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: $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