The Boy Who Loved Math

The most simple perfect squared square (zoom, in Wikimedia Commons and SVG)
The most simple perfect squared square (in 750px, Wikipedia and SVG)

The Boy Who Loved Math: The Improbable Life of Paul ErdősThe Boy Who Loved Math: The Improbable Life of Paul Erdős is a funny children book about the legendary Hungarian mathematician. Author of the book, Deborah Heiligman has got the help of Erdős’s friends and colleagues, also the illustrator of the book, Le Uyen Pham has traveled to Budapest to create great illustrations about the place of birth and childhood of the world wanderer Paul Erdős. According to the New York Times’s review (Nate Silver: Beautiful Minds), this book “should make excellent reading for nerds of all ages.” It contains also several interesting mathematical problems, including the illustrated one: how can we tile a square using other squares whose sizes are all different and have integer lengths. The squaring on the picture is the simplest one, and it was discovered by A. J. W. Duijvestijn in 1978, see its interesting history on Squaring.net.
The LibreLogo source code of the illustration uses the mapping and grid drawing procedures of the tangram drawing example of the previous post, also the new procedure box for drawing a square with random filling color with 50% transparency (using the new FILLTRANSPARENCY command of LibreOffice 4.3) and a title showing the actual size:

TO place x y
POSITION [50+x*4, 500-y*4]
END

TO line x y x2 y2
PENUP place x y
PENDOWN place x2 y2
END

TO grid x y x2 y2
REPEAT y2-y+1 [
    line x y+REPCOUNT-1 x2 y+REPCOUNT-1
]
REPEAT x2-x+1 [
    line x+REPCOUNT-1 y x+REPCOUNT-1 y2
]
END

TO box x y s
PENUP place x+s/2 y+s/2
HEADING 0 FILLCOLOR ANY FILLTRANSPARENCY 50
PENDOWN SQUARE s*4
FONTSIZE MAX (2*4, s*2.5)
TEXT s
END

PICTURE “squaredsquare.svg” [
PENSIZE 0.5 HIDETURTLE
PENCAP “ROUND”
PENCOLOR “SILVER”
FONTFAMILY “Nimbus Sans L”
grid 0 0 112 112
PENSIZE 1 PENCOLOR “BLACK”
box 0 0 33
box 29 33 4
box 33 0 37
box 0 33 29
box 0 33+29 50
box 29 33+4 25
box 29+25 37 16
box 29+25 37+16 9
box 29+25+9 37+16 7
box 29+25+9 37+16+7 2
box 50 37+25 15
box 50 37+25+15 35
box 33+37 0 42
box 33+37 42 18
box 50+15 37+16+7 17
box 50+15+17 18+42 6
box 50+15+17 18+42+6 11
box 50+35 18+42+17 8
box 29+25+16+18 42 24
box 50+35+8 42+24 19
box 50+35 42+24+19 27
]

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