TOYS, TRICKS, & TEASERS
By Donald Simanek
Golden Star Origami
The five-pointed “golden star” is widely used around the world in flags,
heraldry, coats of arms, and other decorations. It’s been used in American
flags of many designs from the earliest days of our republic.
Historical legend tells us that seamstress Betsy
Ross was visited in 1776 by George Washington,
Robert Morris, and George Ross, who asked her to
make an American flag conforming to a resolution
of the Continental Congress.
Washington’s design had 13 alternating stripes
of white and red, and 13 six-pointed stars on a field
of blue. Betsy suggested five-pointed stars instead.
When someone wondered whether five-pointed
stars would be more difficult to make, Betsy showed
how fabric could be cleverly folded to allow a five-pointed star to be made with just one cut of the
scissors.
It’s a pretty story, but like many fables of our early
history, it’s probably a myth. Contemporary documentation of it is totally lacking. Betsy’s grandson
first related the story in 1870, nearly a century after
the fact, admitting that he had no confirmation other
than stories passed down in the family.
The story quickly proliferated, being published in
Harper’s New Monthly Magazine in 1873, finding its
way into other publications and even into textbooks,
persisting even now. And the Betsy Ross House in
Philadelphia is the second-most-visited historic site
there, but there’s no hard evidence that she ever
lived in it.
We’ll leave historians to sort all that out. You can
find out more about the flag myth at makezine.com/
go/flag. What catches my interest is the method
of folding cloth to obtain a five-pointed star with a
single scissors cut. It’s the one believable detail in
this story. Creating five-fold symmetric figures is
a challenge in Euclidean geometry, and with paper
folding, too. But a method is well known to quilters
and seamstresses and was surely known to flag
makers of colonial times and earlier.
Here are the instructions to make a star template
using a sheet of thin 8½"× 11" paper:
»
; Mark the upper right corner “A” so you won’t
lose track of it. Mark the upper left corner “B.”
; Bring corner B over to point C, just at the midpoint of the right edge of the paper, on the crease
you made earlier. The left portion of the top edge
of the paper folds over, making an angle along the
solid line to point C. This angle is the foundation of
the construction (Figure B).
The angle is approximately 35.85584°. This is
smaller than 36°— one tenth of a full circle — but
very close to what we need to define the polygon
vertices that are the basis of a five-pointed star.
This is an approximate construction, not a strictly
Euclidean construction. (Euclidian constructions
don’t use measuring tools. This construction starts
with a measured rectangle of paper.)
Star Construction
; Fold the paper in half, to 8½"× 5½", with the
fold at the top. Then fold the paper in half again to
make a temporary crease to locate point C at the
midpoint of the right edge. This crease is shown
as a dotted line in Figure A.
; Fold the lower left edge up to lie along the
slanted fold that passes through point C (Figure C).
; Grabbing hold of point A, fold the paper backward
along the diagonal so that all edges coincide. This
will make an angle of approximately 36° (Figure D).
; Now turn the whole thing over. Notice that there’s
a right triangle on the top of the folded stack of
paper. Draw a line — starting about 1/3 of the way in
along the long (top) side — to the lower corner of the
triangle (Figure E). Use suitably heavy scissors to cut
the whole stack along the line and unfold the paper.
164 Make: Volume 19
