ReferenceFinder

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ReferenceFinder
Software Details:
Version: 2.1.1
Upload Date: 2 Jun 15
Developer: Robert J. Lang
Distribution Type: Freeware
Downloads: 7

Rating: nan/5 (Total Votes: 0)

ReferenceFinder is a software that finds folding sequences to approximately locate any point in a square using a small number of folds.

When one is designing an origami model using mathematical tools such as TreeMaker, the crease pattern is usually defined mathematically, rather than by folding. Important points in the pattern — junctions of several creases, which are called reference points of the crease pattern — are commonly specified entirely numerically, rather than as a result of a series of folds. To fold such patterns, one can record the coordinates of the important points and then compute, measure and mark their location on the paper to be folded. But making marks on the paper is awkward and inelegant; it is inconvenient to require a ruler and calculator to fold origami! There is an aesthetic benefit to being able to start with an unmarked square and proceed to the completed model entirely by folding. To do this, we need a way of finding reference points by folding alone when all we have is an algebraic or numerical description of the point. This challenge of finding folding sequences for the location of a reference point given its
mathematical definition is a problem of both mathematical and practical interest, and it has seen considerable progress in recent years. Finding reference points is closely related to the concept of geometric construction — a field familiar to anyone who has manipulated compass and
straightedge in high-school geometry. The field of origami constructions is considerably richer than compass-and-straightedge constructions: a partial listing of some of the accomplishments and discoveries in this field includes:

— Construction of any rational fractional distance (expressed as a fraction of the side of the unit square) with algorithms by Husimi, Fujimoto, Noma, Haga, Mosely, and me;
— Construction of any binary rational fraction (a fraction whose denominator is a perfect power of 2);
— How to trisect an arbitrary angle, with constructions by Justin and Abe;
— Construction of cube roots, including a marvelous construction of the cube root of 2 by Peter Messer;
— Solutions of general quadratic and cubic equations and construction of perfect N-gons for broad classes of N by Robert Geretschl

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