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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**

Edukite courses are free to study. To successfully complete a course you must submit all the assignment of the course as part of the assessment. Upon successful completion of a course, you can choose to make your achievement formal by obtaining your Certificate at a cost of £49.

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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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