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.

**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**: $30.

**Course created and delivered by**
Kenneth Williams.

CLICK
HERE to start the course

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**