Folding

The points accessible from by a single fold which leaves , ..., fixed are exactly those pointsinterior to or on the boundary of the intersection of the Circles through with centers at ,for , ..., . Given any three points in the plane , , and , there is an Equilateral Trianglewith Vertices , , and for which , , and are the images of , ,and under a single fold. Given any four points in the plane , , , and , there is some Squarewith Vertices , , , and for which , , , and are the images of ,, , and under a sequence of at most three folds. Also, any four collinear points are the images of theVertices of a suitable Square under at most two folds. Every five (six) points arethe images of the Vertices of suitable regular Pentagon (Hexagon) under atmost five (six) folds. The least number of folds required for is not known, but some bounds are. Inparticular, every set of points is the image of a suitable Regular -gon under atmost folds, where

References

Sabinin, P. and Stone, M. G. ``Transforming -gons by Folding the Plane.'' Amer. Math. Monthly 102, 620-627, 1995.

Sloane, N. J. A. Sequence A007494in ``The On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html.

• Nonnegative Integer
• Nonnegative Partial Sum
• Nonorientable Surface
• Nonpositive
• Nonsquarefree
• Nonstandard Analysis
• Nontotient
• Nonwandering
• Nonzero
• Nordstrand's Weird Surface
• Norm
• Normal
• Normal (Algebraically)
• Normal Curvature
• Normal Curve
• Normal Developable
• Normal Distribution
• Normal Distribution Function
• Normal Equation
• Normal Form
• Normal Function
• Normal Group
• Normalized Vector
• Normalizer
• Normal Magic Square