Origami Design Secrets Robert Lang Now

The is highly recommended as it contains roughly 200 pages of new material, including box pleating and polygon packing. Robert J. Lang - Origami Design Secrets (2nd Edition) : Routledge : $104.99 $83.99 (currently 20% off) Barnes & Noble : $105.36 ThriftBooks : $104.99 (New) AbeBooks : $47.42 (Used - 1st Edition) VitalSource : $46.20 (eBook Rental) Artist Highlight- Robert J. Lang

Lang introduces several revolutionary mathematical methods that bridge the gap between art and science: Circle Packing:

By combining his background in laser physics and engineering with his passion for paper folding, Lang codified the hidden laws of origami. Origami Design Secrets was the first text to thoroughly demystify these principles, making advanced design techniques accessible to artists, mathematicians, and engineers alike. Core Concepts Explained in the Book

: To create these "branches" from a square of paper, you must allocate a specific area of paper for each part. This is visualized as packing circles onto the square; each circle's radius corresponds to the length of the appendage. origami design secrets robert lang

To design a multi-legged creature, an artist must draw circles on the square sheet of paper. These circles cannot overlap, as two flaps cannot share the same paper.

Whether you are a math enthusiast or an artist, this book offers something unique: Origami Design Secrets

Examples of modern built on origami principles The is highly recommended as it contains roughly

You cannot discuss Origami Design Secrets without mentioning , the freeware computer program developed by Lang. TreeMaker is the physical manifestation of the book's mathematical theories.

For centuries, origami was an art form passed down through generations via traditional, static patterns. Crane, frog, and boat designs were memorized and repeated, but creating entirely new models was a matter of trial and error. This changed dramatically with the publication of by Dr. Robert J. Lang.

Robert Lang’s journey into origami began at the age of six, but it was his background as a physicist and engineer that would transform him into a pioneer of the craft. He realized that if he could describe origami with mathematical language, he could then use the tools of mathematics to accomplish artistic goals that seemed impossible. This insight, combined with a doctorate in applied physics from Caltech and a career at NASA's Jet Propulsion Laboratory, gave him a unique perspective to develop the systematic design methods he so clearly explains in his book. This is visualized as packing circles onto the

If you want to explore the world of mathematical paper folding further, let me know:

Lang's approach shifts the focus from following specific instructions to understanding the underlying .

Robert J. Lang is one of the world's foremost origami artists and theorists. Before dedicating himself fully to origami, Lang worked as a physicist and engineer, holding over 50 patents in semiconductor lasers and optoelectronics. This rigorous scientific background allowed him to look at paper folding through the lens of mathematics and engineering.

Lang developed "Tree Theory," which represents the desired subject as a stick figure (a tree graph), where each stick represents a flap and its length represents the required length of that flap. To turn this stick figure into a crease pattern on a square sheet of paper, Lang utilized circle packing.

: Fold the paper according to the mathematical crease pattern to reach a "base"—a raw shape with the correct number and length of parts.