Geometrical and Number Patterns

Geometrical Pattern 1: Square
- A square is a four-sided figure with all sides of equal length and all angles of 90 degrees.
- The number pattern corresponding to a square is the sequence of square numbers: 1, 4, 9, 16, 25, ...
- Each number in the sequence is obtained by squaring the natural numbers: 1^2 = 1, 2^2 = 4, 3^2 = 9, and so on.
- The pattern continues with each successive number being the square of the next natural number.

Geometrical Pattern 2: Triangle
- A triangle is a three-sided figure where the sum of all interior angles is always 180 degrees.
- The number pattern corresponding to a triangle is the sequence of triangular numbers: 1, 3, 6, 10, 15, ...
- Each number in the sequence is obtained by adding consecutive natural numbers: 1, 1+2=3, 1+2+3=6, and so on.
- The pattern continues with each successive number being the sum of the next natural number added to the previous sum.

Geometrical Pattern 3: Circle
- A circle is a closed curve where all points are equidistant from the center.
- The number pattern corresponding to a circle is the sequence of Pi (π) digits: 3.14159...
- Pi is an irrational number that represents the ratio of the circumference of a circle to its diameter.
- The pattern of Pi digits continues indefinitely without repeating in a predictable manner.