5437,639.1752) .. (208.3731,638.7637) .. controls (208.1397,637.8716) and

    (207.5751,636.8804) .. (206.6387,635.7305) .. controls (204.8140,633.5167) and

    (204.2940,633.3228) .. (200.9062,633.1250) -- (197.1934,632.9297) --

    (197.2578,624.7891) .. controls (197.2578,617.2353) and (197.4514,616.2568) ..

    (199.3398,611.3731) .. controls (202.1406,604.2754) and (204.8119,600.4308) ..

    (209.1758,597.3047) .. controls (211.1950,595.8054) and (215.6221,592.2265) ..

    (219.0098,589.2949) .. controls (222.3975,586.3634) and (227.6701,582.1298) ..

    (230.7324,579.9160) .. controls (233.7948,577.7022) and (237.8974,574.5767) ..

    (239.8496,573.0137) .. controls (241.8050,571.3868) and (243.6257,570.0820) ..

    (243.8203,570.0820) -- cycle;

end{tikzpicture}

end{document}

For a tiger, there's a lot of code, so it's available here. The output:

Here is a slightly different visualization of π.

I re-drew this from my copy of Proofs without Words by Roger B. Nelsen. The original was published in Mathematics Magazine, 50.3, May 1977.

Here I have used Metapost using luamplib, so compile with lualatex.

documentclass[border=5mm]{standalone}

usepackage{luatex85}

usepackage{luamplib}

begin{document}

mplibtextextlabel{enable}

begin{mplibcode}

beginfig(0);

    path C, C', S; numeric u; u=68;

    C = fullcircle rotated 90 scaled 2u;

    C' = C rotated 180 shifted (3.14159265359u ,0); 

    S = unitsquare rotated -90 

                   scaled 1.77245385091u

                   shifted point 0 of C'; 



    z0 = (xpart point 2 of C', ypart point 0 of C');

    fill C withcolor 7/8[blue,white]; 

    fill S withcolor 7/8[blue,white]; 



    drawoptions(dashed withdots scaled 1/2);

    draw point 4 of C shifted (-u,0) -- point 3 of S shifted (1/2u,0);

    draw halfcircle rotated 180 

                    scaled abs(point 4 of C - z0)

                    shifted 1/2[point 4 of C,z0];

    drawoptions();

    forsuffixes @=C,C':

        draw @; 

        draw point 0 of @ -- center @ -- point 2 of @ dashed evenly scaled 1/2;

        drawdot point 0 of @ withpen pencircle scaled 3;

    endfor 

    draw point 2 of C' -- z0 dashed evenly scaled 1/2;

    draw S;

    drawarrow subpath(-1/2,-3/2) of C scaled 1.2 withcolor 2/3 red;



    label.top("The Rolling Circle Squares Itself — Thomas Elsner", 

                    1/2[point 0 of C, point 4 of C'] shifted 20 up);

    label.bot("$pi$", 1/2[point 4 of C, point 0 of C']);

    label.lft("$sqrtpi$", 1/2[point 1 of S, point 0 of C']);

    label.rt("$1$", 1/2 point 0 of C);

endfig;

end{mplibcode}

end{document}

My contribuation for pi(e)-day:

The thieves were already there:

One should also honor Euler a bit.

documentclass[tikz,border=3.14mm]{standalone}

usepackage{tikzlings,amsmath}

makeatletter

tikzset{/thing/.cd,

 pie/.code=thing@cheesetruedefthing@cheese{#1}, %<-pretend you didn't see that

 pie/.default=pink!70!red}

makeatother                            

begin{document}

begin{tikzpicture}[font=sffamily]

marmot[pie,whiskers,teeth,shadow]

node[anchor=east,scale=5,transform shape] at (-0.6,1) {$picdotmathsf{e}=text{sffamily pie}$};

end{tikzpicture}

end{document}

The obligatory forest solution:

documentclass{standalone}



usepackage[edges]{forest}

usetikzlibrary{calc}

forestset{

  forked edge'/.style={

    edge={rotate/.option=!parent.grow},

    edge path'={(!u.parent anchor)++(0pt,-30pt) -- (!u.parent anchor)++(0pt,30pt)  |- (.child anchor)},   

  }

}

begin{document}

Huge

begin{forest}forked edges,for tree={edge={line width=4pt}}

[ [ ] [ ]]

end{forest}

end{document}

A few mathematical representations:

documentclass[10pt,a4paper]{article}

begin{document}

    [int_{-infty}^{infty}frac{sin x}{x}dx]

end{document}

Honory representation: Ramanujan's equation

documentclass[10pt,a4paper]{article}

usepackage{amsmath}

begin{document}

    [sqrt{6}cdotprod_{p~text{prime}}^{infty}frac{p}{sqrt{p^2-1}}]

end{document}

In a computer programmer's paradigm:

documentclass[10pt,a4paper]{article}

usepackage{amsmath}

begin{document}

    [4cdotarctan{1}]

end{document}

defTau{ooalign{%

  $bigcirc$cr

  hskip.3em $^circ$cr

  hskip.49em vrule depth .5ex height .95ex width .4pt

}}

$$ Tauover 2 $$

bye

This lua code shows how to use Monte Carlo simulation (MCS) to estimate π. Approach and Matlab solution is here.

documentclass{article}

usepackage{luacode}



begin{document}

luaexec{

tp=tex.print

N=5000000 --[[ the experiment event number ]]

r=1 --[[ the circle radius ]]

n=0 --[[ sucessful event number  ]]

for i = 1,N,1 

do 

   x=-r+2*r*math.random()

   y=-r+2*r*math.random()

   if ((x*x+y*y)<=r*r) then n = n+1  end

end

lua_pi = 4*n/N

tp("Estimated value of pi :")  tp(lua_pi)

}

end{document}

In honor of Archimedes....

documentclass{article}





usepackage[svgnames]{xcolor}

usepackage{tikz}



pagestyle{empty}



begin{document}

    noindent

foreach x/y in {6/Pink,12/Yellow,24/LightGreen,48/Orange,96/Magenta}

 {

begin{tikzpicture}

fill[White] (0,0) circle(3.2cm);

draw[fill=y] (0,0) circle(3cm);

foreach z in {1,...,x}

 {

  pgfmathsetmacrorx{3*cos(360*(z/x))};

  pgfmathsetmacrory{3*sin(360*(z/x))};

  draw (0,0)--(rx,ry);

  pgfmathsetmacrorxp{3*cos(360*((z-1)/x))};

  pgfmathsetmacroryp{3*sin(360*((z-1)/x))};

  draw (rxp,ryp)--(rx,ry);

};

end{tikzpicture} 

}

raisebox{3cm}{Archimedes's algorithm for computing $pi$}

end{document}

A bit rough, but anyway.

documentclass{standalone}

defpgfsysdriver{pgfsys-Gin@driver}

usepackage{pgfsys}

usepackage{pgffor}

usepackage{pgfmath}

usepgflibrary{fpu}

pgfkeys{

 /pgf/fpu=true,

 /pgf/fpu/output format=fixed

}

defpgfpt{dimexprpgfmathresult ptrelax}

begin{document}

Large

hspace{5mm}%

foreach i in {0,...,90}{%

 pgfmathparse{-sin(i) * 50}%

 raisebox{pgfpt}{.}%

 pgfmathparse{(cos(i) - cos(i - 1)) * 5 - 4}%

 hspace{pgfpt}%

}\

hspace{-2mm}%

foreach i in {0,...,50}{.hspace{-3pt}}\

hspace{-8mm}%

foreach i in {0,...,120}{%

 pgfmathparse{-sin(i) * 50}%

 raisebox{pgfpt}{.}%

 pgfmathparse{(cos(i) - cos(i - 1)) * 5 - 3.7}%

 hspace{pgfpt}%

}%

end{document}

Do you know what the value of π is? Here is an answer.

documentclass[tikz]{standalone}

newlength{numheight}

settoheight{numheight}{1}

begin{document}

begin{tikzpicture}[x={numheight/2},y={numheight/2}]

draw (-6,-.2)|-(-5,0) (-5.6,0)--(-5.75,-1) (-5.3,0)--(-5.3,-.875) arc (180:360:.125);

draw (-4.5,.25) to[out=60,in=-120] (-3.5,.25) (-4.5,-.25) to[out=60,in=-120] (-3.5,-.25);

draw (-3,0) arc (-90:90:1 and 0.5) (-3,0) arc (90:-90:1 and 0.5);

draw (-1,-1) circle (.1pt);

draw (.5,-1)|-(0,1) (0,-1)--(1,-1);

draw (2,1)--(1.5,0)--(2.5,0) (2.5,1)--(2.5,-1);

draw (3.5,-1)|-(3,1) (3,-1)--(4,-1);

draw (5.5,1)-|(4.5,0) arc (90:-90:1 and 0.5);

draw (6.5,0)-|(7,.5) arc (0:270:0.5) (7,0) arc (0:-90:1);

draw (7.5,.5) arc (180:-60:0.5) to[out=210,in=90] (7.5,-1)--(8.5,-1);

draw (9,-.5)|-(9.5,0) arc (90:-180:0.5) (9,0) arc (180:90:1);

draw (11.5,1)-|(10.5,0) arc (90:-90:1 and 0.5);

draw (12,0) arc (-90:90:1 and 0.5) (12,0) arc (90:-90:1 and 0.5);

draw (13.5,-.5)|-(14,0) arc (90:-180:0.5) (13.5,0) arc (180:90:1);

end{tikzpicture}

end{document}

Don't worry about the spacing. This is supposed to be in a monospaced font :))

Without code...

My little litle litle...........contribution...with Mathcha.

documentclass[10pt]{article}

usepackage{tikz}

begin{document}

tikzset{every picture/.style={line width=0.75pt}}       

begin{tikzpicture}[x=0.75pt,y=0.75pt,yscale=-1,xscale=1]

draw[line width=2mm, violet] (221,106) .. controls (261,76) and (315.5,126) .. (355.5,96) ;

draw[line width=1.5mm, violet] (254.5,98) -- (239.5,176) ;

draw[line width=1.5mm, violet] (318,107) -- (335.5,179) ;

end{tikzpicture}

end{document}

or.....this

documentclass[10pt]{article}

    usepackage{tikz}

    begin{document}

    begin{tikzpicture}[x=0.75pt,y=0.75pt,yscale=-1,xscale=1]

    draw[line width=3mm, orange] (200,103) .. controls (240,73) and (267.5,123) .. (307.5,93) ;

    draw[line width=2.3mm, orange] (226.5,160) .. controls (244.5,158) and (235.5,136) .. (235.5,94) ;

    draw[line width=2.3mm, orange]  (284.5,160) .. controls (276.5,152) and (276.5,140.75) .. (276.13,134.75) .. controls (275.75,128.75) and (276,122) .. (274.5,103) ;

    end{tikzpicture}

    end{document}

.....and for my students :-) this l(circle)(r)/(2r) = π

documentclass[a4paper,12pt]{article}

usepackage{tikz,amsmath,amssymb}

begin{document}

tikzset{every picture/.style={line width=0.75pt}}        

begin{tikzpicture}[x=0.75pt,y=0.75pt,yscale=-1,xscale=1]

draw   (125,142.25) .. controls (125,90.2) and (167.2,48) .. (219.25,48) .. controls (271.3,48) and (313.5,90.2) .. (313.5,142.25) .. controls (313.5,194.3) and (271.3,236.5) .. (219.25,236.5) .. controls (167.2,236.5) and (125,194.3) .. (125,142.25) -- cycle ;

draw[|-|,red]   (219.25,142.25) -- (287.54,207.96) ;

draw (248,184) node   {$r$};

draw (325,92) node   {$ell(mathcal{C})$};

end{tikzpicture}

end{document}

Happy pi(less) day!!

documentclass{report}

begin{document}

noindent%

rule{30pt}{1pt}\[-1pt]

rule{8pt}{0pt}%

rule{1pt}{30pt}%

rule{12pt}{0pt}%

rule{1pt}{30pt}

end{document}

You can use different representations like :

 documentclass[10pt,a4paper]{article}

 usepackage{amsmath}

 begin{document}

    [sqrt{6sumlimits^{infty}frac{1}{n^2}}]

 end{document}

Or the gamma function :

 documentclass[10pt,a4paper]{article}

 usepackage{amsmath}

 begin{document}

    [Gammaleft(frac{1}{2}right)^2]

 end{document}

You could also use Leibniz Wallis or BBP formula.

OK here we go again, I usually get voted off as my answers are poor TeX because I plagiarise. However in the spirit of the day and as a result of yet another two down votes I have updated my avatar to include this code even though it took me all day to get here.

[Edit thanks to @Marmot] I Have removed some duplication and cleaned other code so it includes 3.14 pt

documentclass[varwidth,11pt]{standalone}begin{document}~\phantom{.}~rule{55pt}{2pt}\[-3.14pt]huge{{~K~}rule{2pt}{22pt}{~J~}rule{2pt}{22pt}{~O~}}\end{document}

Previously I did modify this gif to try and help explain what pi truly represents.

As usual I can not really show off the level of my own TeX skill so have added another plagiarism courtesy of those well known TeX advocates

% Answer dedicated to David and Paulo

documentclass{article}

begin{document} begin{picture}(100,100) put(0,60){ooh Hapi pi dayz} put(0,40){I CAN try, I can really try :-)} put(10,0){ line(0,1){20} } put(0,20){ line(1,0){30} } put(20,0){ line(0,1){20} } put(60,0){[1] p.p. D. Carlisle and P. Cereda} end{picture}

end{document}

My small contribution with some slagroom vlaai ;-) (I really think, we should not omit this one).

documentclass{article}

usepackage{graphicx}

begin{document}

How can we forget this: $pi$.



Anyway a happy pie day:



includegraphics[height=2in, width=2in]{a}



end{document}

After baking the PIE for JouleV in tikz:

%&lualatex

% !TeX TXS-program:compile = txs:///lualatex/[--shell-escape]





documentclass{standalone}

usepackage{pgfplots}

usepackage{tikz}

% % lets bake some pi with a nice recipe from: https://helloacm.com/r-programming-tutorial-how-to-compute-pi-using-monte-carlo-in-r/



begin{document}

begin{tikzpicture}

begin{axis}[]



foreach i in {1,...,10000}{

    % Lets start baking the PI(E)

pgfmathparse{rnd}

%VARIABLES

pgfmathsetmacro{x}{pgfmathresult}



pgfmathparse{rnd}

%VARIABLES

pgfmathsetmacro{y}{pgfmathresult}



pgfmathparse{x*x+y*y)}

%VARIABLES

pgfmathsetmacro{t}{pgfmathresult}



pgfmathparse{t^0.5)}

%VARIABLES

pgfmathsetmacro{z}{pgfmathresult}



% now the comparison

pgfmathparse{notgreater(z,1)} 

ifnumpgfmathresult=1 

addplot[red, mark=*] coordinates {(x,y)};

else

addplot[yellow, mark=*] coordinates {(x,y)};

fi



}

end{axis}



end{tikzpicture}

end{document}

to get: