Geometry: An Interactive Journey to Mastery

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Description

Geometry-in fact, mathematics as a whole-is an intensely human Enterprise. As its nae suggests, derived from the Greek ge for "earth" and metria for "measure," the subject evolved from very practical concerns: the art of accurately measuring tracts of land, performing feats of navigation, and accomplishing success in construction and architectural design, for example. But the study of geometry reveals a deep and rich layer of intellectual delight. Our human minds are drawn to elegance and beauty, both in the results of the hand and in the products of the dance between these two joyful pursuits, and this course is the journey of that dance for you to enjoy.

Content:-

INTRODUCTION

Professor Biography
Course Scope

LESSON 1: Geometry—Ancient Ropes and Modern Phones

LESSON 2: Beginnings-jargon and undefined Terms

LESSON 3: Angles and Pencil-Turning Myseries

LESSON 4: understanding Polygons

LESSON 5: The Puthagorean Theorem

LESSON 6: Distance, Midpoints, and Folding Ties

LESSON 7: The Nature of Paralllelism

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

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

Solutions
Formulas
Glossary
Bibliography

Author Details

"Professor James S. Tanton" 
Mathematical Association of America

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