Updates to Folderol 2, "One Percent Perforation",
in Piano-hinged Dissections: Time to Fold!, by Greg N. Frederickson

Assertion vs. conjecture

In the first paragraph on page 143, I made the assertion
Although triangular stamps have come in a variety of different triangular shapes, only three shapes seem suitable for folding puzzles: equilateral triangles, isosceles right triangles, and 60o-right triangles.
Apparently my assertion was insufficient for mathematicians at Millersville State University, in Pennsylvania, so they set out to prove as their Theorem 1:
A polygon generating an edge tessellation is either a regular hexagon; a 60o-90o-120o kite; a rectangle; a 120o-rhombus; a rectangle; an equilateral, a 30o-right, an isosceles right, or a 120o-isosceles triangle.
which in due course appeared in
Matthew Kirby and Ronald Umble, "Edge tessellations and the stamp folding problem,"
Mathematics Magazine, vol. 84 (2011), pp. 283-289.
Dr. Kirby and Prof. Rumble characterized my assertion as a conjecture, which I guess made them feel comfortable providing a proof. I would prefer the term assertion rather than conjecture, since I had little doubt about its correctness. In any event, I did not see any surprises in their proof, but must nonetheless thank them for dotting the i's and crossing the t's in my assertion.


Copyright 2014, Greg N. Frederickson.
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Last updated October 2, 2014.