Vrftsjtryk

I am teaching a course in history of mathematics and would like to draw something like the following:

The bullet points should be possible to draw on the lines and in between. Can anyone help me? Thank you very much!

As you are going to use this quite a bit you'll need a reasonable interface, so how about using code like this

  abacus{{2,1},{1,1},{3,3,2},{},{4,2},{1}}

  qquad

  abacus{{1},{},{},{},{2},{1}}

to produce something like this:

The way that this works is that the abacus command accepts a comma separated list of "abacus rows", which start from the bottom of the abacus and climb upwards. Each "abacus row" is itself a comma separated list that gives the number of balls in each column of the abacus, from left to right.

Here's the full code:

documentclass{article}

usepackage{tikz}



tikzset{

  pics/abacus/.style = {

     code={

        ifnum#1>0% have to treat 0 balls separately

          foreach ball [evaluate=ball as x 

            using {(ball-0.5-#1/2)*0.2}] in {1,...,#1} {

            fill[black] (x,0) circle (2.5pt);

          }

        fi

      }

    }

  },

  /tikz/abacus/.is family,

  /tikz/abacus,

    xscale/.initial=1,  % default xscale=1 (no scaling)

    yscale/.initial=0.6,% default yscale=0.6

    columns/.initial=2, % default of 2 columns

    rows/.initial=4     % default of 2 rows

}

newcommandAbacusValue[1]{pgfkeysvalueof{/tikz/abacus/#1}}



newcommandabacus[2]{tikzset{abacus, #1}%

  begin{tikzpicture}[

     xscale=AbacusValue{xscale}, 

     yscale=AbacusValue{yscale}

   ]

     foreach ypos in {1,...,AbacusValue{rows}} {

        draw(0,2*ypos-1)--++(6,0);

     }

     foreach xpos in {1,...,AbacusValue{columns}} {

        draw(2*xpos, 0)--++(0,8);

     }

     foreach row [count=ypos] in {#2} {

         foreach col [count=xpos] in row {

             draw (2*xpos-1,ypos) pic{abacus={col}};

         }

     }

  end{tikzpicture}%

}



begin{document}



  abacus{{2,1},{1,1},{3,3,2},{},{4,2},{1}}

  qquad

  abacus{{1},{},{},{},{2},{1}}



end{document}

The abacus command accepts an optional argument that can be used to change the default number of rows and columns and to change the x and y scaling. For example,

abacus[rows=2, columns=4,xscale=0.5,yscale=0.3]{{1,2,3,4},{0,3,1}}

produces:

Here I draw the first picture. You can draw the other based on this.

documentclass[tikz]{standalone}

begin{document}

begin{tikzpicture}[x=1.5cm]

foreach i in {1,2} draw (i,-.2) -- (i,3.2);

foreach i in {0,1,2,3} draw (0,i) -- (3,i);

foreach x/y in {

    .5/0,

    .4/2,

    .6/2,

    .5/2.5

} fill (x,y) circle (2pt);

end{tikzpicture}

end{document}