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Folding/one-cutting a Betsy Ross star from 8-1/2 inch x 10 inch paper

Thanks to Arnold Tubis Department of Physics (Ret.), Purdue University, West Lafayette, IN Visiting Fellow, University of California San Diego, La Jolla, CA, and Crystal E. Mills, California Mathematics Council ComMuniCator, Clayton, CA for providing this information to ushistory.org. See Two Conundrums Concerning the Betsy Ross Five-Pointed Star.


folding/one-cutting a Betsy Ross star
folding/one-cutting a Betsy Ross star

Notes

  • The required folds (see steps 4 and 9) involve making creases for the perpendicular bisector of a line and an angle bisector. The geometric theorems involved are those relating to the properties of the perpendicular bisector of a line and isosceles triangles.
  • The angle measures indicated in steps 7, 8, and 10 are rounded to the nearest integer. A simple geometric/trigonometric analysis of the folding process in the case of idealized, that is, infinitely thin and flexible paper, shows that the apex angles of three of the five overlapping flaps in steps 9 and 10 are of measure 35.992°, and the apex angles of the other two are of measure 36.012°. For the case of real-world paper, these deviations from 36 degree measures are insignificant.

Folding/one-cutting a Betsy Ross star from a Square

folding/one-cutting a Betsy Ross star

Notes

  • The required folds (see steps 7 and 8) involve making creases for the perpendicular bisector of a line and an angle bisector. The geometric theorems involved are those relating to the properties of the perpendicular bisector of a line and isosceles triangles.
  • The angle measures indicated in steps 6, 8, and 10 are rounded to the nearest integer. An analysis of the folding process for idealized paper shows that three of the five overlapping flaps in step 10 have apex angles of measure 35.782° and the apex angles of the other two are of measure 36.327°. For the case of real-world paper, these deviations from 36 degree measures are insignificant.

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