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2018-02-10
Intro to Rational Trigonometry by Norman J Wildberger
source: njwildberger 2017年9月23日
WildTrig: Intro to Rational Trigonometry:
An introduction to Rational Trigonometry and Universal Geometry: simpler and more powerful for calculations, easier to learn, more general, and a richer theory of Euclidean geometry leading to many new discoveries. Also the basis for Universal Hyperbolic Geometry. This series is the first one on my channel, and in some sense the motivation for a lot of the direction of the future of mathematics, in my opinion. With rational trigonometry, we learn that we can do lots of things algebraically that formerly required transcendental functions and irrationalities. Not only liberating, this is also empowering, as a lot of calculations run now faster and more smoothly. And all of metrical geometry gets recast in a much more elegant and general framework.
8:38 0: An Invitation to Geometry: the WildTrig series
9:48 1: Why Trig is Hard
9:59 2: Quadrance via Pythagoras and Archimedes
9:21 3: Spread, angles and astronomy
9:49 4: Five main laws of rational trigonometry
9:28 5: Applications of rational trigonometry
8:37 6: Heron's formula viewed rationally
6:33 7: Solving triangles with rational trigonometry
9:56 8: Centers of triangles with rational trigonometry
8:39 9: The laws of proportion for a triangle
8:37 10: Geometry of circles with rational trigonometry
9:52 11: Applications of rational trig to surveying (I)
9:20 12: Cartesian coordinates and geometry
9:05 13: Why spreads are better than angles
9:46 14: Rational parameters for circles
10:17 15: Complex numbers and rotations
7:19 16: Rational Trigonometry Quiz 1
10:01 17: Rational trigonometry: Solutions to Quiz 1
9:34 18: Medians, altitudes and vertex bisectors
10:01 19: Trigonometry with finite fields (I)
10:02 20: Trigonometry with Finite Fields (II)
10:00 21: Trigonometry with Finite Fields (III)
9:36 22: Highlights from triangle geometry (I)
8:12 23: Highlights from triangle geometry (II)
8:09 24: Spread polynomials
9:58 25: Pentagons and five-fold symmetry
8:35 26: Applications of rational trig to surveying (II)
9:05 27: Stewart's theorem
9:07 28: What size ladder fits around a corner?
8:10 29: Trisecting angles and Hadley's theorem
9:57 30: Polar coordinates and rational trigonometry
7:22 31: Introduction to Projective Geometry
9:51 32: Projective geometry and perspective
7:57 33: Projective geometry and homogeneous coordinates
8:19 34: Lines and planes in projective geometry
10:10 35: Affine geometry and barycentric coordinates
10:05 36: Affine geometry and vectors
10:11 37: The cross ratio
8:47 38: More about the cross ratio
9:22 39: Harmonic ranges and pencils
9:17 40: The fundamental theorem of projective geometry
8:46 41: Conics via projective geometry
9:01 42: An algebraic framework for rational trigonometry (I)
10:02 43: An algebraic framework for rational trigonometry (II)
6:34 44: How to learn mathematics
9:50 45: Einstein's special relativity: an introduction
10:03 46: Red geometry (I)
10:00 47: Red geometry (II)
8:35 48: Red geometry (III)
9:45 49: Circles in red geometry
9:47 50: Green geometry (I)
8:50 51: Green geometry (II)
8:36 52: Pythagorean triples
9:41 53: An introduction to chromogeometry
8:19 54: Chromogeometry and Euler lines
7:37 55: Chromogeometry and the Omega triangle
7:54 56: Chromogeometry and nine-point circles
9:58 57: Proofs in chromogeometry
9:49 58: Triangle spread rules
9:58 59: Triangle spread rules in action
9:17 60: Acute and obtuse triangles
8:03 61: Proofs of the Triangle spread rules
5:46 62: Rational trigonometry Quiz #2
9:35 63: Hints for solutions to Quiz #2
8:11 64: The 6-7-8 triangle
9:36 65: Barycentric coordinates and the 6-7-8 triangle
9:39 66: Squares in a pentagon
9:41 67: Trisecting a right triangle
9:56 68: Euler's Four Point Relation
9:56 69: What is geometry really about?
10:02 70: Determinants in geometry (I)
10:05 71: Determinants in geometry (II)
19:23 72 NEW: Determinants in Geometry (III)
19:26 73: Spreads, determinants and chromogeometry I
20:26 74: Spreads, determinants and chromogeometry II
19:54 75: Spreads, determinants and chromogeometry III
28:52 76: Coloured spreads and generalizations I
26:56 77: Coloured spreads and generalizations II
23:27 78: Geometry with a general dot product
30:12 79: The general rational laws of trigonometry
28:07 81: Rheticus and 17th century trig tables
23:19 82: Maths Education and Rational Trigonometry II
30:54 83: Maths Education and Rational Trigonometry III
22:00 84: Rational trigonometry and mathematics education IV
24:25 85: The true role of the circular functions
28:30 86: Understanding uniform motion: are radians really necessary?
Famous Math Problems by Norman J Wildberger
source: njwildberger 2017年2月28日
We look at famous math problems, both unsolved and solved. These will span both pure and applied mathematics; some will be ancient problems, others relatively new, but hopefully they will all be interesting.
1 42:03 1: Factoring large numbers into primes
2 33:12 2: The Collatz conjecture (3n+1 problem)
3 43:49 3: Apollonius' circle construction problems
4 34:03 4: The Graceful Tree Conjecture
5 32:05 5: Omar Khayyam and the Binomial Theorem
6 43:29 6: Archimedes' squaring of a parabola
7 33:34 7: Newcomb's paradox
8 42:16 8: Euler's triangulation of a polygon
9 40:01 9: Distances to the sun and moon
10 43:32 10a: The integral of x^n
11 39:37 10b: The integral of x^n (cont.)
12 26:05 11: Steiner's regions of space problem
13 41:50 12: Euclid's construction problems I
14 58:24 13a: The rotation problem and Hamilton's discovery of quaternions I
15 59:47 13b: The rotation problem and Hamilton's discovery of quaternions (II)
16 56:14 13c: The rotation problem and Hamilton's discovery of quaternions III
17 1:01:33 13d: The rotation problem and Hamilton's discovery of quaternions IV
18 45:34 14: Japanese Temple Problems I
19 35:48 15: Euler's relation between vertices, edges and faces of the Platonic solids
20 37:30 16: The area of a triangle and Archimedes' formula
21 30:48 17: Are all true mathematical statements provable?
22 44:04 19a: The most fundamental and important problem in mathematics
23 37:40 19b: The rational number line and irrationalities
24 43:30 19c: Stevin numbers, infinitesimals and complex numbers
25 1:10:07 19d: Dedekind cuts and computational difficulties with real numbers
Math Seminars presented by Norman J Wildberger and others
source: njwildberger 2017年5月13日
This series consists of mathematical seminars presented by N J Wildberger and perhaps also seminars by colleagues. It will be aimed at undergraduate math majors, PhD students, mathematicians and physicists. Most but not all of these will have been presented to the School of Mathematics and Statistics, UNSW Sydney.
1 51:55 Seminar: Five-fold symmetry, Schiffler points and the twisted icosahedron
2 46:25 Infinities and Skepticism in Mathematics: Steve Patterson interviews N J Wildberger
3 1:13:36 Primes, Complexity and Computation: How Big Number theory resolves the Goldbach Conjecture
4 4:32 Primes, Complexity and Computation: How Big Number theory resolves the Goldbach Conjecture
5 30:26 Teaching connections between Algebra and Geometry II
6 31:31 Teaching connections between Algebra and Geometry I: a MANSW presentation
7 51:42 A Socratic look at logical weaknesses in modern pure mathematics
8 42:58 Infinity: does it exist?? A debate with James Franklin and N J Wildberger
9 53:13 Bats, echolocation, and a Newtonian view of Einstein's Special Relativity
10 59:13 The Geometry of Relativity and why your GPS works
11 55:31 Towards a more computational mathematics: rational trigonometry and new foundations for geometry
12 50:25 Rational trigonometry, generalized triangle geometry and four-fold incenter symmetry
13 48:49 National Curriculum issues and opportunities for revitalizing geometry thinking in the classroom
14 58:39 Three dimensional geometry, ZOME, and the elusive tetrahedron
15 51:17 Hyperbolic Geometry is Projective Relativistic Geometry (full lecture)
16 1:05:17 Triangle Geometry Old and New: An introduction to Hyperbolic Triangle Geometry
Algebraic Calculus One by Norman J Wildberger
source: Wild Egg mathematics courses
This playlist will contain the videos from the Algebraic Calculus One course, which will set out a new way of understanding integral calculus.
23:38 Invitation to a more logical, solid and careful analysis
25:10 AlgCalcOne: Points and Lines in the Affine Plane
22:02 AlgCalcOne: Points and Lines in the Affine Plane b)
25:35 AlgCalcOne: Vectors, Displacement, and Centre of Mass
22:20 AlgCalcOne: Vectors Displacement and Centre of Mass b)
25:35 AlgCalcOne: Introduction to Signed Area b)
21:15 AlgCalcOne: Introduction to Signed Area
24:01 AlgCalcOne: The Cross Product and Meister's Formula b)
20:42 AlgCalcOne: The Cross Product and Meister's Formula
28:42 AlgCalcOne: Signed Areas of Triangles on Curves
27:53 AlgCalcOne: Data Structures and Polygonal Splines
36:19 AlgCalcOne: Parabolic Splines and Archimedes
27:20 AlgCalcOne: The Mystery of "Circular Area"
24:07 AlgCalcOne: Summation and Sums of Powers
32:11 AlgCalcOne: Faulhaber's Formula and Bernoulli Numbers
31:05 AlgCalcOne: Polynomials, Matrices and Pascal Arrays
33:22 AlgCalcOne: Vexels and Polynumbers via Multisets
24:47 AlgCalcOne: Curves from Antiquity
22:47 AlgCalcOne: Novel Algebraic Operations for Affine Geometry
19:12 AlgCalcOne: Affine Combinations and Barycentric Coords
18:43 AlgCalcOne: Curves in Modern Times
30:28 AlgCalcOne: Galileo, Newton and motions of particles
28:26 AlgCalcOne: De Casteljau Bezier Curves
Old Babylonian Mathematics by Norman J Wildberger & Daniel Mansfield
source: njwildberger 2017年10月3日
Old Babylonian Mathematics and Plimpton 322
A series on the remarkable mathematics from the Old Babylonian period from 1900 B.C.E to 1600 B.C.E. This culture had a rich mathematics that we are just now learning more and more about. Their sexagesimal arithmetical system is powerful and unique, but there were other aspects to their mathematics that are well worth learning about.
This series is presented by Daniel Mansfield and N J Wildberger. One of the main aims is to explain our new understanding of the famous tablet Plimpton 322 as the world's first and most exact trigonometric table! Along the way we will learn quite a bit about this culture and its mathematical thinking.
17:58 : A new perspective (introduction)
26:28 The remarkable OB sexagesimal system
18:49 Geometry in ancient Mesopotamia and Egypt
20:50 A new understanding of the OB tablet Plimpton 322
19:50 How did the OB scribe construct P322?
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