Explore the Triple quad formula, a fundamental theorem in hyperbolic geometry, in this 39-minute video lecture. Delve into the relationship between three quadrances formed by collinear points, comparing it to its Euclidean counterpart. Examine the challenging proof involving a remarkable polynomial identity. Analyze the formula's connection to the Euclidean Triple spread formula and investigate dot products in Euclidean and relativistic contexts. Work through exercises on the Triple spread function, complementary quadrances theorem, and equal quadrances theorem. Gain insights into the algebraic intricacies of hyperbolic geometry and enhance your understanding of this advanced mathematical concept.
Overview
Syllabus
CONTENT SUMMARY: pg 1: @00:11 Triple quad formula; example; suggested exercise @
pg 2: @07:31 Understanding the Triple quad formula; comparing the corresponding formulas in affine/projective geometry; notice the direction of the arrows @
pg 3: @11:39 Triple spread formula from affine RT; spread in vector notation ; spread in vector notation @
pg 4: @ Euclidean dot products; Relativistic dot products
pg 5: @19:40 Why the Triple quad formula holds; note on 4 main laws of hyperbolic trigonometry @
pg 6: @ Triple quad formula; proof
pg 7: @27:44 Triple quad formula; proof continued; a small miracle @30:40 ; remark about proof @32:25 ; encouragement to do algebra @
pg 8: @ The Triple spread function is defined; exercises 21.1,2
pg 9: @ exercises 23.3,4 ; Complimentary quadrances theorem; Equal quadrances theorem THANKS to EmptySpaceEnterprise
Taught by
Insights into Mathematics
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