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25: Using Tensor Diagrams to Represent and Solve Geometric
Problems
Monday, Half Day
1:30 – 5:15 pm
River Room 001
Introduction to tensor diagrams, a really cool algebraic
manipulation tool that can help solve many problems in
analytic geometry.
Prerequisites
Familiarity with homogeneous coordinate geometry and basic
matrix operations. Distaste for page-long algebraic expressions.
Topics
Review of homogeneous coordinate math. Notational problems
with matrices. Einstein Index notation. How tensor diagrams
represent basic operations. Application of tensor diagrams
to 1D homogeneous equations (polynomials), 2D homogeneous
equations (curves), 3D homogeneous equations (surfaces).
Unsolved (at least to the knowledge of the speaker) problems.
Organizer/Lecturer
James F. Blinn
Microsoft Corporation
Schedule
| Module
1 – Basic Tools |
| 1:30 |
Problems
With Conventional Notation
Blinn |
| 1:45 |
Overview
of Tensor Diagrams
Blinn |
| 2:30 |
Substitution
and Unknown Roots
Blinn |
| 2:50 |
The
Epsilon-Delta Identity
Blinn |
| 3:15 |
Break |
| Module
2 - Applications |
| 3:30 |
1D
Homogeneous Problems (Polynomials)
Blinn |
| 4:00 |
2D
Homogeneous Problems (Curves)
Blinn |
| 4:45 |
3D
Homogeneous Problems (Surfaces)
Blinn |
| 5:00 |
Review
of Main Points and Unsolved Problems
Blinn |
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