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Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 5
Textbook Solutions3992
Concept Notes144
Syllabus

Introduction to Patterns

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Topics

  • Square Numbers and Their Formation
  • Triangular Numbers and Their Formation

Square Numbers and Their Formation


Dots can be arranged in various patterns, one of which is a square formation. For example, if there are 4 dots in each row and 4 rows in total, the total number of dots is calculated as:

4 × 4 = 16

This demonstrates that 16 dots can be arranged in a square shape. To form a square, the number of dots in each row and column must be equal.
Other examples of such numbers include:
2 × 2 = 4, 3 × 3 = 9, 4 × 4 = 16, 5 × 5 = 25, 6 × 6 = 36
These numbers, which result from multiplying a number by itself, can always be arranged in a square pattern and are known as square numbers.

Triangular Numbers and Their Formation

Consider the sum of numbers from 1 to 6 as follows:

1 + 2 = 3, 1 + 2 + 3 = 6, 1 + 2 + 3 + 4 = 10, 1 + 2 + 3 + 4 + 5  = 15, 1 + 2 + 3 + 4 + 5 + 6 = 21
If dots are arranged in patterns corresponding to these sums, they naturally form triangular shapes. These arrangements exhibit a unique property—all three sides of the triangle are equal, indicating an equilateral triangle.

For example, a triangular arrangement can be made using 15 dots, forming a symmetrical triangle. Similarly, adding six more dots extends the pattern to 21 dots, maintaining the triangular structure.

Numbers such as 3, 6, 10, 15, and 21 are known as triangular numbers, as they can be represented as an equilateral triangular arrangement.

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