Find out Origami with Explanations: Fun with Folding and MathOrigami, paper folding, originated hundreds of years ago in China and Japan, with independent discovery across the world. Today people do origami, create new models, share their work, and discover mathematical principles. This book continues the approach of Origami with Explanations; but is independent, with basic instructions repeated. Carefully written instructions, using photos and diagrams, will turn you into a successful folder and stimulate your own creativity. The models in this book include action models, money folds, beautiful and useful containers, and modular origami. Mathematics topics touched on include improving estimates, tessellations, mathematical induction, flat-foldability, and fold-and-cut. The Explanations section provide insight into the origami and introduce or re-introduce you to basic and advanced subjects in mathematics.
Contents:
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Kissy Fish:
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3 Ways to Determine Thirds:
- Informal S Method Using Property of Thirds
- Improving Estimate Using Standard Reduction of Error Term (Iteration, Powers of 2)
- Analytic Geometry: Define Coordinate System and Solve Equations
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Reprise on Sinks, Reverse Folds and Squash Folds, Pointing Out the Common Feature of Changing the Sense of Some Folds (Spatial Relations)
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Tetrahedrons:
- Prove Strip Method Produces Equilateral Triangles Using Geometry
- Introduction to Platonic Solids: Classic 3D Geometry
- Introduction to Tessellations with Proof That Only Certain Regular Polygons Tessellate (Tile the Plane)
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Heart Locket:
- Construction of Marks at 3/8 and 5/8 (or 1/8 and 7/8) Positions: Fractions
- Examination of Construction, 2D to 3D: Spatial Relations
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One-Dollar Shirt and Dollar Bill Heart:
- One-Dollar Shirt Construction: Spatial Relations
- Broken Heart: Bisecting Angles: Geometry
- Broken Heart: Examining the Mechanism: Spatial Relations
- Broken Heart: Calculating Certain Dimensions: Algebra, Trigonometry
- Compare Size of the 2 Heart Configurations: Geometry
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Dollar Bill Rosette:
- Iteration to Improve Estimate: Similar to A Method for Thirds, Property of 11
- Identified Category of Primes by Writing A Program: Full Reptend Primes Base 2
- Prove Equivalence of Folding Property to A Category of Primes: Algebraic Manipulation and Mathematical Induction
- Exercise: Compare to Jackson 16 Panel Version
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Masu Box and Shen Basket:
- Rigidity from Layers
- Final Dimensions Using Crease Pattern and Geometry
- Directions to Making Lid, Pointing Out How It Does Not Scale to Size of Paper
- Brief Description of Origami Mathematics Flat Foldability Conditions and How One Condition is Violated at One Point in Folding Shen Basket
- Peek into Crease Pattern Origami (Reference to Robert Lang's Treemaker)
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Ninja Star and Stackable Cubes:
- Number of Layers in Ninja Star and in Cube
- Handedness: Geometry, Transformations and Spatial Relations
- Comparisons to Other Modular Models
- Stack of Cubes as 2nd Order Modular
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One-Snip 5-Pointed Star and One-Snip Square Letter O:
- How to Produce Square Letter 0: Spatial Relations, Patterns
- Brief Mention of Theorem (2 Approaches) on Generality of One-Snip for Polygons, an Acclaimed Example of Origami Mathematics
Readership: For all ages, especially students in college classrooms. Good for home schooling and supplement for K-12 remote learning.
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