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Currently Watching: Watching: Wildtrig19: trigonometry with finite fields i
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WildTrig1: Why Trig is Hard Posted by: njwildberger
Video duration: 586 seconds 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! Related: angle, cosine, distance, diy, rational, sine, trigonometry |
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WildTrig2: Quadrance via Pythagoras and Archimedes Posted by: njwildberger
Video duration: 598 seconds 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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WildTrig5: Applications of rational trigonometry Posted by: njwildberger
Video duration: 568 seconds 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 |
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WildTrig15: Complex numbers and rotations Posted by: njwildberger
Video duration: 617 seconds 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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WildTrig3: Spread, angles and astronomy Posted by: njwildberger
Video duration: 560 seconds 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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WildTrig11: Applications of rational trig to surveying (I) Posted by: njwildberger
Video duration: 591 seconds 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. Related: rational, regiomontanus, right, spreads, surveying, triangle, trigonometry |
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WildTrig4: Five main laws of rational trigonometry Posted by: njwildberger
Video duration: 588 seconds 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 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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WildTrig7: Solving triangles with rational trigonometry Posted by: njwildberger
Video duration: 392 seconds 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\](http://img.youtube.com/vi/hooQuHLS-kk/2.jpg "WildTrig6: Heron\") |
WildTrig6: Heron's formula viewed rationally Posted by: njwildberger
Video duration: 516 seconds 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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WildTrig10: Geometry of circles with rational trigonometry Posted by: njwildberger
Video duration: 516 seconds We derive some of the most fundamental facts about a circle using rational trigonometry---the Subtended spread theorems and the Equal products theorem. Related: chord, circle, diameter, equal, geometry, products, rational, spreads, subtended, theorem, trigonometry |
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WildTrig9: The laws of proportion for a triangle Posted by: njwildberger
Video duration: 518 seconds Using rational trigonometry we develop Menelaus' and Ceva's theorem and some related results, namely the Law of Proportions, and the Alternating spreads theorem. Related: alternating, ceva, laws, menelaus, of, proportion, rational, spreads, theorem, trigonometry |
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WildTrig14: Rational parameters for circles Posted by: njwildberger
Video duration: 584 seconds 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. Related: circle, line, mathematics, parameter, pythagorean, rational, spread, trigonometry, triple |
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WildTrig0: An invitation to geometry: the WildTrig series Posted by: njwildberger
Video duration: 518 seconds Introduces the WildTrig series, inviting you to learn a new approach to geometry and trigonometry. Related: descartes, euclid, geometry, mathematics, rational, teaching, trigonometry, wildberger, wildtrig |
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WildTrig19: Trigonometry with finite fields (I) Posted by: njwildberger
Video duration: 600 seconds 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. Related: fields, finite, fractions, geometry, rational, trigonometry, wildberger |
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WildTrig13: Why spreads are better than angles Posted by: njwildberger
Video duration: 544 seconds 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. Related: angles, cartesian, geometry, lines, mathematics, rational, spreads, trigonometry |
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WildTrig18: Medians, altitudes and vertex bisectors Posted by: njwildberger
Video duration: 574 seconds 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. Related: altitudes, bisectors, inversion, mathematics, medians, rational, trigonometry, wildberger |
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WildTrig16: Rational Trigonometry Quiz 1 Posted by: njwildberger
Video duration: 439 seconds 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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WildTrig23: Highlights from triangle geometry (II) Posted by: njwildberger
Video duration: 492 seconds Equilateral triangles, Napoleon's theorem and Morley's theorem are discussed from the view of rational trigonometry. We give an example over a finite field with 11 elements. Related: equilateral, fields, finite, morleys, napoleons, rational, theorem, triangles, trigonometry |
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WildTrig24: Spread polynomials Posted by: njwildberger
Video duration: 489 seconds 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. Related: chebyshev, geometry, mathematics, polynomials, rational, spread, trigonometry |
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WildTrig17: Rational trigonometry: Solutions to Quiz 1 Posted by: njwildberger
Video duration: 601 seconds Five problems involving a triangle, a surveying problem, a kite, a piece of paper and a cyclic quadrilateral are solved using rational trigonometry. Related: cyclic, kite, mathematics, quadrilateral, quiz, rational, solutions, triangle, trigonometry, wildberger |
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WildTrig22: Highlights from triangle geometry (I) Posted by: njwildberger
Video duration: 576 seconds The Euler line, the nine-point circle, incenters and isogonal conjugation. Related: circle, euler, geometry, incenters, line, nine-point, rational, triangle, trigonometry |
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WildTrig26: Applications of rational trig to surveying (II) Posted by: njwildberger
Video duration: 515 seconds How to cut a train track up a hill, how to compare two vertical spreads, how to measure a height from three vertical spread measurements. Related: mathematics, measurement, rational, slope, spread, surveying, train, trigonometry |
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WildTrig25: Pentagons and five-fold symmetry Posted by: njwildberger
Video duration: 598 seconds Regular pentagons, pentagrams and five fold symmetry. Ruler and compass construction, golden ratio spreads, kite and dart from Penrose tiles Related: five, fold, geometry, golden, mathematics, penrose, pentagon, pentagram, ratio, rational, symmetry, tiles, trigonometry |