Eighty Five (85)
1. It can be expressed as the sum of two squares in two ways. The second pair is the sum of square of 2 consecutive numbers.
85 = 9^2 + 2^2
= 7^2 + 6^2
2. It is one of the member of a Pythagorean triplet (13, 84, 85).
85^2 = 13^2 + 84^2
3. It can be uniquely expresses as the sum of powers of 4 starting from 0 to 3.
85 = 4^0 + 4^1 +4^2 + 4^3
4. It can be partitioned 43 times with each term not larger than 3 and 645 times with each term not larger than 3
5. It is a decagonal number.
6. It is the product of two prime number and therefore is a bi-prime.
85 = 5 x 17
7. It is a centered triangular and centered square number. a centered square number is a figurative number that gives the number of dots in a square with a dot in the center and all other dots surrounding the center in a successive layer.
The first few centered square numbers are- 1, 5, 13, 25…
8. On base 4 , it is a repeated unit number.
85 = (1111)4
9. It is a centered triangular number. a centered triagnualar number is a figurative number that represents a triangle with a dot in the center and other dots surrounding in successive triangular layer. The first few centered triangular numbers are—1, 4, 10, 19, 31….
10. It is the largest known n for which ---
1^2 + 2^2 + 3^2 +---- + n^2 = 1 + 2 +3 +---+m
Dr Rajesh Kr Thakur
rkthakur1974@gmail.com
Tuesday, February 9, 2016
Monday, February 8, 2016
Mathematically 84
Eighty Four (84)
1. It is a tetrahedral number.
2. It is the sum of first 7 triangular number.
1 + 3 + 6 + 10 + 15 + 21 + 28 = 84
3. It is the sum of twin prime.
84 = 41 + 43
4. If you add 84 to 1000, the number 1084 you obtain is the smallest natural number which contains the five vowel in order.
1084 = One thousand eighty four
5. A hepteract is a seven dimensional hypercube with 84 penteract 5 faces. In geometry, a 7 cube or Hepteract is a seven dimensional hypercube with 128 vertices, 448 edges, 672 square faces, 560 cubic cells, 280 tesseract 4- faces, 84 penteract 5 faces, and 14 hexeract 6 faces.
6. It is an abundant number.
7. It is a 29-goanl number.
8. It can be partitioned 43 times with each term no longer than 2 and 631 times with each term no larger than 3.
9. It can be expressed as the sum of first 3 powers of 4 uniquely.
84 = 4^1 + 4^2 + 4^3
10. It is the maximal number of regions into which space can be divided by 7 spheres.
11. The probability of a pregnant woman having twins is 1 : 84.
12. According to Greek Anthalogy , Diophantus the Greek mathematician lived for 84 years. There is no other information known about his life except that comes from this problem which gives the result 84 on solving. The problem says---
This tomb holds Diophantus. Ah, how great a marvel! The tomb tells scientifically the measure of his life. God granted him to be a boy for 1/6 th of his life; and adding a twelfth part to this, he clothed his cheeks with down. He lit him the light of wedlock after a seventh part, and five years after his marriage he gave him a son. Alas, late born wretched child! After attaining the measure of half his father’s life, chill Fate took him. After consoling his grief by the study of numbers for four years, Diophantus ended his life. If Diophantus age is x years then we can write this algebraically as-- Which when solved gives x = 84. Diophanuts is better known as the father of algebra.
1. It is a tetrahedral number.
2. It is the sum of first 7 triangular number.
1 + 3 + 6 + 10 + 15 + 21 + 28 = 84
3. It is the sum of twin prime.
84 = 41 + 43
4. If you add 84 to 1000, the number 1084 you obtain is the smallest natural number which contains the five vowel in order.
1084 = One thousand eighty four
5. A hepteract is a seven dimensional hypercube with 84 penteract 5 faces. In geometry, a 7 cube or Hepteract is a seven dimensional hypercube with 128 vertices, 448 edges, 672 square faces, 560 cubic cells, 280 tesseract 4- faces, 84 penteract 5 faces, and 14 hexeract 6 faces.
6. It is an abundant number.
7. It is a 29-goanl number.
8. It can be partitioned 43 times with each term no longer than 2 and 631 times with each term no larger than 3.
9. It can be expressed as the sum of first 3 powers of 4 uniquely.
84 = 4^1 + 4^2 + 4^3
10. It is the maximal number of regions into which space can be divided by 7 spheres.
11. The probability of a pregnant woman having twins is 1 : 84.
12. According to Greek Anthalogy , Diophantus the Greek mathematician lived for 84 years. There is no other information known about his life except that comes from this problem which gives the result 84 on solving. The problem says---
This tomb holds Diophantus. Ah, how great a marvel! The tomb tells scientifically the measure of his life. God granted him to be a boy for 1/6 th of his life; and adding a twelfth part to this, he clothed his cheeks with down. He lit him the light of wedlock after a seventh part, and five years after his marriage he gave him a son. Alas, late born wretched child! After attaining the measure of half his father’s life, chill Fate took him. After consoling his grief by the study of numbers for four years, Diophantus ended his life. If Diophantus age is x years then we can write this algebraically as-- Which when solved gives x = 84. Diophanuts is better known as the father of algebra.
Mathematically 83
Eighty Three (83)
1. It is a Prime number which can be expressed as the sum of 3 consecutive primes as well as the sum of 5 consecutive primes.
83 = 23 + 29 + 31
= 11 + 13 + 17 + 19 + 23
2. It is also the sum of first 3 primes that ends with 1.
83 = 11 + 31 + 41
3. The atomic number of Bismuth is 83. It is the heaviest stable elements.
4. It can be portioned 42 times with each term not larger than 2.
5. It is a Sophie Germain Prime number. A prime number p is a Sophie Germain prime if 2p +1 is also a prime number. For p = 83 , 2p + 1 = 167 is also a prime number. It is named after the French mathematician Marie Sophie Germain.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
1. It is a Prime number which can be expressed as the sum of 3 consecutive primes as well as the sum of 5 consecutive primes.
83 = 23 + 29 + 31
= 11 + 13 + 17 + 19 + 23
2. It is also the sum of first 3 primes that ends with 1.
83 = 11 + 31 + 41
3. The atomic number of Bismuth is 83. It is the heaviest stable elements.
4. It can be portioned 42 times with each term not larger than 2.
5. It is a Sophie Germain Prime number. A prime number p is a Sophie Germain prime if 2p +1 is also a prime number. For p = 83 , 2p + 1 = 167 is also a prime number. It is named after the French mathematician Marie Sophie Germain.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
Mathematically 82
Eighty two (82)
1. It is the product of two primes with the unique property that the sum of digits of 82 is equal to the product of sum of digits of its prime factors.
82 = 2 x 41 and 8+ 2 = 10 = 2 x ( 4 + 1)
2. It can be expressed as the sum of two primes in 5 different ways.
82 = 3 + 79
= 11 + 71
= 23 + 59
= 29 + 53
= 41 + 41
3. It is a 15 gonal number as well as a centered 27- gonal number.
4. Six hexagons can be linked in 82 different ways. A figure made from 6 hexagons is called hexahex. One arrangement is shown here.
5. The atomic number of Lead is 82.
6. On Ternary base it is a Palindrome digits. (10001)3 = (82)10.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
1. It is the product of two primes with the unique property that the sum of digits of 82 is equal to the product of sum of digits of its prime factors.
82 = 2 x 41 and 8+ 2 = 10 = 2 x ( 4 + 1)
2. It can be expressed as the sum of two primes in 5 different ways.
82 = 3 + 79
= 11 + 71
= 23 + 59
= 29 + 53
= 41 + 41
3. It is a 15 gonal number as well as a centered 27- gonal number.
4. Six hexagons can be linked in 82 different ways. A figure made from 6 hexagons is called hexahex. One arrangement is shown here.
5. The atomic number of Lead is 82.
6. On Ternary base it is a Palindrome digits. (10001)3 = (82)10.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
Matheamatically 81
Eighty One (81)
1. It is a square number.
9^2 = 81
2. It is the sum of first nine odd integers.
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81
3. It is the square of sum of its digits. Apart from 0 and 1 it is the only number with this property.
81 = ( 8 + 1)^2
4. It is the fourth power of a number.
3^4 = 81
5. It is the smallest square whose sum of divisors is also a square number. The divisors of 81 are 1, 3, 9, 27 and 81 and their sum is 121 which is a square number.
1 + 3 + 9 + 27 + 81= 121 = 11^2
6. It is the sum of 9 consecutive numbers.
5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 = 81
7. The fraction 1/ 81= 0.01245679 012345679… is a repeating decimal containing every digits from 0 to 9 except 8.
8. On base 10, it is a Harshad number.
9. It is a heptagonal number as well as centered octagonal number.
10. The atomic number of Thallium is 81.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
1. It is a square number.
9^2 = 81
2. It is the sum of first nine odd integers.
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81
3. It is the square of sum of its digits. Apart from 0 and 1 it is the only number with this property.
81 = ( 8 + 1)^2
4. It is the fourth power of a number.
3^4 = 81
5. It is the smallest square whose sum of divisors is also a square number. The divisors of 81 are 1, 3, 9, 27 and 81 and their sum is 121 which is a square number.
1 + 3 + 9 + 27 + 81= 121 = 11^2
6. It is the sum of 9 consecutive numbers.
5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 = 81
7. The fraction 1/ 81= 0.01245679 012345679… is a repeating decimal containing every digits from 0 to 9 except 8.
8. On base 10, it is a Harshad number.
9. It is a heptagonal number as well as centered octagonal number.
10. The atomic number of Thallium is 81.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
Mathematically 80
Eighty (80)
1. It is the product of 5 primes.
80 = 2 x 2 x 2 x 2 x 5
2. It is a semi perfect number. There are several divisors of 80 –1, 2, 4, 5, 8, 10, 16, 20, 40 and 80.
Adding some of the divisors we get 80 making it a semi perfect number.
80 = 1 + 4 + 5 + 10 + 20 + 40
3. It is the smallest number with the property that n and n+1 are both product of 4 or more primes.
80 = 2 x 2 x 2 x 2 x 5
81 = 3 x 3 x 3 x 3
4. It can be expressed as the sum of two primes in 4 distinct ways.
80 = 7 + 73 = 13 + 67 = 19 + 61 = 37 + 43
5. It is an abundant number.
6. It is a Harshad number.
7. The atomic number of Mercury is 80.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
1. It is the product of 5 primes.
80 = 2 x 2 x 2 x 2 x 5
2. It is a semi perfect number. There are several divisors of 80 –1, 2, 4, 5, 8, 10, 16, 20, 40 and 80.
Adding some of the divisors we get 80 making it a semi perfect number.
80 = 1 + 4 + 5 + 10 + 20 + 40
3. It is the smallest number with the property that n and n+1 are both product of 4 or more primes.
80 = 2 x 2 x 2 x 2 x 5
81 = 3 x 3 x 3 x 3
4. It can be expressed as the sum of two primes in 4 distinct ways.
80 = 7 + 73 = 13 + 67 = 19 + 61 = 37 + 43
5. It is an abundant number.
6. It is a Harshad number.
7. The atomic number of Mercury is 80.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
Matheamatically 79
Seventy Nine (79)
1. It is an odd prime number.
2. It is the sum of three consecutive prime. More interestingly, its reverse 97 is the sum of the reversible prime.
79 = 11 + 31 + 37
97 = 11 + 13 + 73
3. It is a Gaussian prime that can be written in the form of 4n + 3.
79 = 4 x 19 + 3
4. It can be written as the sum of their digits added to the product of their digits.
79 = (7 + 9) + (7 x 9)
In fact, all primes ending with 9 can be expressed as the sum of their digits added to the product of their digits.
5. It is a Pillai prime because 23! + 1 is divisible by 79, but 79 is not one more than a multiple of 23.
6. The atomic number of Gold is 79.
7. It is the maximal number of regions into which 12 lines divide a plane.
8. It is a 13-gonal as well as 26-gonal number.
9. It is a Kynea number. A Kynea number is an integer written in the form of .
The Kenya numbers are 7, 23, 79, 287, 1087...
10. It is a sexy prime number. Sexy primes are prime numbers that differ by 6.
The first 5 sexy prime pairs are – (5, 11), (7, 13), (11, 17), (13, 19), (17, 23) ---
There are infinite many sexy prime triplets and quadruplets numbers. The sexy prime triplets are three prime numbers that differ by 6 and the same happens with the quadruplets. (7, 13, 19), (17, 23, 29), (31, 37, 43) are the examples of sexy prime triplets whereas (5, 11, 17, 23), (11, 17, 23, 29)... are the example of sexy prime quadruplets.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
1. It is an odd prime number.
2. It is the sum of three consecutive prime. More interestingly, its reverse 97 is the sum of the reversible prime.
79 = 11 + 31 + 37
97 = 11 + 13 + 73
3. It is a Gaussian prime that can be written in the form of 4n + 3.
79 = 4 x 19 + 3
4. It can be written as the sum of their digits added to the product of their digits.
79 = (7 + 9) + (7 x 9)
In fact, all primes ending with 9 can be expressed as the sum of their digits added to the product of their digits.
5. It is a Pillai prime because 23! + 1 is divisible by 79, but 79 is not one more than a multiple of 23.
6. The atomic number of Gold is 79.
7. It is the maximal number of regions into which 12 lines divide a plane.
8. It is a 13-gonal as well as 26-gonal number.
9. It is a Kynea number. A Kynea number is an integer written in the form of .
The Kenya numbers are 7, 23, 79, 287, 1087...
10. It is a sexy prime number. Sexy primes are prime numbers that differ by 6.
The first 5 sexy prime pairs are – (5, 11), (7, 13), (11, 17), (13, 19), (17, 23) ---
There are infinite many sexy prime triplets and quadruplets numbers. The sexy prime triplets are three prime numbers that differ by 6 and the same happens with the quadruplets. (7, 13, 19), (17, 23, 29), (31, 37, 43) are the examples of sexy prime triplets whereas (5, 11, 17, 23), (11, 17, 23, 29)... are the example of sexy prime quadruplets.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
Subscribe to:
Posts (Atom)
-
Palindromic Number:- Numbers which remains the same when read from the left to right or vice-versa. Indian mathematician Mahavira has men... -
Importance of 5 1. It is the fifth number of Fibonacci sequence. In Fibonacci sequence the nex...
-
Seventeen (17) 1. Seventeen can be poartioned in 297 ways. 2. Studies have shown that if you ask the people to pick...