Course 10
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.

Details:
- 100% online, and self-paced: the course is always open and anyone can join
- Courses are available world-wide
- Prior knowledge of Vedic Mathematics is not required
- 8 video lessons
- A trainer is available to answer questions
- Regular tests and discussion forum
- A certificate for those who pass

Course created by Kenneth Williams.

Prices: these depend on country so you will need to register at the Math2Shine link below to see this.
There are options for enroling for 2, 6 or 12 months.

CLICK HERE for more details and enrollment (goes to Math2Shine website)

Suitability: The course is not based on any school curriculum and so would be most 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

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

Part 9: QUADRUPLES
Quadruple Generators
Code numbers
Solving Quadruples
Orbit planes