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.
Course created and delivered by Kenneth Williams.
Any queries can be sent to firstname.lastname@example.org
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
Part 3: EXPRESSING A NUMBER AS A SUM OF SQUARES – SPECIAL METHODS
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
Solving Palindromic equations
Trigonometrical equations involving reciprocals
Triples with negative elements
Part 7: TRIPLE CODE NUMBERS
Angle Bisector Theorem
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