Triangle spread rules | WildTrig: Intro to Rational Trigonometry | N J Wildberger
The three spreads of a triangle satisfy the Triple spread formula, and given two such spreads this gives a quadratic equation for the third. The Triangle spread rules give information about which of the two solutions of this quadratic equation to take in particular circumstances. The notio
From playlist WildTrig: Intro to Rational Trigonometry
Rational trigonometry in three dimensions | Universal Hyperbolic Geometry 40 | NJ Wildberger
We extend rational trigonometry to three dimensions, using a vector approach and the dot product to define quadrance of a vector and spread between two vectors. The main laws of Pythagoras' theorem, the Triple quad formula, the Cross law, Spread law and the Triple Spread formula still appl
From playlist Universal Hyperbolic Geometry
Spreads, determinants and chromogeometry (I) | WildTrig: Intro to Rational Trigonometry
We give a review of some formulas for the spread between two lines, and rewrite some of them using vector language and the theory of determinants. We get the important understanding that a spread between two vectors is just a renormalization of the squared area of the parallelogram spanned
From playlist WildTrig: Intro to Rational Trigonometry
Triangle spread rules in action | WildTrig: Intro to Rational Trigonometry | N J Wildberger
We look at a quadrilateral problem using rational trigonometry and the Triangle spread rules. The triangle spread rules allow us to determine which of two solutions of the Cross law or Triple spread formula is appropriate in many situations. This video is part of the WildTrig series, whi
From playlist WildTrig: Intro to Rational Trigonometry
The Spread law in Universal Hyperbolic Geometry | Universal Hyperbolic Geometry 27 | NJ Wildberger
The spread between two lines in hyperbolic geometry is exactly dual to the notion of the quadrance between two points. The Spread law is the third of the four main laws of trigonometry in universal hyperbolic geometry. Its proof also relies on a remarkable polynomial identity, just as did
From playlist Universal Hyperbolic Geometry
Advice for prospective research mathematicians | Rational Trigonometry and spread polynomials 1
Here is a quick introduction / review of the essentials of Rational Trigonometry, with an aim to explaining the important spread polynomials / polynumbers which are more pleasant variants of the Chebyshev polynomials of the first kind. Our treatment here is quite concise, relying on a pri
From playlist Maxel inverses and orthogonal polynomials (non-Members)
N J Wildberger Research Snapshot: Rational trigonometry and universal geometry
A brief introduction to the author's novel theory of rational trigonometry and how it allows us to extend Euclidean geometry to general fields and arbitrary quadratic forms.
From playlist Research Snapshots
Trigonometry with rational numbers | Arithmetic and Geometry Math Foundations 27 | N J Wildberger
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
From playlist Math Foundations
Towards a more computational mathematics: rational trigonometry and new foundations for geometry
This is a seminar given at the University of Newcastle in April 2013. We explore the possibilities for a new more computational approach to mathematics which replaces the current dubious reliance on `real numbers' with the much more solid and natural rational numbers. The key idea is that
From playlist MathSeminars
Three dimensional geometry, Zome, and the elusive tetrahedron (Pure Maths Seminar, Aug 2012)
This is a Pure Maths Seminar given in Aug 2012 by Assoc Prof N J Wildberger of the School of Mathematics and Statistics UNSW. The seminar describes the trigonometry of a tetrahedron using rational trigonometry. Examples are taken from the Zome construction system.
From playlist Pure seminars
Rational Trigonometry - Summer of Math Exposition
My entry in The Summer of Math Exposition. If you are interested and want to learn more about Rational Trigonometry check out Norman J Wildberger's series on the subject: https://www.youtube.com/watch?v=GGj399xIssQ&list=PL3C58498718451C47&ab_channel=InsightsintoMathematics If you want t
From playlist Summer of Math Exposition Youtube Videos
Three dimensional geometry, ZOME, and the elusive tetrahedron
Lectures notes at http://www.maths.unsw.edu.au/seminars/2012-07/three-dimensional-geometry-zome-and-elusive-tetrahedron. The geometry of three dimensional space, despite its obvious importance, is a sadly neglected topic in modern mathematics. One of the reasons is that the topic is rather
From playlist MathSeminars
Advice for Research Mathematicians | Rational Trigonometry and Spread Polynomials II | Wild Egg Math
Spread polynomials arise in Rational Trigonometry as variants of the Chebyshev polynomials of the first kind. However the spread polynomials arise in a purely algebraic setting, without any need for appeal to "transcendental functions" which can't actually be evaluated -- such as cos x or
From playlist Maxel inverses and orthogonal polynomials (non-Members)
Spread, Angles and Astronomy | WildTrig: Intro to Rational Trigonometry | N J Wildberger
Angles have their origin in astronomy and spherical trigonometry. Here we introduce the rational alternative, called spread, and give examples from ISO paper sizes to the faces of a dodecahedron. ************************ Screenshot PDFs for my videos are available at the website http://w
From playlist WildTrig: Intro to Rational Trigonometry
Rational trigonometry: an overview | Universal Hyperbolic Geometry 39 | NJ Wildberger
This important video introduces Rational Trigonometry from first principles using a vector approach. The main notions of quadrance and spread replace distance and angle, and are introduced purely algebraically. The scalar/inner/dot product plays an important role, and allows us to introduc
From playlist Universal Hyperbolic Geometry
Trigonometry in elliptic geometry | Universal Hyperbolic Geometry 41 | NJ Wildberger
We here introduce new laws for spherical and elliptic trigonometry. These are natural consequences of applying Rational Trigonometry to the three dimensional projective setting. Remarkably, the main laws end up being exactly the same as those in Universal Hyperbolic Geometry! It means ther
From playlist Universal Hyperbolic Geometry
Spread polynomials | WildTrig: Intro to Rational Trigonometry | N J Wildberger
Spread polynomials are the rational trigonometry equivalent of Chebyshev polynomials. This video shows what they look like, how to compute them and how they link to geometry. ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com. These give
From playlist WildTrig: Intro to Rational Trigonometry