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. 3^{2} + 4^{2} = 5^{2}).
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**