Importance of Number 2

                                        Important Characteristics of Number 2

Read More on Numbers in My Book “The Power of Mathematical Number “by Rajesh Kumar Thakur

1.    Two is the only number x such that the sum of the reciprocals of the powers of x equal to itself.              1 + ½ + ¼ + ¹/₈ + --- = 2

2.  Square root of 2, i.e √2 is the first known irrational number discovered by Pythagoras. Though Baudhayana also gave the approximate value of square root of 2

           समस्य द्विकरणी । प्रमाणं तृतीयेन वर्धयेत, तच्चतुर्थेनात्म चतुस्त्रिंशोनेन सविशेषतः । 

3.      Two (2) is the only even prime number.

4.      There are no integers x, y, z for which xⁿ + yⁿ = zⁿ  is valid if n > 2. This is known as Fermat’s last Theorem. This theorem was proposed by Piere de Fermat in the year 1670 and it remained a mystery for the mathematicians for over 350 years until it was proved in year 1995 by Andrew Wiles. In case n = 2, the equation turns out to be a Pythagoras Theorem.

5.      N² ± N is divisible by 2 where N is a natural number.

6.     H, I, O and X have two lines of symmetry.                                                                                                                                                                                                                                                    

 7.      The common symmetry found in nature is bilateral. A single axis has two sides one goes in positive direction and another goes in negative direction. Our bodies are bilaterally symmetrical and we naturally distinguish the thing in two ways , e.g Right and Left, Up and Down etc.

8.      A number is divisible by 2 if it ends with 0, 2, 4, 6 and 8.                                 

         Example: 248, 98634, 666, 900 are divisible by 2 but 41, 333, 79 are not divisible by 2.

9.      2 can be partitioned in two ways.

10.  A binary code is written to base 2 and has just 2 digits 0 and 1. In binary system the odd number ends with 1 and even number ends with 0. This system was first used by Leibniz in 1679 though it is referred to in a Chinese book which supposedly dates from about 3000BC. Leibniz associated 0 with nothingness and 1 with odd.  In binary number system 14 is written as 1110 and is represented as (14)_{10 =} (1110)_2.

11.  For any polyhedron, the Euler’s formula is V – E + F = 2, where V , E and F represent Vertices, Edges and Faces respectively.
12.  Atomic number of Helium is 2.

13.  Two has a unique property such that 2 + 2 = 2 x 2.
14.  Chess, Squash and Sumo wrestling are all games played by two competitors.

15.  A figure having length and breadth but no depth is called a 2- dimensional object.

16. There are 20 digits in the expansion of 2⁶⁴ but surprisingly the base 2 is disappeared.         

       2⁶⁴ = 1,84,46,74,40,73,70,95,51,616

17.All known Perfect Numbers are Even, i.e. divisible by 2

18. Goldbach conjecture says that every even number greater than 2 is the sum of two prime numbers. Example : 8 = 3 + 5

19.  In many culture 2 symbolizes balance, harmony, and partnership, as seen in the concept of yin and yang in Chinese philosophy.

20. It is the first Ramanujan Prime. In 1919, Ramanujan published a new proof of Bertrand's postulates which was first proved by Chebyshev.  At the end of the two-page published paper, Ramanujan derived a generalized result, and that is:

${\displaystyle \pi (x)-\pi \left(\frac{x}{2}\right)\ge 1,2,3,4,5,\dots \text{ for all }x\ge 2,11,17,29,41,\dots \text{ respectively}}$  where  is the prime counting function that is equal to the number of primes less than or equal to x.