 Triple Geometry

Description: This course takes up the subject of triples, like 3,4,5, which represent the sides of right-angled triangles (e.g. 32 + 42 = 52). Most of the techniques developed though are not restricted to integer-sided triangles. We see how to find two sides of a right-angled triangle given only one side, and the many applications of this, including in equations, in 2 and 3-dimensional geometry and astronomy (see contents below). The course is independent of any other of our courses and the content is not repeated in any of them. No calculator required.

You can join this course any time.

Enrolling in the course you have:
- a trainer to answer questions,
- regular tests,
- a certificate for those who pass.

Course start: You can join this course any time.

Mode: 100 % Online.
9 Video Lessons
with online Tests (plus 14 optional Challenge Questions).
Self paced: watch videos at any time that suits you. Lessons are 20 minutes long on average. Each week has a test and there are additional exercises in the videos.

Suitability: The course is not based on any school curriculum and so would be suitable for anyone who:
- is over the age of about 10 years,
- seeks the challenge of something entirely different,
- wishes to expand their thinking - perhaps to train for competitive exams,
- wants to see new applications of Vedic mathematics.

Cost: \$45.

Course created and delivered by Kenneth Williams.

Any queries can be sent to academy@vedicmaths.org

Course Content

Part 1: INTRODUCTION
Types of number, Factorisation, Squaring,
Triple notation, Pythagoras Theorem, Sines, Cosines etc.,
Triple Code Numbers

Part 2: EXPRESSING A NUMBER AS A DIFFERENCE OF SQUARES
Tirthaji’s formula
Solving equations
Geometrical applications

Part 3: EXPRESSING A NUMBER AS A SUM OF SQUARES – SPECIAL METHODS
By Observation
By Proportion
By Vertically and Crosswise

Part 4: EXPRESSING A NUMBER AS A SUM OF SQUARES – GENERAL METHOD
By the Deficiency
Raising the diagonal
Summary, Examples of all types

Part 5: APPLICATIONS OF SUM OR DIFFERENCE OF SQUARES
Equations in 1 and 2 variables
Dealing with decimals and fractions
Trigonometric Equations in 1 and 2 variables
Finding two sides given the hypotenuse
Solving combined triangles

Part 6: RECIPROCAL AND PALINDROMIC EQUATIONS
Sum & difference of reciprocals
Disguises
Solving Palindromic equations
Trigonometrical equations involving reciprocals
Triples with negative elements

Part 7: TRIPLE CODE NUMBERS
Angle Bisector Theorem
Base/height formula
Geometrical applications – isosceles triangles, circle problems
Coordinate Geometry applications

Part 8: 3-DIMENSIONAL APPLICATIONS
Pyramid, Cone, Cuboid
Increasing the number of solutions