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WildTrig2: Quadrance via Pythagoras and Archimedes WildTrig2: Quadrance via Pythagoras and Archimedes
Posted by: njwildberger

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.

Related: archimedes, formula, geometry, pythagoras, quad, quadrance, rational, trigonometry, triple

WildTrig12: Cartesian coordinates and geometry WildTrig12: Cartesian coordinates and geometry
Posted by: njwildberger

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.

Related: cartesian, coordinates, descartes, fermat, lines, parallel, perpendicular, points, quadrance, spread

WildTrig4: Five main laws of rational trigonometry WildTrig4: Five main laws of rational trigonometry
Posted by: njwildberger

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.

Related: cross, formula, law, mathematics, pythagoras, quad, quadrance, rational, spread, theorem, trigonometry, triple

WildTrig20: Trigonometry with Finite Fields (II) WildTrig20: Trigonometry with Finite Fields (II)
Posted by: njwildberger

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.

Related: arithmetic, fermats, fields, finite, mathematics, quadrance, rational, spread, theorem, trigonometry

WildTrig5: Applications of rational trigonometry WildTrig5: Applications of rational trigonometry
Posted by: njwildberger

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.

Related: applications, distance, flagpole, kite, ladder, line, quadrance, rational, spread, trigonometry

WildTrig15: Complex numbers and rotations WildTrig15: Complex numbers and rotations
Posted by: njwildberger

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.

Related: complex, dilations, mathematics, numbers, quadrance, rational, rotations, similarity, trigonometry

WildTrig7: Solving triangles with rational trigonometry WildTrig7: Solving triangles with rational trigonometry
Posted by: njwildberger

Video duration: 392 seconds
Global video hits: 2556

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

Related: quadrance, rational, solving, spread, triangles, trigonometry

WildTrig6: Heron\ WildTrig6: Heron's formula viewed rationally
Posted by: njwildberger

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.

Related: archimedes, formula, herons, quadrance, rational, trigonometry

WildTrig16: Rational Trigonometry Quiz 1 WildTrig16: Rational Trigonometry Quiz 1
Posted by: njwildberger

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.

Related: circles, mathematics, quadrance, quiz, rational, spread, trigonometry, wildberger

WildTrig28: What size ladder fits around a corner? WildTrig28: What size ladder fits around a corner?
Posted by: njwildberger

Video duration: 547 seconds
Global video hits: 111

The famous ladder problem, here solved using rational trigonometry.

Related: ladder, mathematics, minimize, problem, quadrance, rational, spread, trigonometry

WildTrig3: Spread, angles and astronomy WildTrig3: Spread, angles and astronomy
Posted by: njwildberger

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.

Related: angle, dodecahedron, mathematics, quadrance, rational, spread, tetrahedron, trigonometry

WildTrig30: Polar coordinates and rational trigonometry WildTrig30: Polar coordinates and rational trigonometry
Posted by: njwildberger

Video duration: 597 seconds
Global video hits: 78

After a review of the usual polar coordinates, we introduce the rational version, and illustrate via an ellipse, a lemniscate and the trisectrix

Related: coordinates, ellipse, geometry, lemniscate, mathematics, polar, quadrance, rational, spread, trigonometry, trisectrix, wildberger

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