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Interesting Number Patterns

Some interesting number patterns are shown in the table below. Just check the table and reflect
on the questions based on it.

Counting Numbers 1, 2, 3, 4, 5, 6, ...
Odd Numbers 1, 3, 5, 7, 9, 11, ...

Even Numbers 2, 4, 6, 8, 10, 12, ...
Triangular Numbers 1, 3, 6, 10, 15, 21, ...

Square Numbers 1, 4, 9, 16, 25, 36, ...
Cube Numbers 1, 8, 27, 64, 125, ...

Pentagonal Numbers 1, 5, 12, 22, 35, 51, ...
Hexagonal Numbers 1, 6, 15, 28, ...

Tetrahedral Numbers 1, 4, 10, 20, 35, ...
Virahanka Numbers 1, 2, 3, 5, 8, 13, 21, 34, ...
Powers of 2 1, 2, 4, 8, 16, 32, 64, ...

Powers of 3 1, 3, 9, 27, 81, 243, ...

Maths Talk
1. Write each sequence of the above table in your notebook. Write the next three numbers of
each sequence and discuss the rules for forming the numbers in the sequence.
2. The Fibonacci sequence was discovered much earlier in India, and it is known as the Virahanka number. Can
you find Virahanka number in nature?

Knowledge Desk

Lesson From Indian History
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Fibonacci in the 12 century, claimed to have discovered a mathematical sequence in which every next
term is the sum of the preceding two terms, but this was well known to Indians in 6th century and prior.
Acharya Pingala, in his book Chhandahsastra written in 200 BCE, had given an idea of how musical nodes can
be played following a pattern which transforms into a number pattern now known as Fibonacci sequence.
Moreover, Virahanka, in the 6 century, in his book Vrattajati Samuccaya (o`ÙktkfrleqPp;%) gave a comprehensive
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explanation of Prastaar and Sankhya Pratyayas for matra Vrutta.
,"k ,o çLrkjks ek=kko`Ùkkuka lkfèkr% fdUrq A ek=kk ;=k u iw;Zrs izFkea Li'k± r=k nsfg AA (o`ÙktkfrleqPp;% 6.20)

He further writes –
}kS }kS iwoZfodYikS ;k esyf;Rok tk;rs lÄ~[;k A lk mÙkjek=kk.kka lÄ~[;k;k ,"k funsZ'k% AA (o`ÙktkfrleqPp;% 6.49)
Mathematically,
1, 2, 3 , 5 , 8 , 13 , 21 , 34 , …
1 + 2 2 + 3 3 + 5 5 + 8 8 + 13 13 + 21
On 23rd November (11/23), mathematics lover across the globe celebrate Fibonacci Day because the date
shows the first four terms 1, 1, 2, 3 of the Fibonacci sequence.

11 Patterns in Mathematics