arithmetic progression

In this edition of ‘Adventures’ we study a few miscellaneous problems.

Magic triangles can be added to each other term by term, the same way that magic squares can be added to each other. We show here how two third order magic triangles can yield another third order magic triangle through addition.

In the July 2018 issue of At Right Angles, the topic of magic triangles was explored, a ‘magic triangle’ being “an arrangements of the integers from 1 to n on the sides of a triangle with the same number of integers on each side so that the sum of integers on each side is a constant, the 'magic sum' of the triangle. There was some error in the proof and here in this article we will track down the error.

Magic Triangles and Squares are often used as a 'fun activity' in the math class, but the magic of the mathematics behind such constructs is seldom explained and often left as an esoteric mystery for students. An article that can be used by teachers in the middle school (6-8) to justify to students that everything in mathematics has a reason and a solid explanation behind it. Plus a good way to practise some simple algebra.

In this short note we present a classroom vignette involving surds.
Magic squares have been a source of recreation and leisure from ancient times. There is something about the symmetry and patterns contained in such squares that carry great appeal. In this piece, we shall prove two simple results about 3 × 3 and 4 × 4 magic squares.
 
And also,
Magic squares have been a subject of fascination for centuries. Probably it is the elegance and the simplicity in the subject that attract people. Here we explore the question of how to construct magic squares composed solely of prime numbers.

Here are some problems for students in Senior School.

Paul Erdős has been described as one of the most universally adored mathematicians of all time. No mathematician prior to him or since has had quite the lifestyle he adopted: the peripatetic traveller living out of a suitcase, moving from one friend’s house to another for decades at a stretch, and all the while collaboratively generating papers; no one has had quite the social impact he has had, within the community of mathematicians.

A short writeup by A. Ramachandran which can spur the motivated teacher to design investigative tasks that connect geometry and sequences.

 
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