Cool math titbits
umasundresh
2021
National Mathematics Day
December 22 is celebrated as the National Mathematics Day in honor of the birth anniversary of Indian Mathematical genius Srinivasa Ramanujan.
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Ruth-Aaron Pair
Ruth-Aaron pair consists of consecutive numbers such that the sum of their prime factors are equal.
Ruth and Aaron are baseball players. Aaron scored 715 home runs and broke the previous record of 714 home runs held by Ruth.
The name Ruth-Aaron pair was given by Carl Pomerance. It was first noticed and solved by his colleague’s student.
The prime factors of 715 and 714 are as follows,
715 = 2 X 3 X 7 X 17
714 = 5 X 11 X 13
The sum of the prime factors of both the numbers is 29 respectively.
The mathematicians Carl Pomerance and his colleagues Carol Nelson and David.E.Penny tried to find more Ruth-Aaron pairs, Some of the few examples are given below
- 5 and 6
5 = 5
6 = 2 X 3
2. 8 and 9
8 = 2 X 2 X 2
9 = 3 X 3
3. 15 and 16
15 = 3 X 5
16 = 2 X 2 X 2 X 2
4. 77 and 78
77 = 7 X 11
78 = 2 X 3 X 13
5. 714 and 715
715 = 2 X 3 X 7 X 17
714 = 5 X 11 X 13
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Bertrand’s Postulate
For every number greater than 1, there is at least one prime number between the number and its double.
Bertrand’s postulate states that there is at least one prime number p, such that n < p < 2n.
Pictorial representation
This Postulate was first proposed by Bertrand in 1845.
However, Bertrand did check that his conjecture was true up to 3 million.
It was first proved in 1850 by Chebyshev so is also called the Bertrand-Chebyshev Theorem.
Chebyshev on a 2021 stamp of Russia
The Indian Mathematician Ramanujan, who was not aware of Chebyshev’s proof, came up with an easier proof on 1919.
In 1932, a Hungarian Mathematician, Paul Erdos, came with another different proof.
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Bertrand Russell
Bertrand Russell (18 – 05 – 1872 to 02 – 02 -1970), a famous British mathematician.
In his autobiography he mentioned
It was my desire to know more about Mathematics that kept me away from suicide
Bertrand Russell
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Goldbach’s Conjecture
Goldbach’s conjecture is one of the oldest unsolved problems in mathematics.
Any even number greater than 2 can be written as the sum of two prime number.
Every odd whole number greater than 5 can be written as the sum of three primes.Â
Goldbach’s conjectures
Goldbach, a Prussian mathematician(1690-1764)
On 7 June 1742, Goldbach wrote a letter to the mathematician Euler in which he proposed the conjectures he found.
Euler responded back on 30 June 1742 as
Every integer greater than 2 is a sum of two primes, I regard this as a completely certain theorem, although I cannot prove it.
Euler
Though the Goldbach’s conjecture looks simple to understand, it has not yet been proved.
In the modern times, the conjectures proposed by Goldbach is identified as weak or strong Goldbach conjecture.
STRONG GOLDBACH CONJECTURE
Any even whole number greater than 2 can be written as the sum of two prime number.
WEAK GOLDBACH CONJECTURE
Every odd whole number greater than 5 can be written as the sum of three primes.Â
In 2013, Harold Helfgott, a Peruvian mathematician released two papers claiming the proof of Goldbach weak conjecture and The proof was accepted for publication in the Annals of mathematics series in 2015, and has been undergoing further review and revisions.
In March 2000 the publishers of the book ‘Uncle Petros and Goldbach’s conjecture (Bloomberg in the USA and Faber and Faber in the UK) offered a prize of one million dollars for anyone who could prove the Goldbach’s conjecture
Any even whole number greater than 2 can be written as the sum of two prime number.
The prize was kept open for two years, but nobody claimed it.
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Co-prime numbers
A set of numbers which has 1 as the only common factor is called as co-prime.
We require at least two numbers to check whether they are co-prime or not, they are also called as co-prime pair.
The numbers need not be prime numbers to form a co-prime.
Finding whether any set of numbers are co-prime is very easy ✌.
Finding GCF gives the answer
If their GCF is 1, then that is co-prime.
GCF or HCF of the set of numbers should be 1.
Properties of Co-prime numbers
How to check Co-Prime numbers?
Happy learning!!!
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Odd(number) Fact
A cool fact about odd numbers.
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2520 – Amazing fact about this number.
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Dudeney Number
Henry Dudeney, a self taught Mathematician known for his puzzles, first noted the existence of these numbers while framing one of his puzzles.
What’s so special about these numbers?
What is the pattern followed behind the construction of these numbers?
Yes! There is a very interesting pattern behind these numbers.
Let’s check that pattern in the following video.
