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This new theory dispenses with the usual complicated circular functions cos and sin and tan and their many complicated relations and establishes a trigonometry based entirely on elementary arithmetic and algebra. The [course_title] will provide an overview of Rational Trigonometry and how it allows us to reformulate spherical and elliptic geometries, hyperbolic geometry, and inversive geometry, and leads to the new theory of chronogeometry, along with many practical applications.

Assessment

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

Certification

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Course Credit: Open Culture

 

Course Curriculum

Module:01
WildTrig0: An Invitation to Geometry: the WildTrig series 00:08:00
WildTrig1: Why Trig is Hard 00:10:00
WildTrig2: Quadrance via Pythagoras and Archimedes 00:10:00
WildTrig3: Spread, angles and astronomy 00:09:00
WildTrig4: Five main laws of rational trigonometry 00:10:00
WildTrig5: Applications of rational trigonometry 00:09:00
WildTrig6: Heron’s formula viewed rationally 00:08:00
WildTrig7: Solving triangles with rational trigonometry 00:06:00
WildTrig8: Centers of triangles with rational trigonometry 00:10:00
WildTrig9: The laws of proportion for a triangle 00:08:00
WildTrig10: Geometry of circles with rational trigonometry 00:08:00
Module:02
WildTrig11: Applications of rational trig to surveying (I) 00:10:00
WildTrig12: Cartesian coordinates and geometry 00:09:00
WildTrig13: Why spreads are better than angles 00:09:00
WildTrig14: Rational parameters for circles 00:10:00
WildTrig15: Complex numbers and rotations 00:10:00
WildTrig16: Rational Trigonometry Quiz 1 00:07:00
WildTrig17: Rational trigonometry: Solutions to Quiz 1 00:10:00
WildTrig18: Medians, altitudes and vertex bisectors 00:09:00
WildTrig19: Trigonometry with finite fields (I) 00:10:00
WildTrig20: Trigonometry with Finite Fields (II) 00:10:00
WildTrig22: Highlights from triangle geometry (I) 00:09:00
WildTrig23: Highlights from triangle geometry (II) 00:08:00
Module:03
WildTrig24: Spread polynomials 00:08:00
WildTrig25: Pentagons and five-fold symmetry 00:10:00
WildTrig26: Applications of rational trig to surveying (II) 00:08:00
WildTrig27: Stewart’s theorem 00:09:00
WildTrig28: What size ladder fits around a corner? 00:09:00
WildTrig29: Trisecting angles and Hadley’s theorem 00:08:00
WildTrig30: Polar coordinates and rational trigonometry 00:10:00
WildTrig31: Introduction to Projective Geometry 00:07:00
WildTrig32: Projective geometry and perspective 00:10:00
WildTrig33: Projective geometry and homogeneous coordinates 00:08:00
WildTrig34: Lines and planes in projective geometry 00:08:00
Module:04
WildTrig35: Affine geometry and barycentric coordinates 00:10:00
WildTrig36: Affine geometry and vectors 00:10:00
WildTrig37: The cross ratio 00:10:00
WildTrig38: More about the cross ratio 00:09:00
WildTrig39: Harmonic ranges and pencils 00:09:00
WildTrig40: The fundamental theorem of projective geometry 00:09:00
WildTrig41: Conics via projective geometry 00:09:00
WildTrig42: An algebraic framework for rational trigonometry (I) 00:09:00
WildTrig43: An algebraic framework for rational trigonometry (II) 00:10:00
WildTrig44: How to learn mathematics 00:06:00
WildTrig45: Einstein’s special relativity: an introduction 00:10:00
Module:05
WildTrig46: Red geometry (I) 00:10:00
WildTrig47: Red geometry (II) 00:10:00
WildTrig48: Red geometry (III) 00:08:00
WildTrig49: Circles in red geometry 00:10:00
WildTrig50: Green geometry (I) 00:10:00
WildTrig51: Green geometry (II) 00:09:00
WildTrig52: Pythagorean triples 00:08:00
WildTrig54: Chromogeometry and Euler lines 00:08:00
WildTrig55: Chromogeometry and the Omega triangle 00:07:00
WildTrig56: Chromogeometry and nine-point circles 00:08:00
WildTrig57: Proofs in chromogeometry 00:10:00
Module:06
WildTrig58: Triangle spread rules 00:10:00
WildTrig59: Triangle spread rules in action 00:10:00
WildTrig60: Acute and obtuse triangles 00:09:00
WildTrig61: Proofs of the Triangle spread rules 00:09:00
WildTrig62: Rational trigonometry Quiz #2 00:06:00
WildTrig63: Hints for solutions to Quiz #2 00:09:00
WildTrig64: The 6-7-8 triangle 00:08:00
WildTrig65: Barycentric coordinates and the 6-7-8 triangle 00:09:00
WildTrig66: Squares in a pentagon 00:09:00
WildTrig67: Trisecting a right triangle 00:09:00
WildTrig68: Euler’s Four Point Relation 00:10:00
WildTrig69: What is geometry really about? 00:10:00
WildTrig70: Determinants in geometry (I) 00:10:00
WildTrig71: Determinants in geometry (II) 00:10:00
Assessment
Submit Your Assignment 00:00:00
Certification 00:00:00

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