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WildTrig2: Quadrance via Pythagoras and Archimedes Posted by: njwildberger
Video duration: 598 seconds Global video hits: 4666 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 |
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quadrance.mpg Posted by: nicainsoy
Video duration: 401 seconds Global video hits: 13 Quadrance debut! Malone's Santa Ana Saturday November 29th Jef and Adrian on Bass Mark on Guitar Tigran on Flute Lori Voice DC Drums Related: atmospheric, experimental, improvised, rock |
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Quadrance The Airliner Los Angeles December 27 2008 Posted by: nicainsoy
Video duration: 154 seconds Global video hits: 1 Shopping craziness outside of Chinatown going on. 5 pm is not exactly an idea time to showcase bands. Related: band, experimental, improv, indie, jam, rock |
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WildTrig20: Trigonometry with Finite Fields (II) Posted by: njwildberger
Video duration: 602 seconds Global video hits: 329 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 |
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WildTrig4: Five main laws of rational trigonometry Posted by: njwildberger
Video duration: 588 seconds Global video hits: 2915 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 |
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WildTrig12: Cartesian coordinates and geometry Posted by: njwildberger
Video duration: 559 seconds Global video hits: 2987 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 |
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WildTrig15: Complex numbers and rotations Posted by: njwildberger
Video duration: 617 seconds Global video hits: 4026 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 |
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WildTrig28: What size ladder fits around a corner? Posted by: njwildberger
Video duration: 547 seconds Global video hits: 155 The famous ladder problem, here solved using rational trigonometry. Related: ladder, mathematics, minimize, problem, quadrance, rational, spread, trigonometry |
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WildTrig7: Solving triangles with rational trigonometry Posted by: njwildberger
Video duration: 392 seconds Global video hits: 2700 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 |
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WildTrig5: Applications of rational trigonometry Posted by: njwildberger
Video duration: 568 seconds Global video hits: 4402 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 |
![WildTrig6: Heron\](http://img.youtube.com/vi/hooQuHLS-kk/2.jpg "WildTrig6: Heron\") |
WildTrig6: Heron's formula viewed rationally Posted by: njwildberger
Video duration: 516 seconds Global video hits: 2075 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 |
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WildTrig3: Spread, angles and astronomy Posted by: njwildberger
Video duration: 560 seconds Global video hits: 3842 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 |
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WildTrig16: Rational Trigonometry Quiz 1 Posted by: njwildberger
Video duration: 439 seconds Global video hits: 585 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 |
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WildTrig30: Polar coordinates and rational trigonometry Posted by: njwildberger
Video duration: 597 seconds Global video hits: 155 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 |