Video duration: 598 seconds
Global video hits: 4237
We show how the basic notion of rational trigonometry---quadr ance---arises from the geometry of the ancient Greeks. The little-known sister theorem to Pythagoras features prominently, and is closely related to a theorem of Archimedes.
Video duration: 559 seconds
Global video hits: 2645
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.
Video duration: 588 seconds
Global video hits: 2728
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.
Video duration: 602 seconds
Global video hits: 302
This video explains more about arithmetic in a finite field, shows how to visualize points in a finite plane, and how to compute quadrance and spread. Examples are taken from the field with seven elements.
Video duration: 568 seconds
Global video hits: 4184
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.
Video duration: 617 seconds
Global video hits: 3400
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.
Video duration: 516 seconds
Global video hits: 1855
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.
Video duration: 439 seconds
Global video hits: 508
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.
Video duration: 560 seconds
Global video hits: 3540
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.