Monday, May 27, 2019

Geometry: An Interactive Journey to Mastery (Free PDF)

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In Geometry: An Interactive Journey to Mastery, Professor Tanton guides students as they build an understanding of geometry from the ground up. With this approach, the instruction focuses on the intellectual play of the subject and its beauty as much as its utility and function. Students begin with elementary building blocks like points, lines, and angles and observe how those basic units interact. From a clear understanding of the fundamental principles, students use logical reasoning to expand their understanding of geometry. Like building a house brick by brick, each new discovery stands upon the others--without any sudden or confusing jumps.

Professor Biography
Course Scope
LESSON 1: Geometry—Ancient Ropes and Modern Phones
LESSON 2: Beginnings- Jargon and Undefined Terms
LESSON 3: Angles and Pencil-Turing Mysteries
LESSON 4: Understanding Polygons
LESSON 5: The Pythagorean Theorem
LESSON 6: Distance, Midpoints, and Folding Ties
LESSON 7: The Nature of Parallelism
LESSON 8: Proofs and Proof Writing
LESSON 9: Similarity and Congruence
LESSON 10: Practical Applications of Similarity 
LESSON 11: Making Use of Linear Equations
LESSON 12: Equidistance—A Focus on Distance
LESSON 13: A Return to Parallelism
LESSON 14: Exploring Special Quadrilaterals
LESSON 15: The Classification of Triangles
LESSON 16: “Circle-ometry”—On Circular Motion
LESSON 17: Trigonometry Through Right Triangles
LESSON 18: What Is the Sine of 1°?
LESSON 19: The Geometry of a Circle
LESSON 20: The Equation of a Circle
LESSON 21: Understanding Area
LESSON 22: Explorations with Pi
LESSON 23: Three-Dimensional Geometry-Solids
APPENDIX TO LESSON 23: The Volume and Surface Area of a Sphere
LESSON 24: Introduction to Scale
LESSON 25: Playing with Geometric Probability
LESSON 26: Exploring Geometric Constructions 
LESSON 27: The Reflection Principle
LESSON 28: Tilings, Platonic Solids, and Theorems
LESSON 29: Folding and Conics
LESSON 30: The Mathematics of Symmetry
LESSON 31: The Mathematics of Fractals
LESSON 32: Dido’s Problem
LESSON 33: The Geometry of Braids-Curious Applications
LESSON 34: The Geometry of Figurate Numbers
LESSON 35: Complex Numbers in Geometry
LESSON 36: Bending the Axioms-New Geometries

Author Details
"Professor James S. Tanton" is the Mathematical in Residence at the mathematical Association of America (MAA) in Washington DC. He Received his Ph.D. in mathematics from princeton University in 1994.

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