WELCOME TO THE EXCITING WORLD OF MATHEMATICS

Dear class XII Students, Hope this time all of you must have performed well in the exam. I am providing you with the question paper and the solution key. Question Paper Solution Key   Here is the Sample Paper released by CBSE for 2016 exam. Click here for the sample papers of the other subjects. You may also  check my  Previous Posts   where reference material, assignments, book by DOE(govt. Schools) etc. All the best for your board examination. Amit Sir

Dear Reader, Srinivasa Ramanujan (22 December 1887 – 26 April 1920) was an Indian mathematician, who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. Ramanujan independently compiled nearly 3900 results (mostly identities and equations). His work continues to inspire mathematicians even today!  Srinivasa Ramanujan, born into a poor Brahmin family at Erode on Dec. 22, 1887, attended school in nearby Kumbakonam. By the time he was 13, he could solve unaided every problem in Loney's Trigonometry, and at 14 he obtained the theorems for the sine and the cosine that had been anticipated by L. Euler. Ramanujan became so absorbed in mathematics that when he entered the local government college in 1904 with a merit scholarship, he neglected his other subjects and lost the scholarship. Ramanujan married in 1909, and while working as a clerk he continued his mathematical investigations. In January 1913 Ramanujan...

Dear Reader, CRPF Public School has fulfilled its motto of striving towards excellence by organizing and successfully completing its Sixth Intra School Mathematics Olympiad on 6 November 2015. Around 250 students enthusiastically participated in the Olympiad held in school premises. Hopefully, it was a great learning experience for all. It surely provided an extended platform for all the participating students and it is wished that it is utilized to its fullest. Check out the result here: VI-VIII RANK HOLDERS IX - XII RANK HOLDERS VI-XII MERIT HOLDERS Congratulations to all the rank and merit holders for their brilliant performance in the Olympiad. You may again like to see the  question papers and their solution

Dear Reader, Math is important. It really is. Despite how you felt about algebra class or geometry class or even basic addition and subtraction, math is a life skill that applies to everyone, not just accountants and engineers. It is the language of many fields, some of which may surprise you. But math matters, in more ways than one. And while numbers and equations are a necessary evil to some and pure enjoyment to others, we need math to live. Below are five reasons why math is worth knowing. Starting with… Building Stuff: Balancing a cheque-book? Dividing rent among four roommates? Determining your share of the electric bill? How about taxes and student loans? Paying bills is the worst, no doubt about it. But you need to know some math in order to stay on top of your finances, balance your budget, and avoid all those overdrafts. Cooking: Surprised? Baking cupcakes and roasting a chicken requires math skills. You need to measure the ingredients in terms of teaspoon, tables...

1.  Russian King Peter the Great announced that no member of the Royal Family should marry until they pass in arithmetic, geometry and navigation. 2. There is no equilateral triangle, the coordinates of whose vertices are all integers. 3. There are only five Heronian triangles (triangles having integer sides) such that the perimeter is equal to the area. They are: (5, 12, 13) , (6, 8, 10) , (6, 25, 29) , (7, 15, 20) and (9, 10, 17). The first two triangles are right triangles also. 4. A plane can be filled with squares, equilateral triangles and regular hexagons. No other regular polygons can fill the plane without gaps. 5. Three legged stool is more stable than any other stool. The principle underlying is this fact is we can draw only one circle through three given points which are not collinear. That is why old people walk with the assistance of a stick (third leg) , or even think of tripod. 6. An angle of 3 degrees is the only constructible angle of prime mea...

Dear All, Mathematics, often called as language of nature has become an integral part of everyone’s life. In today's highly competitive world, one has to bear a lot of mental stress and also have to get involved in so many things in order to acquire knowledge. This is where co-scholastic activities play a very significant role. They provide the much needed exposure for a student. CRPF Public School has fulfilled its motto of striving towards excellence by organizing and successfully completing its Fifth Intra School Mathematics Olympiad on 6 November 2015. Around 250 students enthusiastically participated in the Olympiad held in school premises. Such Olympiads and events provide a great and extended platform for the students to nurture and showcase their ability and talent. It was a towering learning experience for the students of the school from class VI to XII. To encourage students, merit certificates will be given to those scoring at least 60% along with the normal prize...

A box of manuscripts and three notebooks. That's all that's left of the work of Srinivasa Ramanujan, an Indian mathematician who lived his remarkable but short life around the beginning of the twentieth century. Yet, that small stash of mathematical legacy still yields surprises. Two mathematicians of Emory University, Ken Ono and Sarah Trebat-Leder, have recently a made a fascinating discovery within its yellowed pages. It shows that Ramanujan was further ahead of his time than anyone had expected, and provides a beautiful link between several milestones in the history of mathematics. And it all goes back to the innocuous-looking number 1729. Ramanujan's story is as inspiring as it is tragic. Born in 1887 in a small village around 400 km from Madras (now Chennai), Ramanujan developed a passion for mathematics at a young age, but had to pursue it mostly alone and in poverty. Until, in 1913, he decided to write a letter to the famous Cambridge number theorist G.H. Hardy...

George Boole (2 November 1815 – 8 December 1864) , the British mathematician whose work on logic laid many of the foundations for the digital revolution, has been honoured on the 200th anniversary of his birth with a special Google Doodle. He was an English mathematician, educator, philosopher and logician. He worked in the fields of differential equations and algebraic logic, and is best known as the author of The Laws of Thought which contains Boolean algebra. Boolean logic is credited with laying the foundations for the information age. George Boole was the son of a shopkeeper. This working class of people was not given a high level of education. He had common schooling and a commercial course. His father, who had studied some mathematics privately, tutored George in the subject. George wanted to learn Latin and Greek so that he could advance in society. He was given some basic tutoring from the local bookseller, a friend of his father. George managed to learn Latin by ...

Dear class XI Students, I hope that you must have performed well in the Mathematics exam held today i.e. 26 September 2015. I am providing you with the question paper and the solution key. Question Paper Solution Key All the best for your board examination. Amit Sir

Dear class XII Students, I hope that you must have performed well in the Mathematics exam held today i.e. 18 September 2015. I am providing you with the question paper and the solution key. Question Paper Solution Key All the best for your board examination. Amit Sir

Dear Reader, Today I watched the movie Ramanujan (2014) , the only movie ever made about life of genius Indian mathematician Srinivasa Ramanujan, . Though it was in tamil but to one who worship him like a God , language was not a barrier. Well, thanks to english subtitles. It is really a very nice movie. Every Mathematics lover should watch this movie. Also those who have not read his biography 'A man who knew infinity' by Robert Kanigel, should spare some time and must read that book. Amit Bajaj

Dear Students, Hope you have done well in Math’s XII class weekly test held today. I am providing Question paper and its solution key for your ready reference. Question Paper              Solution Key All the best! Amit Sir

Dear Reader, Well, today is Pi Approximation Day. Pi Approximation Day celebrates the mathematical constant π (pi). It is observed on July 22, due to π being roughly equal to 22/7. The fractional approximation of π ,22⁄7, resembles the date July 22 in the day/month format, where it is written 22/7. Pi Approximation Day is therefore celebrated on July 22. In geometry, pi is defined as the ratio of a circle's circumference to its diameter. July 22, often written as 22/7, is an appropriate day to explore pi, since 22 divided by 7 is an approximation of pi. Pi Approximation Day is celebrated in a number of ways, including contests to memorize pi to the most decimal places, solving math problems involving pi, discovering the history of pi, ruminating on how life would be different without pi and—of course—eating pie. So, enjoy this mathematical day ... Amit Sir

1. A Beautiful Mind (2001) 2. A Brilliant Young Mind (2014) 3. Good Will Hunting (1997) 4. IQ(1994) 5. The Number 23 (2007) 6. Proof (2005) 7. Contact (1997) 8. Sphere (1998) 9. Stand and Deliver (1988) 10. cube(1997) 11. 21 (2008) 12. The 4th Dimension (2006) 13. Bianca (1984) 14. Fermat's Last Tango (2001 Video) 15. Fermat's Room (2007) 16. Hotel Hilbert (1996 TV Movie) 17. Numb3rs (2005) 18. The Man Without a Face (1993) 19. A Brief History of Time (1992) 20. The Theory of Everything (2014 film) 21. Primer (2004) 22. Enigma (2001) 23. Sneakers(1992) 24. 21 grams (2003) 25. Pi(1998) 26. Straw dogs (1971) 27. A summer's tale (1996)

How would you continue the sequence 1,2,3,4,5,6,7,8,9? The next number might be: • 10, if this is the sequence of natural numbers; • 1, if this is the sequence of the digital sums of natural numbers; • 11, if this the sequence of palindromes; • 0, if this is the sequence of digital products of natural numbers; • 13, if this is the sequence of numbers such that 2 to their powers doesn’t contain 0; • 153, if this is the sequence of numbers that are sums of fixed powers of their digits; • 22, if this is the sequence of numbers for which the sum of digits equals the product of digits; or • any number you want.

1. 30 is the sum of the first four squares, which makes it a square pyramidal number. 2. The icosahedron and the dodecahedron are Platonic solids with 30 edges.  3. 30 is a Harshad number ( an integer that is divisible by the sum of its digits) 4. The atomic number of zinc is 30 5. The minimum age for United States senators. 6. February 30 is usually used as a sarcastic date for referring to something that will never happen or will never be done.

1. None of the first 29 natural numbers have more than two different prime factors. This is the longest such consecutive sequence. 2. 29 is the sum of three consecutive squares i.e. 29 =  2^2 + 3^2 + 4^2 3. The number of days February has in leap years. 4. The atomic number of copper 5. Saturn requires over 29 years to orbit the Sun. 6. Number of states in india

1. 28 is a triangular number since it is the sum of the first seven counting numbers: 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. 2. 28 is also a perfect number since the sum of its aliquot divisors (factors that are less than the number itself) is also 28. The aliquot factors of 28 are 1, 2, 4, 7, and 14, and 1 + 2 + 4 + 7 + 14 = 28. The next smallest perfect number is 6, and the next highest perfect number is 496. 3. 28 is an example of a happy number. When you square the digits, add them, and repeat this process on the resulting number, you eventually end up with 1: 2^2 + 8^2 = 68 6^2 + 8^2 = 100 1^2 + 0^2 + 0^2 = 1 4. The sum of the first five prime numbers is 2 + 3 + 5 + 7 + 11 = 28. 5. 28 is a hexagonal number, but not a centered hexagonal number. Every hexagonal number is also a triangular number, but not every triangular number is a hexagonal number. 6. A polygon with 28 sides is called an icosikaioctagon. 7...

1. Twenty-seven is a perfect cube = 3^3. 2. In base 10, it is the first composite number not evenly divisible by any of its digits. 3. 27 is the only positive integer that is 3 times the sum of its digits. 4. 27 is a Harshad number (a number divisible by sum of its digits). 5. 27 is the smallest 2-digit number in which the sum of digits is equal to the sum of prime factors, e.g.: 27 = 3 x 3 x 3 and 2 + 7 = 3 + 3 + 3 = 9 6. 23 is the largest integer which is the sum of the digits of its cube: 27^3 = 19,683 and 27 = 1 + 9 + 6 + 8 + 3 7. 27 is the number of "cubies" in a Rubik's cube. 8. The numbers of atoms in the body of an average male (about 80 kg) is about 10^27. 9. The Chemical Element Cobalt has an atomic number of 27. 10. The primitive Greek alphabet had 27 letters. 11. There are 27 signs of the zodiac in Indian astrology

1. 26 is the only number sandwiched between a square (5^2) and a cube (3^3). 2. There are 26 letters in the English alphabet. 3. In base ten, 26 is the smallest number that is not a palindrome to have a square (26^2 = 676) that is a palindrome. 4. In a normal deck of cards, there are 26 red cards and 26 black cards. 5. The Chemical Element Iron has an atomic number of 26. 6. 26 is the number of bones in the normal human Foot and Ankle. 7. There are 26 weeks in half a year.

1. It is a square number, being 5^2 = 5 × 5. It is the smallest square that is also a sum of two (non-zero) squares: 2^5 = 3^2 + 4^2. 2. 25 is the sum of the first 5 odd numbers(= 1 + 3 + 5 + 7 + 9). 3. Couples who have been married for 25 years celebrate their Silver Wedding. 4. The Chemical Element Manganese has an atomic number of 25. 5. 25 is the number of days approximately that takes the sun to do a complete rotation on itself.

1. 24 is the factorial of 4 (24 = 4!). 2. 24 is an Abundant Number. In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself. The first few abundant numbers are 12, 18, 20, 24, 30, 36, ... There are only 21 abundant numbers less than 100, and they are all even. 3. 24 is the largest number divisible by all numbers less than its square root. 4. It is a highly composite number, having more divisors than any smaller number. 5. 24 is a semiperfect number, since adding up all the proper divisors of 24 except 4 and 8 gives 24. 6. Subtracting 1 from any of its divisors (except 1 and 2, but including itself) yields a prime number; 24 is the largest number with this property. 7. 24 is a Harshad number (number divisible by its sum of digits). 8. The product of any four consecutive numbers is divisible by 24. 9. 24 is the only nontrivial solution to the cannonball p...

1. According to the birthday paradox, in a group of 23 (or more) randomly chosen people, the probability is more than 50% that some pair of them will have the same birthday. For 60 or more people, the probability is greater than 99 per cent! 2. 23 is the smallest prime number with consecutive digits. 3. 23! is 23 digits long. 4. Twenty-three is the sum of three other, consecutive, prime numbers; 5, 7 and 11. It is the first prime number showing this characteristic. 5. The sum of the first 23 primes is 874, which is divisible by 23, a property shared by few other numbers. 6. Repeat the digit 1, 23 times like this: 11,111,111,111,111,111,111,111 and you obtain a prime number. 7. Every positive whole number can be written as the sum of eight cubes (including 0^3 when necessary) except 23 (and 239). Those two numbers require 9 cubes. 8. Nobel Prize-winning economist John Forbes Nash, the inspiration for the film A Beautiful Mind, was obsessed with t...

1. Twenty-two is a pentagonal number. 2. 22 is a palindromic number in decimal system 3. 22 divided by 7 approximates the irrational number π, the ratio of the circumference of a circle to its diameter. 4. There are, in fact, precisely 22 ways to express 8 as a sum of positive integers. i.e. 8 can be partitioned in 22 ways: 8, 7+1, 6+2, 6+1+1, 5+3, 5+2+1, 5+1+1+1, 4+4, 4+3+1, 4+2+2, 4+2+1+1, 4+1+1+1+1, 3+3+2, 3+3+1+1, 3+2+2+1, 3+2+1+1+1, 3+1+1+1+1+1, 2+2+2+2, 2+2+2+1+1, 2+2+1+1+1+1, 2+1+1+1+1+1+1, and 1+1+1+1+1+1+1+1 5. 22 is the smallest number which can be expressed as the sum of 2 primes in 3 ways: 3 + 19, 5 + 17, and 11 + 11 6. 22 is the number of different ways of linking 5 hexagons together. 7. The Chemical Element Titanium has an atomic number of 22. 8. The Human head is constituted of 22 bones: 8 for the cranium and 14 for the face. 9. By the old English measuring system there are 22 yards in a chain. This is the l...

1. Twenty-one is a Fibonacci number, a Harshad number, triangular number and an octagonal number, as well as a composite number, its proper divisors being 1, 3 and 7. 2. 21 is the sum of the first six natural numbers (1+2+3+4+5+6=21), making it a triangular number. Also, the number of spots on a standard cubical (six-sided) die (1+2+3+4+5+6) 3. 21 is the smallest non-trivial example of a Fibonacci number whose digits are Fibonacci numbers and whose digit sum is also a Fibonacci number. 4. 21 is a repdigit in base 4 (1114). 5. 21 is the third star number. Star numbers can be represented by a square with a triangle on each side. 6. 221 - 21 is prime. 7. The current century—spanning the years from 2001 to 2100—is referred to as the 21st century. 8. 21 grams is the weight of the soul, according to research by Duncan MacDougall, generally regarded as meaningless. 9. The Chemical Element Scandium has an atomic number of 21....

1. 20 = 2 + 4 + 6 + 8 2. 20 = 1 + 3 + 6 + 10. i.e. 1 + (1 + 2) + (1 + 2 + 3 ) + (1 + 2 + 3 + 4 ) 3. 20 is an Abundant Number. In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself. The first few abundant numbers are 12, 18, 20, 24, 30, 36, ... There are only 21 abundant numbers less than 100, and they are all even.  4. 20 is a Tetrahedral Number. 5. One month in the religious Mayan calendar contained twenty days. 6. 20 is the base of the ancient Mayan numeral system. 7. A set of 20 units may also be referred to as a score. 8. The Chemical Element Calcium has an atomic number of 20.

1. 19 is a prime number. 2. 19 is the maximum number of 4th powers needed to sum to any number 3. 19 is the largest prime number that is palindromic in Roman numerals (XIX). 4. 19 is an Octahedral Number. 5. The Chemical Element Potassium has an atomic number of 19. 6. "The Sun" is numbered with 19 in Tarot cards.

1 . 18 is a Heptagonal Number. 2. 18 is an Abundant Number. In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself. The first few abundant numbers are 12, 18, 20, 24, 30, 36, ... There are only 21 abundant numbers less than 100, and they are all even.  3. 18 is a Lucas Number (No. from the sequence 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, … where first two numbers are fixed as 1 and 3, next number is the sum of its two preceding terms). 4. The 18 Regular Solids: the 5 Platonic Solid + the 13 Archimedean Solids. 5. 18 is the area and also the perimeter of a rectangle with 6 and 3-unit sides. 6. 18 is the only number that is twice the sum of its digits. 7. On Earth, the length of a day 900 million years ago was only about 18 hours. 8. There are ...

1. 17 is a prime number. 2. 17 is the sum of the first 4 prime numbers: 17 = 2 + 3 + 5 + 7 3. 17 is a palindromic number in binary system (10001). 4. 17 is a Leyland number, 17 = 3^2 + 2^3(In number theory, a Leyland number is a number of the form x^y + y^x where x and y are integers greater than 1. They are named after the mathematician Paul Leyland. The first few Leyland numbers are 8, 17, 32, 54, 57, 100, 145, 177, 320, 368, 512, 593, 945, 1124… 5. 17 is the 7th prime number and the only prime of the form p^q + q^p, where p and q are prime: 17 = 2^3 + 3^2 6. 17 is the lowest possible number of givens for a Sudoku puzzle with a unique solution (this was proven in 2012 by Gary McGuire, Bastian Tugemann, and Gilles Civario). 7. No odd Fibonacci Number is divisible by 17. 8. abcdefghabcdefgh is divisible by 17 (replace each letter with a digit. E.g. 1234567812345678). The reason is that any number of that form is a multiple...

1. 16 is the only number of the form x^y = y^x with x and y being different integers. 2. 16 is a Square Number (4x4). 3. 16 is the maximal number of regions into which 5 lines divide a plane. 4. 16= 1 + 3 + 5 + 7 i.e. sum of first four odd numbers 5. The base 16 notational system for representing real numbers, called hexadecimal, is particularly important and used extensively in computer science, since four bits (each consisting of a 'one' or 'zero') can be succinctly expressed with just a single hexadecimal digit. The 16 distinct digits used to represent numbers in hexadecimal notation are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. 6. The Chemical Element Sulfur has an atomic number of 16.

1. 15 is a triangular number  as 15 = 1 + 2 + 3 + 4 + 5 2. 15 is a hexagonal number 3. 15 is a palindromic number in binary system (1111) 4. 15 is the magic constant for a 3×3 magic square, the smallest possible nontrivial magic square. An N×N magic square consists of the N2 integers from 1 to N arranged in an N×N square grid, such that the sum of any row, or any column, or of one of the two diagonals, is equal to any other. There is only one solution for a 3×3 square, not counting its rotations and reflections:   4  9  2   3  5  7   8  1  6 This magic square was known to the Chinese at least 3000 years ago and is called the Lo Shu. 5. The Chemical Element Phosphorus has an atomic number of 15. 6. The only 15-letter word that can be spelled without repeating a letter is "uncopyrightable".

1. 14 is a square pyramidal number as 14 = 1 + 4 + 9 = 12 + 22 + 32  2. In September 1752, Great Britain switched from the Julian Calendar to the Gregorian Calendar. In order to achieve the change, 11 days were 'omitted' from the calendar: the day after 2 September 1752 was 14 September 1752. 3. The Chemical Element Silicon has an atomic number of. 14.

1. 13 is a Fibonacci number 2. 13 is the number of Archimedian solids. 3. 13 is a Prime Number. 13 is a Fibonacci Number. 4. The Chemical Element Aluminum has an atomic number of 13. 5. The card deck includes 13 hearts, 13 spades, 13 squares, 13 clubs. While the Earth revolves once, the Moon revolves 13 times. 6. There is always at least one Friday 13th in each year. The probability of being born on a Friday the 13th is about 1/214 7. According to historians, there were 13 people at Christ's Last Supper and Christ was crucified on Friday 13th. So, Friday 13th is considered as unlucky. 8. The fear of the number 13 is called 'Triskaidekaphobia'. 

1. 12 is a pentagonal number 2. 12 is the smallest abundant number. 3. 12 is a pentagonal number. 4. 12 is the smallest number with exactly six divisors. 5. 12 is the largest known even number expressible as the sum of two primes in one way (5 + 7). 6. A dozen is a group or set of 12. 7. The Cube is a Platonic Solid with 12 Edges. 8. The Dodecahedron is a Platonic Solid with 12 Faces. 9. The Icosahedron is a Platonic Solid with 12 Vertices. 10. The Chemical Element Magnesium has an atomic number of 12. 11. The 12 Star signs: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagitarius, Capricorn, Aquarius and Pisces.

1. 11 is a palindromic number in decimal system. It is only palindromic prime with an even number of digits. 2. 11 is a Lucas Number. 3. 6 can be Partitioned in 11 ways. 4. 11 is the third honest number, because 11 = "two plus nine". 5. An average room holds 11 x 100 pounds of air! 6. A million seconds is 11 days and a half. 7. The Chemical Element Sodium has an atomic number of 11. 8. The sun spot cycle repeats about every 11 years.

1. 10 is the base of our number system. 2.10 is the sum of the first 3 prime numbers: 10 = 2 + 3 + 5 3. 10 is both a triangular (1 + 2 + 3 + 4 = 10) and tetrahedral number. 4.10 is asemiprime number. A semiprime is a natural number that is the product of two (not necessarily distinct) prime numbers. The semiprimes less than 100 are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, and 95. The Chemical Element Neon has an atomic number of 10. 5. 1 0! = 6! x 7! = 3! x 5! x 7! (Unique solution to the factorial equation n! =a! x b! x c! with consecutive prime factors) 6. In most advertisements, including newspapers, the time displayed on a watch is approximately 10:10. The reason for this is to "frame" the logo of the watch maker. The hands at that number cause the eyes to look right at the logo! 7. Marion's theorem states...

1. 9 is the largest single-digit number. 2. 9 is a Square Number (3x3). 3. 9 is a palindromic number in decimal system 4. 9 is a palindromic number in binary system (1001) 5. The Chemical Element Beryllium has an atomic number of 9. 6. Water expands by about 9% as it freezes. 7. A full moon is nine times brighter than a half moon.

1. The smallest "non-trivial" cube: 8=23=2×2×2. 2. 8 is a Fibonacci number. Also it is the largest cube in the Fibonacci sequence. 3. 8 is an Octagonal Number. 4. 8 is the smallest sum of two factorials of distinct primes: 2! + 3! 5. When specifying directions on a map, most people choose from one of these 8 directions: north, northeast, east, southeast, south, southwest, west, and northwest. 6. In three-dimensional space there are 8 "diagonal" ways to move, corresponding to the eight "octants" you get if you divide the three-dimensional space with three mutually-perpendicular planes. 7. The Chemical Element Oxygen has an atomic number of 8.

1. 7 is a Prime Number. 2. 7 is a palindromic number in decimal system. Also 7 is a palindromic number in binary system (111). 3. 7 is a Mersenne Number (number of the form 2^n -1) 4. 7 is an Octahedral Number. 5. 7 is a Lucas Number. 6. Sum of the first 4 Fibonacci numbers= 1 + 1 + 2 + 3 = 7 7. 7 is the smallest number of sides of a regular polygon that is not constructible by straightedge and compass. 8. Topologists have been able to prove that 7 colors may be needed on a donut shaped map to ensure that no adjacent areas are the same. 9. The smallest positive integer whose reciprocal has a pattern of more than one repeating digit: 1/7 = 0.142857142857... 10. The opposite sides of a die cube always add up to 7. 11. A square piece of paper cannot be folded in half more than 7 times... However, Britney Gallivan (of Pomona, California) found...

1. 6 is the smallest perfect number, that is a number whose divisors add up to itself, e.g.: 1 x 2 x 3 = 1 + 2 + 3 = 6 2. 6 (= 1 + 2 + 3) is a triangular number 3. 3! = 6 4. 6 is a Hexagonal Number. 5. 6 is a congruent number because it is the area of a 3, 4, 5 triangle (a congruent number is an integer that is the area of a right triangle with three rational number sides). 6. 6 is the smallest number of colors needed to color the regions on a Möbius strip. A Möbius strip is a continuous closed surface with only one side; formed from a rectangular strip by rotating one end 180 degrees and joining it with the other end. 7. 6 circles of the same size (try this with 6 coins of the same denomination) will always perfectly surround, all touching, without gaps, 1 circle of that same size. 8. The Chemical Element Carbon has an atomic number of 6.

Dear All, I have been collecting information from various resources regarding the special properties being associated with today's date. It's already 5th June today. So, today I will share properties from the dates (numbers) 1 to 5. In future I would prefer to post day wise. In case you also wish to share something interesting kindly do it. Any suggestions are also welcome. Amit Bajaj Special properties of number 5 (Today’s Date) 1. 5 is the only prime number that ends in 5. 2. there are 5   Platonic solids 3. A five-sided polygon (pentagon) has 5 diagonals. This is the only shape for which the number of sides and diagonals is the same   4. 5   is a   Fibonacci Number . 5. 5   is a   Pentagonal Number . 6. The   Chemical Element   Boron has an atomic number of   5. 7. The   five   natural senses of sight, hearing, smell, taste, and touch. 8. The   5   Elements: Fire, air, water and Earth and Spiri...