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

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

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

Mathematically 89

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

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

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

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