the12list dotcom on its third year

1. Twelve is a composite number, the smallest number with exactly six divisors, its divisors being 1, 2, 3, 4, 6 and 12. Twelve is also a highly composite number, the next one being twenty-four. Twelve is also a superior highly composite number, the next one being sixty. It is the first composite number of the form p²q; a square-prime, and also the first member of the (p²) family in this form. 12 has an aliquot sum of 16 (133% in abundance). Accordingly, 12 is the first abundant number (in fact a superabundant number) and demonstrates an 8-member aliquot sequence; {12,16,15,9,4,3,1,0} 12 is the 3rd composite number in the 3-aliquot tree. The only number which has 12 as its aliquot sum is the square 121. Only 2 other square primes are abundant (18 and 20).
2. Twelve is a sublime number, a number that has a perfect number of divisors, and the sum of its divisors is also a perfect number.^[11] Since there is a subset of 12's proper divisors that add up to 12 (all of them but with 4 excluded), 12 is a semiperfect number.
3. If an odd perfect number is of the form 12k + 1, it has at least twelve distinct prime factors.
4. Twelve is a superfactorial, being the product of the first three factorials. Twelve being the product of three and four, the first four positive integers show up in the equation 12 = 3 × 4, which can be continued with the equation 56 = 7 × 8.
5. Twelve is the ninth Perrin number, preceded in the sequence by 5, 7, 10,^[14] and also appears in the Padovan sequence, preceded by the terms 5, 7, 9 (it is the sum of the first two of these).^[15] It is the fourth Pell number, preceded in the sequence by 2 and 5 (it is the sum of the former plus twice the latter).
6. Twelve is probably the last even number that is the sum of only one pair of prime numbers (5+7). (Goldbach's conjecture)
7. A twelve-sided polygon is a dodecagon. A twelve-faced polyhedron is a dodecahedron. Regular cubes and octahedrons both have 12 edges, while regular icosahedrons have 12 vertices. Twelve is a pentagonal number. The densest three-dimensional lattice sphere packing has each sphere touching 12 others, and this is almost certainly true for any arrangement of spheres (the Kepler conjecture). Twelve is also the kissing number in three dimensions.
8. Twelve is the smallest weight for which a cusp form exists. This cusp form is the discriminant Δ(q) whose Fourier coefficients are given by the Ramanujan τ-function and which is (up to a constant multiplier) the 24th power of the Dedekind eta function. This fact is related to a constellation of interesting appearances of the number twelve in mathematics ranging from the value of the Riemann zeta function at −1 i.e. ζ(−1) = −1/12, the fact that the abelianization of SL(2,Z) has twelve elements, and even the properties of lattice polygons.
9. There are twelve Jacobian elliptic functions and twelve cubic distance-transitive graphs.
10. There are 12 Latin squares of size 3 × 3.  
11. The duodecimal system (12₁₀ [twelve] = 10₁₂), which is the use of 12 as a division factor for many ancient and medieval weights and measures, including hours, probably originates from Mesopotamia.
12. In base thirteen and higher bases (such as hexadecimal), twelve is represented as C. In base 10, the number 12 is a Harshad number.

Source:

https://en.wikipedia.org/wiki/12_(number)

The Boolean Man - George Boole

1. Today is the 200th birthday of George Boole, the man famous for his Boolean logic, 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.
2. He was born on 2 November 1815 at Lincoln, Lincolnshire, England.
3. His legacy was Boolean logic, a theory of mathematics in which all variables are either "true" or "false", or "on" or "off". 
4. The mathematician became one of the founding fathers of modern computer science and engineering – despite never finishing school  but it took him several years to master calculus as he had no tutor. 
5. His system of Boolean Logic paved the way for modern electrical engineering and computer science  and his ideas were put to use more than 70 years after his death when Victor Shestakov at Moscow State University in Russia proposed using the system to design electrical switches, according to the Scientific American. 
6. He was a polymath having learned French, German, Latin and Greek.
7. He founded a school when he was just 19 in the year 1839 and also in 1840.
8. He became the first professor of mathematics at the newly founded Queen’s College, Cork (now University College Cork) in Ireland in 1849. 
9. Boole was awarded the Keith Medal by the Royal Society of Edinburgh in 1855 and was elected a Fellow of the Royal Society in 1857. He received honorary degrees of LL.D. from the University of Dublin and Oxford University.
10. He died of fever-induced pleural effusion on 8 December 1864 (aged 49) at Ballintemple, County Cork, Ireland and was buried in the Church of Ireland cemetery of St Michael's, Church Road, Blackrock (a suburb of Cork City). There is a commemorative plaque inside the adjoining church.
11. Boolean algebra is named after him, as is the crater Boole on the Moon. The keyword Bool represents a Boolean datatype in many programming languages, though Pascal and Java, among others, both use the full name Boolean.[33] The library, underground lecture theatre complex and the Boole Centre for Research in Informatics[34] at University College Cork are named in his honour. A road called Boole Heights in Bracknell, Berkshire is named after him.
12. Google honored him today, 2 November 2015, for his  11001000th birthday with a doodle.

Sources:

George Boole: Five things you probably didn’t know about the man behind today's Google Doodle 
George Boole: How mathematical genius's Boolean logic led to the digital age 
George Boole

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The First 12 Numbers in the Fibonacci Sequence

Fibonacci was an Italian mathematician, considered by some as "the most talented western mathematician of the Middle Ages". Leonardo Pisano Bigollo was his name and was also known as Leonardo of Pisa, Leonardo Pisano, Leonardo Bonacci and Leonardo Fibonacci. He was best known in Europe for spreading the use of Hindu-Arabic numerical system when his book Liber Abaci (Book of Calculation) was published. Fibonacci sequence was used as an example in this book by introducing it as an exercise involving a population of rabbits in 1202. This sequence of numbers was named after him but he did not discovered it, rather it was already appeared in the natural world that dates back to over two millenia and was first use by Indian mathematicians.

His sample problem:

"A certain man put a pair of rabbits in a place surrounded by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair from which the second month on becomes productive?" (Liber abbaci, chapter 12, p. 283-4)
Solution:

At month zero, there is one pair of rabbits. At the beginning of the first month (January 1st), there is one pair of rabbits that has mated, but not yet given birth. At the beginning of the second month, the original pair gives birth, giving rise to another pair of rabbits...and so on. After one full year, there are 377 pairs of rabbits.
The Fibonacci numbers was formed from a recurrent sequence. Beginning with 1, each term of the Fibonacci sequence is the sum of the two previous numbers.

   0+1=1     1+1=2     1+2=3     2+3=5     3+5=8    5+8=13

Fibonacci began the sequence not with 0, 1, 1, 2, as modern mathematicians do but with 1,1, 2, etc.

Hence, the first 12 numbers in the Fibonacci sequence are:

   1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144