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Lazy Geometry

Homework: What is the laziest way to construct a regular pentagon using a straight edge, a compass and a piece of paper?

Answer: Fold or tear the paper into a strip. Loop the strip throuh itself like a knot. You now have a regular pentagon!


  Euclid and Thomas L. Heath (editor), Thirteen Books of Euclids Elements, Books 1 and 2, Dover, 1956.
  Euclid and Thomas L. Heath (editor), Thirteen Books of Euclids Elements, Books 3 - 9, Dover, 1956.
  Euclid and Thomas L. Heath (editor), Thirteen Books of Euclids Elements, Books 10 - 13, Dover, 1956.
Euclid's Elements Euclid's Elements is a complete reference on Euclidean geometry, both on the plane and in space. The first two volumes are very readable to high school students. The third volume is about solid geometry. It might be more challenging to some teenagers. In any case, Euclid's Elements is a classic and should be on every shelf. These Dover books are very affordable and long-lasting.
  David Hilbert and Leo Unger (translator), Foundations of Geometry, Open Court, 1988.
Foundations of Geometry Hilbert is one of the most brilliant mathematicians of the 20th century. In Foundations of Geometry, Hilbert takes us through the various sets of axioms of geometry. We see that some sets of axioms result in non-Euclidean geometry while some are plain inconsistent. This inexpensive paperback is good reading for advanced high school students and college math majors.
  Tomoko Fuse, Unit Origami: Multidimensional Transformations, Japan, 1990.
  Kunihiko Kasahara, Origami Omnibus: Paper-Folding for Everybody, Kodansha International, 1998.
  Kunihiko Kasahara and Toshie Takahama, Origami for the Connoisseur, Kodansha International, 1998.
Unit Origami These origami books are truly spectacular. Unit Origami is a book about folding paper into colorful patterns, shapes and assembling them into 3-dimensional objects. The constructions are precisely designed and engineered. Origami for the Connoisseur is exactly what it says: unique creations by modern masters, including Kawasaki's Rose, the most famous of all modern origami.

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