Welcoming 2019 Pi day: How to draw the letter π?

Question

First of all: don't forget that exactly 140 years ago, Albert Einstein was born; but exactly one year ago, Stephen William Hawking passed away. What a special day for science!

---

Question

How to draw the letter π not in the standard way (i.e. \pi)?

I mean "draw", not "type"! Today there will be no \pi, but there will be something like this

\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}
\draw (0,2)--(3,2);
\draw (1,0)--(1,2);
\draw (2,0)--(2,2);
\end{tikzpicture}
\end{document}

(inspired by David Carlisle – I draw this in TikZ just because I don't know how to use picture ;))

Or this

\documentclass[tikz]{standalone}
\usepackage{tikzducks}
\begin{document}
\begin{tikzpicture}
\duck
\duck[xshift=1cm,yshift=2cm]
\duck[xshift=1cm,yshift=4cm]
\duck[xshift=1cm,yshift=6cm]
\duck[xshift=0cm,yshift=8cm]
\duck[xshift=-2cm,yshift=7.5cm]
\duck[xshift=2cm,yshift=8cm]
\duck[xshift=4cm,yshift=8cm]
\duck[xshift=6cm,yshift=8cm]
\duck[xshift=8cm,yshift=8cm]
\duck[xshift=5cm,yshift=6cm]
\duck[xshift=5cm,yshift=4cm]
\duck[xshift=5.5cm,yshift=2cm]
\duck[xshift=6.5cm,yshift=0cm]
\duck[xshift=8cm,yshift=1cm]
\node[font=\huge] at (4,11) {Happy $\pi$ day with \verb|tikzducks|!};
\end{tikzpicture}
\end{document}

They are my proudest π drawings, and as today is Pi day, I'd like to see yours!

---

Well, why didn't I delay the time of asking the question by 8 minutes? I asked this at 1:51:31 UTC time, and the "Pi second" of this year is at 1:59:26 today!

Answer 1

Here's one with \shapepar, with great thanks to flowframtk.

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{libertine}
\usepackage{shapepar}

\newcommand{\sep}{\discretionary{}{}{}}

\begin{document}

\small%
\shapepar[1.00375pt]{{137.821777}%
{0.0}b{27.0}%
\\{0.0}t{27.0}{249.0}%
\\{11.955168}t{14.0}{250.0}%
\\{23.910336}t{2.0}{249.0}%
\\{27.074219}t{0.0}{135.5}st{135.5}{111.5}%
\\{35.865504}t{57.0}{35.0}t{179.0}{35.0}%
\\{47.820672}t{56.0}{34.0}t{178.0}{34.0}%
\\{59.775841}t{55.0}{34.0}t{177.0}{34.0}%
\\{71.731009}t{53.0}{35.0}t{175.0}{35.0}%
\\{83.686177}t{52.0}{34.0}t{174.0}{34.0}%
\\{95.641345}t{51.0}{34.0}t{173.0}{34.0}%
\\{107.596513}t{49.0}{35.0}t{171.0}{35.0}%
\\{119.551681}t{48.0}{34.0}t{170.0}{34.0}%
\\{131.506849}t{47.0}{34.0}t{169.0}{34.0}%
\\{135.137695}t{46.0}{35.0}t{168.0}{35.0}%
\\{143.462017}t{45.0}{35.0}t{168.0}{34.0}%
\\{154.276367}t{44.0}{34.0}t{166.0}{35.0}%
\\{155.417186}t{44.0}{34.0}t{166.0}{35.0}%
\\{163.378906}t{43.0}{34.0}t{166.0}{34.0}%
\\{167.372354}t{43.0}{34.0}t{165.0}{35.0}t{256.0}{3.0}%
\\{171.936859}t{42.0}{34.0}t{165.0}{35.0}t{253.0}{8.0}%
\\{179.327522}t{41.0}{35.0}t{165.0}{35.0}t{248.0}{13.0}%
\\{182.050781}t{41.0}{34.0}t{165.0}{36.0}t{245.0}{15.0}%
\\{187.185547}t{40.0}{35.0}t{166.0}{36.0}t{240.0}{17.0}%
\\{191.28269}t{40.0}{34.0}t{166.0}{39.0}t{235.0}{19.0}%
\\{193.214996}t{40.0}{34.0}t{166.0}{40.0}t{232.0}{20.0}%
\\{197.688477}t{39.0}{35.0}t{167.0}{50.0}jt{217.0}{31.0}%
\\{198.388672}t{39.0}{35.0}t{167.0}{80.0}%
\\{203.237858}t{39.0}{34.0}t{169.0}{72.0}%
\\{207.880219}t{38.0}{34.0}t{171.0}{64.0}%
\\{207.958008}t{38.0}{34.0}t{171.0}{64.0}%
\\{215.193026}t{37.0}{19.0}t{175.0}{49.0}%
\\{215.660156}t{37.0}{18.0}t{176.0}{47.0}%
\\{222.195312}t{37.0}{2.0}t{186.0}{23.0}%
\\{222.195312}e{37.0}%
\\{223.362305}t{191.0}{13.0}%
\\{223.362305}e{191.0}%
}%
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\end{document}

Answer 2

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...

Answer 3

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/

Answer 4

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}

Answer 5

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;}

\def\mpdefineoutlines#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.

Answer 6

Time for a bad joke...

\documentclass[margin=1cm]{standalone}
\usepackage{tikz}

\begin{document}

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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:

Answer 7

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("$\sqrt\pi$", 1/2[point 1 of S, point 0 of C']);
    label.rt("$1$", 1/2 point 0 of C);
endfig;
\end{mplibcode}
\end{document}

Answer 8

\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}

\def\x{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}

Unnecessary edit: Today is a pi's day!

Answer 9

My contribuation for pi(e)-day:

The thieves were already there:

Answer 10

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}

Answer 11

One should also honor Euler a bit.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tikzlings,amsmath}
\makeatletter
\tikzset{/thing/.cd,
 pie/.code=\thing@cheesetrue\def\thing@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) {$\pi\cdot\mathsf{e}=\text{\sffamily pie}$};
\end{tikzpicture}
\end{document}

Answer 12

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}
    \[\sqrt{6}\cdot\prod_{p~\text{prime}}^{\infty}\frac{p}{\sqrt{p^2-1}}\]
\end{document}

In a computer programmer's paradigm:

\documentclass[10pt,a4paper]{article}
\usepackage{amsmath}
\begin{document}
    \[4\cdot\arctan{1}\]
\end{document}

Answer 13

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}
 {
  \pgfmathsetmacro\rx{3*cos(360*(\z/\x))};
  \pgfmathsetmacro\ry{3*sin(360*(\z/\x))};
  \draw (0,0)--(\rx,\ry);
  \pgfmathsetmacro\rxp{3*cos(360*((\z-1)/\x))};
  \pgfmathsetmacro\ryp{3*sin(360*((\z-1)/\x))};
  \draw (\rxp,\ryp)--(\rx,\ry);
};
\end{tikzpicture} 
}
\raisebox{3cm}{Archimedes's algorithm for computing $\pi$}
\end{document}

Answer 14

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}

Answer 15

\def\Tau{\ooalign{%
  $\bigcirc$\cr
  \hskip.3em $^\circ$\cr
  \hskip.49em \vrule depth .5ex height .95ex width .4pt
}}
$$ \Tau\over 2 $$
\bye

Answer 16

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...

Answer 17

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(C)/(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}

Answer 18

A bit rough, but anyway.

\documentclass{standalone}
\def\pgfsysdriver{pgfsys-\Gin@driver}
\usepackage{pgfsys}
\usepackage{pgffor}
\usepackage{pgfmath}
\usepgflibrary{fpu}
\pgfkeys{
 /pgf/fpu=true,
 /pgf/fpu/output format=fixed
}
\def\pgfpt{\dimexpr\pgfmathresult pt\relax}
\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}

Answer 19

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}

Answer 20

You can use different representations like :

 \documentclass[10pt,a4paper]{article}
 \usepackage{amsmath}
 \begin{document}
    \[\sqrt{6\sum\limits^{\infty}\frac{1}{n^2}}\]
 \end{document}
 

Or the gamma function :

 \documentclass[10pt,a4paper]{article}
 \usepackage{amsmath}
 \begin{document}
    \[\Gamma\left(\frac{1}{2}\right)^2\]
 \end{document}

You could also use Leibniz Wallis or BBP formula.

Answer 21

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)} 
\ifnum\pgfmathresult=1 
\addplot[red, mark=*] coordinates {(\x,\y)};
\else
\addplot[yellow, mark=*] coordinates {(\x,\y)};
\fi

}
\end{axis}

\end{tikzpicture}
\end{document}

to get:

Answer 22

Run both with latex->dvips->ps2pdf

\documentclass[border=15pt,pstricks]{standalone}
\usepackage{pst-plot,pst-text} 
\newcommand*\PI{%
3{,}%
1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679%
8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196%
4428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273%
7245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094%
3305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912%
9833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132%
0005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235%
4201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859%
5024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303%
5982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989%
3809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913151%
5574857242454150695950829533116861727855889075098381754637464939319255060400927701671139009848824012%
8583616035637076601047101819429555961989467678374494482553797747268471040475346462080466842590694912%
9331367702898915210475216205696602405803815019351125338243003558764024749647326391419927260426992279%
6782354781636009341721641219924586315030286182974555706749838505494588586926995690927210797509302955%
3211653449872027559602364806654991198818347977535663698074265425278625518184175746728909777727938000%
8164706001614524919217321721477235014144197356854816136115735255213347574184946843852332390739414333%
4547762416862518983569485562099219222184272550254256887671790494601653466804988627232791786085784383%
8279679766814541009538837863609506800642251252051173929848960841284886269456042419652850222106611863%
0674427862203919494504712371378696095636437191728746776465757396241389086583264599581339047802759009%
9465764078951269468398352595709825822620522489407726719478268482601476990902640136394437455305068203%
4962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382%
6868386894277415599185592524595395943104997252468084598727364469584865383673622262609912460805124388%
4390451244136549762780797715691435997700129616089441694868555848406353422072225828488648158456028506%
0168427394522674676788952521385225499546667278239864565961163548862305774564980355936345681743241125%
1507606947945109659609402522887971089314566913686722874894056010150330861792868092087476091782493858%
9009714909675985261365549781893129784821682998948722658804857564014270477555132379641451523746234364%
5428584447952658678210511413547357395231134271661021359695362314429524849371871101457654035902799344%
0374200731057853906219838744780847848968332144571386875194350643021845319104848100537061468067491927%
8191197939952061419663428754440643745123718192179998391015919561814675142691239748940907186494231961%
}
\pagestyle{empty}
\begin{document}
\DeclareFixedFont{\ps}{U}{psy}{m}{n}{12cm}
\begin{pspicture}(-6,-6)(15,5.5)
  \pstextpath{\pscustom[linestyle=none]{%
  \parametricplot[plotpoints=500]{0}{3510}{t cos t 600 div mul t sin t 600 div mul}
  \psline(!3510 cos 3510 600 div mul 30 add 3510 sin 3510 600 div mul)}}{\PI}
  \rput(0,-3.2){\pscharpath[linecolor=black!20,strokeopacity=0.8,
    fillstyle=solid,fillcolor=blue!40,opacity=0.75]{\rput[b](0,0){\ps p}}}
\end{pspicture}

\end{document}

\documentclass[pstricks]{standalone}
\usepackage[tiling]{pst-fill}      % PSTricks package for filling/tiling
\usepackage{pst-text}              % PSTricks package for character path
\begin{document}
\DeclareFixedFont{\ptsmall}{T1}{ptm}{m}{sc}{5mm}
\DeclareFixedFont{\ps}{U}{psy}{m}{n}{8cm}
\psboxfill{\ptsmall$\pi$}
\begin{pspicture}(-3,0)(2,4.5)
    \pscharpath[fillstyle=solid,fillcolor=cyan!20,addfillstyle=boxfill,
                fillangle=30,fillsep=0.6mm]%
                {\rput[b](-0.5,0){\ps\char112}}
\end{pspicture}

\end{document}

Answer 23

\usetikzlibrary{decorations.text,calc,math}
\begin{tikzpicture}[decoration={text effects along path,
text={3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233},
text effects/.cd,
character count=\i, character total=\n,
characters={text along path, evaluate={\c=\i/\n*100;},
text=orange!\c!blue, scale=\i/\n+0.5}}]
\draw[decorate , domain=-10:1080,variable=\t,samples=100]
      plot ({(\t+300)*cos(\t)/(720)},
           {(\t+300)*sin(\t)/(720)});

\node at (0,0){\Huge$\pi$};

\end{tikzpicture}

Answer 24

\documentclass{article}
\usepackage{pstricks}
\begin{document}
\psset{xunit=1pt,yunit=1pt,runit=1pt}
\begin{pspicture}(800,1200)
\pscustom[linewidth=15]{\newpath\moveto(170,992)\curveto(165,928)(152,855)(107,813)}
\pscustom[linewidth=15]{\newpath\moveto(253,973)\curveto(229,913)(250,823)(282,809)}
\pscustom[linewidth=15]{\newpath\moveto(88,962)\curveto(172,1053)(223,922)(327,996)}
\end{pspicture}
\end{document}

Answer 25

\begin{tikzpicture}
\filldraw[blue] (-3.32,1.88) .. controls (-2.62,4.28) and (0.04,2.87) .. (1.48,3.41) .. controls (1.38,2.54) and (0.57,2.53) .. (0.09,2.48) .. controls (0.08,1.03) and (-0.48,-1.4) .. (0.82,-0.31) .. controls (0.78,-1.24) and (-1.71,-2.57) .. (-0.31,2.51) .. controls (-0.87,2.5) and (-0.87,2.5) .. (-1.48,2.53) .. controls (-1.49,1.31) and (-2.05,-1.77) .. (-2.93,-1.1) .. controls (-3.48,-0.36) and (-2.27,-0.74) .. (-1.88,2.55) .. controls (-2.47,2.51) and (-2.79,2.36) .. (-3.32,1.88);
\end{tikzpicture}