Geometry with Vectors - Wild Linear Algebra A 2 - NJ Wildberger

This lecture introduces vector constructions, vector arithmetic, affine combinations, the zero vector, and linear independence. It applies these ideas to prove results about parallelogram diagonals, triangle medians, and related geometric ratios.

Syllabus

CONTENT SUMMARY: pg 1: @ how to approach the course; geometry with vectors
pg 2: @ constructions; translate a vector; create equally spaced points; add two vectors
pg 3: @ constructions; bisect a segment; trisect a segment; subtract vectors
pg 4: @ Vector Arithmetic
pg 5: Affine Combinations;
pg 6: general affine combination of vectors a and b; a way of describing the line parametrically; coefficients of the vectors add up to 1;
pg 7: The zero vector; Linear independence;
pg 8: Theorem: The diagonals of a parallelogram bisect each other; proof;
pg 9: Theorem: The medians of a triangle are concurrent, meeting at a point G which divides each in the proportion 2:1 ; proof
pg 10: Theorem concerning the ratio of 2 parallel vectors a and b contained by 2 vectors c and d radiating from the same point; exercise 2.1 Varignon's theorem
pg 11: exercise 2.2; exercise 2.3 THANKS to EmptySpaceEnterprise
Introduction
Constructions
Vector Arithmetic
Affine combinations
A special vector
Diagonals of a parallelogram