3 Famous Number Patterns and Analysis With Examples

 The Fibonacci Sequence

The Fibonacci sequence is a series of numbers

0,1,1,2,3,5,8,13,21,34,..........

The next number is found by adding up the two numbers before it -

The 2 is found by adding up the two numbers before it(1+1).

The 3 is found by adding the two numbers before it (1+2).

The 5 is (2+3),  and so on.

For example, the next number in the sequence above is 21+34=55

Longer List

0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368,75025.121393,196418,317811,514229,………

The sequence goes even, odd, odd, even, odd, odd, even, odd, odd,........

0,1,1,2,3,5,8,13,21,34,55,69,.........

Because adding two odd numbers produces an even number, but adding even and odd ( in any order) produces an odd number. 

Pascal Triangle

One of the most interesting number patterns in Pascal's triangle(named after Blaise Pascal, a famous French Mathematician and Philosopher).

To build the triangle, start with 1 at the top, then continue placing numbers below it in a triangular pattern. 

Patterns Within Triangles

1. Diagonals numbers

2. Symmetry

3. Horizontal sums

4. Exponents of 11

Ramanujan's Magic Square

A magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns and both diagonals sum to the same constant.

A normal magic square contains the integers from 1 to n square. The term magic square is also sometimes used to refer to any of the various types of word square. 

Ramanujan, a magic square is a special kind of magic square that was invented by the Indian mathematician Srinivasa Ramanujan. It is a 3*3 grid in which each of the nine cells contains a number from 1 to 9 and each row, column, and diagonal have the same sum. 

Final Thoughts

These patterns, ranging from the simplicity of arithmetic sequences to the complexity of Fibonacci numbers, weave a tapestry of mathematical beauty and logic.

Exploring these patterns not only enhances our understanding of mathematical principles but also unveils the interconnectedness between seemingly disparate numerical concepts. 

 Edited By - Zoya 

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