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 compas or strange tools... We just
need a paper sheet, a pencil, a L-shaped square and a pair of scissors.
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
How to transform your equilateral triangle into
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 L-shaped 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.