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Encapsulate
math

PaTTERNS iN MaTHEMaTiCS

Patterns
The repetition of a certain image, number following some rule is called pattern. For example, mandalas,
rangolis, etc.

Number Pattern Geometrical Patterns in Numbers
A sequence of numbers that follow a certain rule Triangular
is known as number pattern.
Numbers
interesting Number Patterns
Square
Counting Numbers 1, 2, 3, 4, 5, 6, ... Numbers
Odd Numbers 1, 3, 5, 7, 9, 11, ...
Even Numbers 2, 4, 6, 8, 10, 12, ... Cubic
Triangular Numbers 1, 3, 6, 10, 15, 21, ... Numbers
Square Numbers 1, 4, 9, 16, 25, 36, ...
Cube Numbers 1, 8, 27, 64, 125, ... Tetrahedral
Tetrahedral Numbers 1, 4 ,10, 20, 35, ... Numbers
Hexagonal Numbers 1, 6, 15, 28, ...
Virahanka Numbers 1, 2, 3, 5, 8, 13, 21, 34, ...
Powers of 2 1, 2, 4, 8, 16, 32, 64, ... Pentagonal
Powers of 3 1, 3, 9, 27, 81, 243, ... Numbers

Hexagonal
Patterns in Shapes Numbers

Patterns in shape may be one, two or three
dimensions. Example of shape sequence are:
Regular Polygon Relations among Number Sequences
(a) Triangular numbers and square numbers.
Example, 1 + 3 = 4
(b) Odd numbers and square numbers.
Stacked Triangles Example, 1 + 3 = 4 = 2 × 2
1 + 3 + 5 = 9 = 3 × 3
(c) Cubic numbers and odd numbers.
Example, 1 × 1 × 1 = 1
2 × 2 × 2 = 8 = 3 + 5
Stacked Squares
3 × 3 × 3 = 27 = 7 + 9 + 11
(d) Triangular numbers and tetrahedral numbers.
Example, 1 + 3 = 4
1 + 3 + 6 = 10

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