sequence

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.

Almost a thousand years ago, an Indian scholar called Hemachandra discovered a fascinating number sequence. A century later, the same sequence caught the attention of Italian mathematician Fibonacci, who wrote about it. The Fibonacci sequence, as it began to be called, was straightforward enough - what made it fascinating was that this particular set of numbers was repeated many, many times in nature - in flowers, seashells, eggs, seeds, stars... Find out more inside this book!

 

There is an interesting twist to this age old tale of finding what come next! The underlying question is this: given the initial (say) five terms of a sequence, can we say with any degree of certainty what the next term must be? Let’s say we have found a nice pattern in the given initial portion; can we be sure that the sequence has been generated with just that pattern in mind?

When something is being passed around, children are always anxious to see when their own turn would come. This activity utilizes that excitement.

 

Here are some sequencing games. Place the pictures in right chronological order. Decide what came before and what came after. You have  3 games. One on inventions, one on monuments and one on freedom movement. Take your pick, now!

 

 

This short note is based on a note written by K. R. S. Sastry in which he puts into practice the constructive
pedagogy of George Pólya: “First guess, then prove”.

This continues the ‘Proof’ column begun in the last issue. In this ‘episode’ too we study some problems from number theory; more specifically, from patterns generated by sums of consecutive numbers.

In this article we are going to explore a very interesting sequence of numbers known as the Fibonacci sequence.
The exploration of the sequence can lead to an absorbing classroom activity for students at the middle school and secondary school level. Students can explore many patterns within the sequence using a spreadsheet like MS Excel and the observations can lead to an enriching discussion in the classroom.

This continues the ‘Proof’ column begun in the last issue. In this ‘episode’ too we study some problems from number theory; more specifically, from patterns generated by sums of consecutive numbers.

Click here for the part 1 of 'How to Prove It'.

Starting with this issue we will run a regular column on the art and science of proof, and in honour of George Pólya’s book, ‘How To Solve It’, we have named it "How To Prove It." There is of course no single way to prove things in mathematics. But there are many general ideas and strategies that do help, and that’s what this column is about.

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