triangular number

Sums of squares of the natural numbers from the Pascal triangle.

The purpose of the present article is to narrate some interesting episodes of Ramanujan’s life and to provide a few elementary problems solved by him to demonstrate how he attacked those problems and using his intuition generalized the results in some cases.

An article on Harmonic Triangular Triples

The concept of digital root of a natural number has been known for some time. Before the development of computer devices, the idea was used by accountants to check their results. We will examine the basis for this procedure presently.
A “proof without words” sounds like a contradiction in terms! How can you prove something if you are not permitted the use of any words? In spite of the seeming absurdity of the idea, the notion of a proof without words — generally shortened to PWW — has acquired great popularity in mathematics in recent decades, and every now and then we come across new, elegant PWWs for old, familiar propositions. In this short article the seemingly contradictory nature of a PWW is discussed, and some examples of PWWs are presented.

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.

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'.

A well-known puzzle that can be posed to even young children is as follows...

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