Eighty Nine (89)
1. It is a Fibonacci prime number.
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89…
2. The inverse of 89 gives a fraction with a sequence of 44 recurring digits.
1/89 = 0. 01123595505617977528089887640449438202247191…
The best part of the result is that this number is the sum of the sequence of number from the Fibonacci series where by each number moves a decimal point to the right.
0.01 + 0.001 + 0.0002 + 0.00003 +0.000005 +0.0000008 +0.00000013 +0.000000021 + 0.0000000034 +…=0.011235955---
3. The first pair of consecutive prime that differ by 8 is 89 and 97.
4. It is a Markov number discovered by Andrey Markoff. A Markov number is a positive integer x, y or z such that-
x^3 +y^3+z^3 = 3xyz
The first ten Markov numbers are 1, 2, 5, 13, 29, 34, 89, 169, 194 and 233.
5. It is a Chen prime named after Chen Jingrun. A number p is a Chen prime if p+2 is either a prime or a product of two primes. The first ten Chen primes are- 2, , 5, 7, 11, 13, 17, 19, 23 and 29.
6. The atomic number of Actinium is 89.
Dr Rajesh K Thakur
rkthakur1974@gmail.com
Tuesday, February 9, 2016
Mathematically 88
Eighty Eight (88)
1. A piano has 88 keys with 36 black and 52 white.
2. It is the 6th number that stays same when written upside down.
3. It is the only known number whose square has no isolated digits.
88^2 = 7744
4. It is the sum of 4 consecutive primes.
88 = 17 + 19 + 23 + 29
5. It is an untouchable number. An untouchable number is a positive integer that can’t be expressed as the sum of all the proper divisor of any number.
The first 10 untouchable numbers are- 2, 5, 52, 88, 96, 120, 124, 146, 162 and 188.
6. International Astronomical Union has defined 88 constellations divided into 8 families—Ursa Major family, Zodiacal family, Perseus family, Heavenly waters, Orion Group, Bayer Group, La Cille family and Hercules family.
7. It is a 16 gonal number.
8. It is an abundant number.
9. It is a centered 29-gonal number.
Dr Rajesh K Thakur
rkthakur1974@gmail.com
1. A piano has 88 keys with 36 black and 52 white.
2. It is the 6th number that stays same when written upside down.
3. It is the only known number whose square has no isolated digits.
88^2 = 7744
4. It is the sum of 4 consecutive primes.
88 = 17 + 19 + 23 + 29
5. It is an untouchable number. An untouchable number is a positive integer that can’t be expressed as the sum of all the proper divisor of any number.
The first 10 untouchable numbers are- 2, 5, 52, 88, 96, 120, 124, 146, 162 and 188.
6. International Astronomical Union has defined 88 constellations divided into 8 families—Ursa Major family, Zodiacal family, Perseus family, Heavenly waters, Orion Group, Bayer Group, La Cille family and Hercules family.
7. It is a 16 gonal number.
8. It is an abundant number.
9. It is a centered 29-gonal number.
Dr Rajesh K Thakur
rkthakur1974@gmail.com
Mathematically 87
Eighty Seven (87)
Number
Divisors
1. It is the sum of divisors of the first ten integers.
2. It is the sum of square of the first four primes.
87 = 2^2 + 3^2 + 5^2 + 7^2
3. It is the sum of 6 consecutive numbers.
87 = 12 + 13 + 14 + 15 + 16 + 17
4. It is a 30 –gonal number.
5. It can be partitioned 44 times with each term not larger than 2
6. It is regarded as an unlucky number in Cricket as it is 13 short of 100.
Dr Rajesh Kr Thakur
rkthakur1974@gmail.com
Number
1. It is the sum of divisors of the first ten integers.
2. It is the sum of square of the first four primes.
87 = 2^2 + 3^2 + 5^2 + 7^2
3. It is the sum of 6 consecutive numbers.
87 = 12 + 13 + 14 + 15 + 16 + 17
4. It is a 30 –gonal number.
5. It can be partitioned 44 times with each term not larger than 2
6. It is regarded as an unlucky number in Cricket as it is 13 short of 100.
Dr Rajesh Kr Thakur
rkthakur1974@gmail.com
Mathematically 86
Eighty Six (86)
1. It is the largest known n for which 2^n contains no zeros.
2^86 = 77, 371,252,455,336,267,181,195,264
2. It is the sum of 4 consecutive squares.
86 = 3^2 + 4^2 + 5^2 + 6^2
3. It is a member of a Padovan sequence. It is similar to Fibonacci sequence. The sequence runs from 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16 ,21, 28, 37, 49, 65, 86 …
The Padovan sequence is --A0 = 0; A1 = 1; A2 = 1; AN+1 = AN-1 + AN-2.
4. It is the total number of parts in all partitions of 8.
5. An ancient tablet was discovered with 86 notches on it. This tablet may also be a pregnancy calendar designed to estimate when a pregnant woman will give birth. This tablet is 32400 years old found in 1979 in Germany. On one side of the tablet is the man like being with his legs apart and arms raised. Between his legs hangs what could be a sword and his waist in narrow. His left leg is shorter than his right one. It is the number of days that must be subtracted from a year to equal the average number of days of a human gestation. It gives the roughly estimation that a child is born after 9 months.
365 – 86 = 279 = 9 x 30 + 9
6. It is a repeated digit on base 6.
86 = (222)6
7. It is the sum of four consecutive integers.
86= 20 + 21 + 22 + 23
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
1. It is the largest known n for which 2^n contains no zeros.
2^86 = 77, 371,252,455,336,267,181,195,264
2. It is the sum of 4 consecutive squares.
86 = 3^2 + 4^2 + 5^2 + 6^2
3. It is a member of a Padovan sequence. It is similar to Fibonacci sequence. The sequence runs from 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16 ,21, 28, 37, 49, 65, 86 …
The Padovan sequence is --A0 = 0; A1 = 1; A2 = 1; AN+1 = AN-1 + AN-2.
4. It is the total number of parts in all partitions of 8.
5. An ancient tablet was discovered with 86 notches on it. This tablet may also be a pregnancy calendar designed to estimate when a pregnant woman will give birth. This tablet is 32400 years old found in 1979 in Germany. On one side of the tablet is the man like being with his legs apart and arms raised. Between his legs hangs what could be a sword and his waist in narrow. His left leg is shorter than his right one. It is the number of days that must be subtracted from a year to equal the average number of days of a human gestation. It gives the roughly estimation that a child is born after 9 months.
365 – 86 = 279 = 9 x 30 + 9
6. It is a repeated digit on base 6.
86 = (222)6
7. It is the sum of four consecutive integers.
86= 20 + 21 + 22 + 23
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
Mathematically 85
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
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
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
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