Question

I want how to understand forming squares in this chapter

Answer 1

Here is a number in the form of a triangle:

This is number 10. (Count them) Since 10 can be pictured in this way, we call 10 a triangular number.

Now, how do we generate a triangular number? We begin with 1:

We say that 1 is the first triangular number. To form the next, we add 2:

So the next triangular number is 3. The number we add to the previous triangular number is called the gnomon (NOH-mon). We added the gnomon 2 to 1.

To form the next triangular number, we add the gnomon 3:

It produces the next triangular number, 6.

To form the next, we add 4:

o
and the first four triangular numbers are 1, 3, 6, 10. Each one is the sum of consecutive numbers.

	1.
1 + 2	=	3.
1 + 2 + 3	=	6.
1 + 2 + 3 + 4	=	10.

In mathematics square triangular number(or triangular square number) is a number which is both a triangular number and a perfect square.There are infinitely many square triangular numbers; the first few are 0, 1, 36, 1225, 41616, 1413721, 48024900, 1631432881, 55420693056, 1882672131025