Squaring
Triangle (Dudeney's Triangle)
The
puzzle we'll make together starts as an equilateral triangle,
but it unfolds and folds to make a square! Magic? No, simply
mathematical! To make our triangular puzzle we don't need
any compass or strange tools... We just need a paper sheet,
a pencil, a Lshaped square and a pair of scissors.
How
to make an equilateral triangle with a paper sheet
Take a standard paper sheet and fold it lengthwise in two
equal parts as shown in fig. 2 below. Now, unfold your paper
sheet (notice the foldmark in its middle). Then, fold back
a corner of the paper sheet on the foldmark and draw a line
along the corner side (see fig. 4). Repeat this operation
with the opposite corner of the paper sheet. Cut your sheet
along the two lines you've drawn (fig. 7). Compliments! You
have now a perfect equilateral triangle.
How
to transform your equilateral triangle into a square
Fold back the 3 corners of the triangle to make a rectangle
as per fig. 9. Then, unfold your triangle. Important: the
foldmarks define a rectangle ABCD. Trace the diagonal BD
of the rectangle ABCD (fig. 11). Now, with the help of a
Lshaped square trace 2 perpendiculars to the diagonal BD,
one passing through point A, the other one through point
C, as shown in fig. 12. Your triangle is now divided in 4
pieces. Cut them out and reassemble them as shown in fig.
15.
