<Text-field layout="Heading 1" style="Heading 1">Code for plotting cards</Text-field>

# These two commands tell maple to load some useful plotting stuff # such as the "rectangle" command with(plottools): with(plots): # This defines a procedure which will plot a stack n cards that overhangs maximally # Just use overhang(5) to draw a stacking picture with 5 cards overhang := proc(n::posint) local lcx, lcy, i, len, hgt, table, vline; # len is the length of the card (viewed from the side) # hgt is the height of the card len := 2: hgt := 1: # This rectangle will be a table table := rectangle([-2*len,-2*hgt], [0,0], color=brown): # This line makes it clear which cards don't overlap the table vline := line([0,0],[0,n*hgt],color=black,linestyle=3,thickness=3): # lcx stores the left x-coordinate of each card, initialized for the bottom card # lcy stores the bottom y-coordinate of each card, initialized for the bottom card lcx := -len: lcy := -hgt: # The following loop creates cards card1, card2, card3, ... # with the cards being counted from the top for i from 1 to n do # the i'th card is shifted 1/(n+1-i) to the right of the one below lcx := lcx+1/(n+1-i): # each card is hgt units higher than the one below lcy := lcy+hgt: # || is the concatenation operator card||i := rectangle([lcx,lcy+hgt], [lcx+len,lcy], color=blue): od: # Now we plot both the table and all the cards # We also put a few helpful labels on the axes display({table, vline, seq(card||i, i=1..n)}, xtickmarks=[-2,0,sum(1/k, k=1..n)], ytickmarks = [0,n], axes=frame); end: