Ninety Six (96)
1. It is a sixth star number.
2. It is the smallest number that can be written as the difference of 2 squares in 4 ways.
96 = 252 – 232 = 142 - 102 = 112 – 52 = 102 – 22
3. It can be expressed as the difference of factorials of two consecutive numbers.
96 = 5! – 4! = 120 – 24
4. It is the 7th number that stays same when written upside down.
5. It is the second smallest number with 6 prime factors.
96 = 3 x 2 x 2 x 2 x 2 x 2
6. It is a refactorable number. A number is called refactorable or tau number if it is divisible by the count of its divisors. 96 has 12 divisors – 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96. Such numbers were first studied by Curtis Cooper and Robert E Kennedy and later rediscovered by Simon Colton. The first 10 Tau numbers are- 1, 2, 8, 9, 12, 18, 24, 36, 40 and 56.
7. It is an octagonal number.
8. It is an abundant number.
9. It is a 33 gonal number.
10. The atomic number of Curium is 96.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
Saturday, February 27, 2016
Mathematically 95
Ninety Five (95)
1. It is the sum of 7 consecutive prime starting from 5.
95 = 5 + 7 + 11 + 13 + 17 + 19 + 23
2. It can be expressed as the sum of squares of 4 numbers distinctly.
95 = 1^2 + 2^2 + 3^2 + 9^2
3. It is a hexagonal pyramidal number.
4. It is a Thabit number. A number that can be expresses as 3 x 2n – 1 for n > 0 is known as Thabit number. It is named after Iraqi mathematician of 9th century Thabit ibn Qurra. The first ten Thabit numbers are- 2, 5, 11, 23, 47, 95, 191, 383, 767 and 1535.
5. The number of planar partition of 10 is 95.
6. The atomic number of Americium is 95.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
1. It is the sum of 7 consecutive prime starting from 5.
95 = 5 + 7 + 11 + 13 + 17 + 19 + 23
2. It can be expressed as the sum of squares of 4 numbers distinctly.
95 = 1^2 + 2^2 + 3^2 + 9^2
3. It is a hexagonal pyramidal number.
4. It is a Thabit number. A number that can be expresses as 3 x 2n – 1 for n > 0 is known as Thabit number. It is named after Iraqi mathematician of 9th century Thabit ibn Qurra. The first ten Thabit numbers are- 2, 5, 11, 23, 47, 95, 191, 383, 767 and 1535.
5. The number of planar partition of 10 is 95.
6. The atomic number of Americium is 95.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
Mathematically 94
Ninety Four (94)
1. It is a Smith number. A number is called Smith number if the sum of digits of its prime factor is equal to the sum of the digits of the number.
94 = 2 x 47 and 9 + 4 = 2 + 4 + 7
2. It is a 17- gonal number.
3. Apart from 2 and 4, it is the smallest even number which cannot be written as the sum of two distinct semi primes.
4. It is a centered 31 gonal number.
5. It can be partitioned 48 times with each term not larger than 2 and 784 times with each term not larger than 3.
6. The atomic number of Plutonium is 94. It is the notorious chemical element which doesn’t exist naturally and was first created artificially in 1940.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
1. It is a Smith number. A number is called Smith number if the sum of digits of its prime factor is equal to the sum of the digits of the number.
94 = 2 x 47 and 9 + 4 = 2 + 4 + 7
2. It is a 17- gonal number.
3. Apart from 2 and 4, it is the smallest even number which cannot be written as the sum of two distinct semi primes.
4. It is a centered 31 gonal number.
5. It can be partitioned 48 times with each term not larger than 2 and 784 times with each term not larger than 3.
6. The atomic number of Plutonium is 94. It is the notorious chemical element which doesn’t exist naturally and was first created artificially in 1940.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
Mathematically 93
Ninety Three (93)
1. With just a straight cut, a potato can be divided into 93 pieces.
2. It is an odd number with the property that the digit at ten’s place is thrice the digit at one’s place.
3. It is a 32 gonal number.
4. It can be partitioned 47 times with each tern not larger than 2 and 768 times where each term is not larger than 3.
5. It is the first member of the triplet of consecutive semi-primes 93, 94 and 95. A number is called semi primes if it can be expressed as the product of two prime numbers.
93 = 3 x 31 94 = 2 x 47 95 = 5 x 19
6. It is a palindrome number on base 2.
(93)10 = (1011101)2
7. On base 5, it is a repeated digit.
(93)10 = (333)5
8. It can be expressed as the sum of squares of three numbers. Interestingly all the three numbers used are in Arithmetic Progression with common difference 3.
93 = 2^2 + 5^2 + 8^2
9. It is the sum of 6 consecutive numbers.
93 = 13 + 14 + 15 + 16 + 17 + 18
10. It is a Blum integer. A natural number n is a Blum integer if n = p x q is a semi prime and p and q are written in the form of 4x + 3. It is named after computer scientist Manuel Blum.
93 = 3 x 31
where 3 and 31 are prime numbers
31 = 4 x 7 + 3
11. The atomic number of Neptunium is 93.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
1. With just a straight cut, a potato can be divided into 93 pieces.
2. It is an odd number with the property that the digit at ten’s place is thrice the digit at one’s place.
3. It is a 32 gonal number.
4. It can be partitioned 47 times with each tern not larger than 2 and 768 times where each term is not larger than 3.
5. It is the first member of the triplet of consecutive semi-primes 93, 94 and 95. A number is called semi primes if it can be expressed as the product of two prime numbers.
93 = 3 x 31 94 = 2 x 47 95 = 5 x 19
6. It is a palindrome number on base 2.
(93)10 = (1011101)2
7. On base 5, it is a repeated digit.
(93)10 = (333)5
8. It can be expressed as the sum of squares of three numbers. Interestingly all the three numbers used are in Arithmetic Progression with common difference 3.
93 = 2^2 + 5^2 + 8^2
9. It is the sum of 6 consecutive numbers.
93 = 13 + 14 + 15 + 16 + 17 + 18
10. It is a Blum integer. A natural number n is a Blum integer if n = p x q is a semi prime and p and q are written in the form of 4x + 3. It is named after computer scientist Manuel Blum.
93 = 3 x 31
where 3 and 31 are prime numbers
31 = 4 x 7 + 3
11. The atomic number of Neptunium is 93.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
Mathematically 92
Ninety Two (92)
1. It is an eighth pentagonal number.
2. It is the maximal number of regions into which 13 lines divide a plane.
3. The maximum number of regions into which a plane can be divided by 10 circles is 92.
4. A snub dodecahedron is a solid with 92 faces,, each consisting of 80 equilateral triangle and 12 pentagons.
5. There is a very interesting puzzle involving 92.
Puzzle: - Multiply 92 by 8, then the product by 8 and so on. List the product one under the other shifting the digit two places to the right and add, the sum of these number is a string of 9.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
1. It is an eighth pentagonal number.
2. It is the maximal number of regions into which 13 lines divide a plane.
3. The maximum number of regions into which a plane can be divided by 10 circles is 92.
4. A snub dodecahedron is a solid with 92 faces,, each consisting of 80 equilateral triangle and 12 pentagons.
5. There is a very interesting puzzle involving 92.
Puzzle: - Multiply 92 by 8, then the product by 8 and so on. List the product one under the other shifting the digit two places to the right and add, the sum of these number is a string of 9.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
Mathematically 91
Ninety One (91)
1. It is the sum of first 13 consecutive number.
1 + 2 + 3 +--- + 13 = 91
2. The sum of consecutive squares of first 6 numbers is 91.
1^2 + 2^2 + 3^2 +4^2 +5^2 + 6^2 = 91
3. A 6 x 6 square board has 91 square in total.
4. It is a centered cube number.
5. It is a pyramidal number.
6. It is the sum of cubes of two consecutive numbers.
91 = 3^3 + 4^3
7. It is a centered 15 gonal and 30 gonal numbers.
8. The number of days in a quarter year is 91. A year has 52 weeks so a quarter year has 13 weeks, each of 7 days.
9. It is a centered hexagonal number.
1 + 6 + 12 + 18 + 24 + 30 = 91
10. It is the smallest positive integer which can be expressed as the sum of distinct squares in different ways.
91 = 1^2 + 3^2 + 9^2
= 1^2 + 4^2 + 5^2 + 7^2
11. It is a repeated digit on base 9.
91 = (111)9
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
1. It is the sum of first 13 consecutive number.
1 + 2 + 3 +--- + 13 = 91
2. The sum of consecutive squares of first 6 numbers is 91.
1^2 + 2^2 + 3^2 +4^2 +5^2 + 6^2 = 91
3. A 6 x 6 square board has 91 square in total.
4. It is a centered cube number.
5. It is a pyramidal number.
6. It is the sum of cubes of two consecutive numbers.
91 = 3^3 + 4^3
7. It is a centered 15 gonal and 30 gonal numbers.
8. The number of days in a quarter year is 91. A year has 52 weeks so a quarter year has 13 weeks, each of 7 days.
9. It is a centered hexagonal number.
1 + 6 + 12 + 18 + 24 + 30 = 91
10. It is the smallest positive integer which can be expressed as the sum of distinct squares in different ways.
91 = 1^2 + 3^2 + 9^2
= 1^2 + 4^2 + 5^2 + 7^2
11. It is a repeated digit on base 9.
91 = (111)9
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
Tuesday, February 9, 2016
Mathematically 90
Ninety (90)
1. It is the product of two consecutive integers. Such numbers are called Oblong numbers because it corresponds to the area of an oblong rectangle whose length is one greater than its width.
90 = 9 x 10
2. An angle of 90 degree is called a right angle.
3. Tangents touches the circle at 90 degree.
4. It is the sum of first 9 consecutive even numbers
. 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 = 90
5. It is the sum of two successive primes.
90 = 43 + 47
6. The interior angle of a square is 90 degree.
7. It is a Harshad number because it is divisible by sum of its digits.
8. The atomic number of Thorium is 90.
9. It is a 31 gonal number.
10. A truncated dodecahedron had 90 edges.
Dr Rajesh Kr Thakur
rkthakur1974@gmail.com
1. It is the product of two consecutive integers. Such numbers are called Oblong numbers because it corresponds to the area of an oblong rectangle whose length is one greater than its width.
90 = 9 x 10
2. An angle of 90 degree is called a right angle.
3. Tangents touches the circle at 90 degree.
4. It is the sum of first 9 consecutive even numbers
. 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 = 90
5. It is the sum of two successive primes.
90 = 43 + 47
6. The interior angle of a square is 90 degree.
7. It is a Harshad number because it is divisible by sum of its digits.
8. The atomic number of Thorium is 90.
9. It is a 31 gonal number.
10. A truncated dodecahedron had 90 edges.
Dr Rajesh Kr Thakur
rkthakur1974@gmail.com
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