Trigonometry with rational numbers | Arithmetic and Geometry Math Foundations 27 | N J Wildberger

Описание: Rational trigonometry works over the rational numbers, and allows us a more elementary and logical approach to the basics of trigonometry. This video illustrates the Spread law, the Cross law and the Triple spread formula. These are among the most important formulas in geometry, indeed in all of mathematics, and they allow us to recast trigonometry into a simpler and more computationally elegant subject. See the WildTrig YouTube series for lots of applications of these laws.

This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics.

Video Contents:
00:00 Trigonometry expressed in terms of quadrance and spread
02:24 Illustrating how to compute with quantities
05:50 Spread law, Cross law, Triple spread law

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My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/...

My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.

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