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John Montroll was born in Washington, D.C. [1] He is the son of Elliott Waters Montroll, an American scientist and mathematician.He has a Bachelor of Arts degree in Mathematics from the University of Rochester, a Master of Arts in Electrical Engineering from the University of Michigan, and a Master of Arts in applied mathematics from the University of Maryland.
The orizuru (折鶴 ori-"folded," tsuru "crane"), origami crane or paper crane, is a design that is considered to be the most classic of all Japanese origami. [ 1 ] [ 2 ] In Japanese culture, it is believed that its wings carry souls up to paradise, [ 2 ] and it is a representation of the Japanese red-crowned crane , referred to as the ...
The origami crane diagram, using the Yoshizawa–Randlett system. The Yoshizawa–Randlett system is a diagramming system used to describe the folds of origami models. Many origami books begin with a description of basic origami techniques which are used to construct the models.
Wet-folding is an origami technique developed by Akira Yoshizawa that employs water to dampen the paper so that it can be manipulated more easily. This process adds an element of sculpture to origami, which is otherwise purely geometric. Wet-folding is used very often by professional folders for non-geometric origami, such as animals.
Geometric Origami is a book on the mathematics of paper folding, focusing on the ability to simulate and extend classical straightedge and compass constructions using origami. It was written by Austrian mathematician Robert Geretschläger [ de ] and published by Arbelos Publishing (Shipley, UK) in 2008.
In 1954, his first monograph, Atarashii Origami Geijutsu (New Origami Art) was published. In this work, he established the Yoshizawa–Randlett system of notation for origami folds (a system of symbols, arrows and diagrams [3]), which has become the standard for most paperfolders. The publishing of this book helped Yoshizawa out of his poverty.
There are several different styles of origamic architecture. In one style, a folded paper is cut in such a way that when the paper is opened to form a 90-degree angle, a three-dimensional image can be created, similar to most pop-up books. [7] A second style requires attaching a cut-out form to a base sheet of paper with thread.
The placement of a point on a curved fold in the pattern may require the solution of elliptic integrals. Curved origami allows the paper to form developable surfaces that are not flat. [41] Wet-folding origami is a technique evolved by Yoshizawa that allows curved folds to create an even greater range of shapes of higher order complexity.