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pg 10: @ claim: In the plane, every bi-vector is a multiple of the bi-vector of base vectors; geometric proof; algebraic proof
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Area and Volume - Wild Linear Algebra A | NJ Wildberger
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- 1 CONTENT SUMMARY: pg 1: @ area and volume; setting up affine geometry as independent of distance;
- 2 pg 2: @ area of a parallelogram;
- 3 pg 3: @ general formula for area of a parallelogram; one of the most important formulas in mathematics;
- 4 pg 4: @ algebraic approach to measuring area; bi-vector Herman Grassmann; Grassmann algebra;
- 5 pg 5: @ Bi-vectors; torque;
- 6 pg 6: @ linear momentum; conservation of momentum; momentum and force; Bi-vectors; angular momentum; torque
- 7 pg 7: @ Bi-vector and electromagnetism; cross_product mentioned;
- 8 pg 8: @ Bi-vectors in the plane; operations on bi-vectors;
- 9 pg 9: @ bi-vector Distributive laws:
- 10 pg 10: @ claim: In the plane, every bi-vector is a multiple of the bi-vector of base vectors; geometric proof; algebraic proof
- 11 pg 11: @ example using the result of the previous page; in affine geometry area is a relative concept;
- 12 pg 12: @ 2 more examples; Ratios of areas are affine geometry invariants;
- 13 pg 13: @45:52 3_dim affine space; vector, bi-vector, tri-vector; pg 14: @ using tri-vectors to compute a volume;
- 14 pg 15: @ exercises 4.1:2;
- 15 pg 16: @ exercise 4.3. THANKS to EmptySpaceEnterprise
