```The Pythagorean PuzzleEarl Zwicker                   Illinois Institute of Technology                               Biological Chemical and Physical Sci Dept                               IIT Center                               Chicago IL 60616-3793                               (312) 567-3384 Dedication: Thanks to Professor Harald Jensen (1898-1994), PhysicsDepartment, Lake Forest College, who originally worked this idea with thehigh school physics teachers at several summer institutes during the1970s.  This fine example of a phenomenological presentation would notexist if it were not for him.

Sketch 1

In order to draw the puzzle on your own, use 2 sheets of 8.5 x 11 paper, a
pencil, a ruler, a straight edge and a scissors.

Draw a square three inches on a side.  (This is easily done by starting at
one corner of one of the papers and measuring 3 inches down each edge.)
Cut out the square.

Place the square so that its edges lie along the bottom right corner edges
of the second sheet of paper.  Now raise and tilt the square so that its
right bottom corner has moved up the right edge of the page by about 1.5
inches; its left bottom corner should lie at the bottom edge of the page,
about 2.5 inches from the right bottom corner of the page.  The now tilted
bottom of the square will be the hypotenuse of a right triangle, and the
right bottom edges of the page will be the altitude and base of the
triangle.  Use some tape to hold the square in place on the sheet.

Next, draw a horizontal line across the page so that it passes through the
top-most corner of the tilted square.  Then draw a vertical line so that it
passes through the left-most corner of the tilted square.  The square will
now be circumscribed within a larger square formed by the horizontal and
vertical lines drawn on the sheet.  This also leaves the original tilted
square surrounded by four identical triangles; the hypotenuses of the
triangles are the four sides of the tilted square.

For the upper-left triangle, draw a square using one of the triangles
sides as one side of the square.  Draw another square using the other side
of the triangle.

Now draw vertical lines through the vertical sides of the smallest square
(on the left of the triangle).
Then draw horizontal lines through the horizontal sides of the mid-size
square (on the top of the triangle).

You should now have formed three identical rectangles with long sides
vertical (and equal in length to the altitude of the triangles), and short
sides horizontal (and equal in length to the base of the triangles).

Your puzzle is now complete.  Cut it out and play with it.  Enjoy!

Sketch 2
(an 'extra' piece for the second part)

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