2014
TTC Video
James Tanton
18 h
English

Inscribed over the entrance of Plato's Academy were the words, "Let no one ignorant of geometry enter my doors." To ancient scholars, geometry was the gateway to gaining a profound knowledge of the world. Today, geometry's core skills of logic and reasoning are essential to success in school, work, and many other aspects of life.
Like other math fields, geometry teaches us how to think. It leads students to uncover new truths based on already established ideas and facts. It requires us to test and examine the conclusions of others. It teaches us to lay out our thinking clearly, describing each step so that others can follow along and verify our results.
This systematic way of thinking is essential in many fields. Drawing conclusions from experimental data is the basis of scientific discovery. Our justice system depends on compelling evidence to render a verdict in a court of law. And we use logical reasoning in everyday conversations to win friends over to our point of view.
In fact, the great Greek scholar Euclid demonstrated just how much you can do with logic. He worked out that basically all of geometry stands on just 10 core principles. You can build the rest using straightforward, logical reasoning.
In short, geometry is among the great intellectual feats of humankind. However, geometry goes far beyond being just an intellectual exercise. Its real-world applications extend to navigation, architecture, engineering, physics, technology, and even art.


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

http://www.thegreatcourses.com/courses/geometry-an-interactive-journey-to-mastery.html

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