Number Zone by Dr Rajesh Kumar Thakur

Friday, November 1, 2024

November 2, 2024

Everyday has its own importance.

2nd November 2024 = 307th day of year 2024

307 is the number whose square is a Palindrome number

$307^{2} = 94249$

George Boole (2 Nov 1815 - 8 Dec 1864) : A self taught English mathematician , who was the son of a shoemaker. He is best known as the author of 'The Laws of Thought' which contains Boolean Algebra, a branch of mathematics widely used in computer algorithm.

Plaque at George Boole's House

A plaque beneath Boole's window in Lincoln Cathedral

Boole's Grave at Ireland

Bronze statue of Boole at Lincoln Central Train Station

(Source:- All four images are taken from Wikipedia George Boole - Wikipedia)

On 2nd November 2015 , Google released a Doodle on Boole to mark his 200 th Birthday.

Interesting things to know George Boole

1. His wife name was Mary Everest Boole ( her uncle was George Everest, whose name is given to the highest peak of the world- Mount Everest)

2. In late November 1864, Boole walked, in heavy rain, from his home at Lichfield Cottage in Ballintemple to the university, a distance of three miles, and lectured wearing his wet clothes. He soon became ill, developing pneumonia. As his wife believed that remedies should resemble their cause, she wrapped him in wet blankets – the wet having brought on his illness. Boole's condition worsened and on 8 December 1864, he left for heavenly abode.

Thanks for Reading

Give your comments in the comment section

Rajesh Kr Thakur

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:

\pi (x)-\pi \left({\frac {x}{2}}\right)\geq 1,2,3,4,5,\ldots {\text{ for all }}x\geq 2,11,17,29,41,\ldots {\text{ respectively}}

where

\pi (x)

is the prime counting function that is equal to the number of primes less than or equal to x.

Wednesday, September 13, 2023

List of Some Interesting Numbers

Dear Friends ---

Numbers are very fascinating. Every number is unique and I have written the properties of number 1 - 100 in my blog highlighting some of their characteristics.

I have been very interested in collecting the name of some of the numbers alphabetically and the list is yet incomplete. Please find the name of some of the numbers I have collected from different sources --

1.   Abundant Number
2.   Achilles Number
3.   Admirable Number
4.   Alternating Number
5.   Amenable Number
6.   Amicable Number
7.   Anti- Perfect Number
8.   Apocalyptic Number
9.   Astonishing Number
10.                Automorphic Number
11.                Beast Number
12.                Bell Number
13.                Binomial Number
14.                Cake Number
15.                Cube Number
16.                Catalan Number
17.                Cardinal Number
18.                Composite Number
19.                Congruent Number
20.                Cullen Number
21.                Cyclic Number
22.                Deficient Number
23.                Deceptive Number
24.                Decagonal Number
25.                Economical Number
26.                Esthetic Number
27.                Eulerian Number
28.                Evil Number
29.                Even number
30.                Factorial Number
31.                Fibonacci Number
32.                Friedman Number
33.                Gilda Number
34.                Happy Number
35.                Harmonic Number
36.                Harshad Number
37.                Heptagonal number
38.                Hex number
39.                Hexagonal number
40.                Highly composite number
41.                Hoax number
42.                Hungry number
43.                Impolite number
44.                Inconsummate number
45.                Irrational number
46.                Junctioin number
47.                Kaprekar number
48.                Lehmer number
49.                Leyland number
50.                Lonely number
51.                Lucas number
52.                Lucky number
53.                Magic number
54.                Modest number
55.                Motzkin number
56.                Narcissistic number
57.                Natural number
58.                Nonagonal number
59.                Nude number
60.                Octagonal number
61.                Odd number
62.                Ormiston number
63.                Palindrome number
64.                Pancake number
65.                Pandigital number
66.                Partition number
67.                Pentagonal number
68.                Perfect number
69.                Perrin number
70.                Persistent number
71.                Palindrome number
72.                Practical number
73.                Prime number
74.                Primorial number
75.                Pseudo perfect number
76.                Rare number
77.                Rational number
78.                Real number
79.                Repdigit number
80.                Sastry number
81.                Self number
82.                Semi prime number
83.                Sliding number
84.                Smith number
85.                Sophie German number
86.                Square number
87.                Taxi cab number
88.                Tetrahedral number
89.                Tetranacci number
90.                Transcendental number
91.                Triangular number
92.                Tribonacci number
93.                Twin prime number
94.                Uban number
95.                Ulam number
96.                Untouchable number
97.                Vampire number
98.                Wasteful number
99.                Weird number
100.            Woodall number
101.            Zeisel number
102.            Zuckerman number

I do promise that I will start writing about all these numbers in coming days but that needs your support.

Regards

Dr Rajesh Kumar Thakur