AUTHOR'S CORNER: YouTube Videos

Dr. N. J. Wildberger is posting a series of videos that help explain rational trigonometry, and some related mathematics, to a wide general audience. You need some interest in geometry, high school level understanding of elementary algebra, and a willingness to go over points carefully.

There is a lot of info in these videos. Go through them slowly, follow along with pen and paper, and try your hand at some examples! More will be posted. These videos will help with the material from `Divine Proportions.'

YouTube videos: The WildTrig series

WildTrig0: An invitation to geometry: the WildTrig series --- Introduces the WildTrig series, inviting you to learn a new approach to geometry and trigonometry.

WildTrig1: Why trig is hard --- The usual trigonometry is overly complicated, inaccurate and logically dubious. This is the first of a series that shows you a better way---rational trigonometry!

WildTrig2: Quadrance via Pythagoras and Archimedes --- This video introduces the main notion of quadrance by going back to how the ancient Greeks thought about geometry. Pythagoras' theorem and a sister theorem called the Triple quad formula are the main results, and they are proven!

WildTrig3: Spread, angles and astronomy --- 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.

WildTrig4: Five main laws of rational trigonometry --- We derive from first principles the main laws of rational trigonometry, using the concepts of quadrance and spread to replace the usual distance and angle. Most everything works out much simpler.

WildTrig5: Applications of rational trigonometry --- Rational trigonometry is applied to solve four examples of practical problems, concerning a flagpole, a ladder, a kite and the distance from a point to a line.

WildTrig6: Heron's formula viewed rationally --- Heron's formula, originally due to Archimedes, is here recast in a simpler and more natural form. And we prove it, using one of the basic laws of rational trigonometry.

WildTrig7: Solving triangles with rational trigonometry --- Shows how to solve triangles using the framework of rational trigonometry with quadrances and spreads replacing distance and angle.

WildTrig8: Centers of triangles withrational trigonometry --- We study the circumcenter, orthocenter and centroid of a triangle using rational trigonometry.

WildTrig9: The laws of proportion for a triangle --- Using rational trigonometry we develop Menelaus' and Ceva's theorem and some related results, namely the Law of Proportions, and the Alternating spreads theorem.

WildTrig10: Geometry of circles with rational trigonometry --- We derive some of the most fundamental facts about a circle using rational trigonometry---the Subtended spread theorems and the Equal products theorem.

WildTrig11: Applications of rational trig to surveying (I) --- Rational trigonometry can be used to solve surveying problems, usually more simply than the current way. This video gives three examples: finding the height of a mountain, Regiomontanus' problem, and spreads over a right triangle.

WildTrig12: Cartesian coordinates and geometry --- Cartesian coordinates allow us to talk precisely about points and lines, parallel and perpendicular, and quadrance and spread---the two main concepts from rational trigonometry.

WildTrig13: Why spreads are better than angles --- This video reconciles two different definitions of the spread between two lines. It also shows why spreads are generally superior to angles in a Cartesian framework.

WildTrig14: Rational parameter for circles --- The usual unit circle is best described by rational parameters, not transcendental ones. This approach is much older, and connects with Pythagorean triples, along with rational trigonometry.

WildTrig15: Complex numbers and rotations --- Complex numbers are here explained using geometry and their intimate connection with dilations and rotations. Pure rotations are related to the parametrization of the unit circle.

WildTrig16: Rational trigonometry Quiz 1 --- This is a quiz on Rational Trigonometry, with seven interesting and challenging questions. You can also try to solve them using classical trigonometry---but remember: only correct answers are allowed.

WildTrig17: Rational Trigonometry: Solutions to Quiz 1 --- Five problems involving a triangle, a surveying problem, a kite, a piece of paper and a cyclic quadrilateral are solved using rational trigonometry.

WildTrig18: Medians, altitudes and vertex bisectors --- We discuss inversion in a circle, and medians, altitudes and vertex bisectors of a triangle. These are solutions to the final two questions of Quiz 1 in WildTrig16.

WildTrig19: Trigonometry with Finite Fields (I) --- An introduction to finite fields, based on first understanding rational numbers. This will be the basis of extending geometry and trigonometry to the finite setting.