April & May Numbers

As promised in the post The Power of Organization, here is the post with the number facts I wrote this month and also last month. Hope you will find it useful and interesting. Lets get going:

• Number 9. Nine is a Motzkin number. In mathematics, a Motzkin number for a given number n is the number of different ways of drawing non-intersecting chords between n points on a circle (not necessarily touching every point by a chord). The Motzkin numbers are named after Theodore Motzkin, and have very diverse applications in geometry, combinatorics and number theory. In the image you can see the example for number 9. 
• Pair (8,9). In mathematics, a Ruth–Aaron pair consists of two consecutive integers (e.g. 8 and 9) for which the sums of the prime factors of each integer are equal: 8 = 2 x 2 x 2 and 9 = 3 x 3 with 2 + 2 + 2 = 3 + 3 = 6. The following interesting question appears: are there infinitely many Ruth-Aaron pairs? 
• Number 121. An interesting fact is that 121 is the sum of three consecutive primes: 37 + 41 + 43. Another fascinating thing about 121 is that there are no squares besides 121 known to be of the form 1 + p + p^2 + p^3 + p^4, where p is prime, in our case 3 (because 1 + 3 + 9 + 27 + 81 = 121). Other such squares must have at least 35 digits. Moreover, 121 is special because there are only two other squares known to be of the form n! + 1 ( because 5! + 1 = 120 + 1 = 121). 
• Number 13. In some cultures 13 is an unlucky number, but mathematicians know better Through a Mathematician’s Eyes 13 is a happy number. A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. 
• Number 21. It is a good example of square – free integer. A positive integer m is called square free if m is the product of finitely many pairwise different prime numbers, or equivalently, if there is no prime number p such that p^2|m. The image shows the number 21 in front of the Baťa’s scryscraper in Zlín, Czech Republic. And so we are also traveling with math ^_^ 
• Number 0. Although we use zero on a daily basis, few of us ponder its significance. The theoretical leap required to develop a symbol that represents nothing is very impressive – and neither the ancient Greeks nor the Romans had a representation of zero. The Indian mathematician Brahmagupta was the author of the 1st text to treat zero as a number. It’s sometimes said that you cannot ponder the infinite until you have pondered zero. 
• Square root of 2. The square root of 2 is very important in the history of math. It was a big deal to the Pythagoreans. The discovery that the square root of 2 was irrational really bothered them. To the Pytagoreans the world was all about rational numbers. The idea that a number could not be expressed as a fraction was inconceivable. Legend has it that Hippasus of Metapontum, a disciple of Pythagoras, produced a proof of the irrationality of the square root of 2. Because the Pythagoreans could not accept this, Hippasus was sentenced to death by drowning. An alternative story suggests that his discovery was made at sea, so he was simply thrown overboard. Who knows for sure? Maybe they just expelled him from the group, but it makes for a good story and illustrates just how irrational people can be about numbers. 

Hope you are enjoying my new series. I will probably be once a month or once every 2 months. If you have a favorite number you want to know more about from a mathematical point of view let me know in comment box bellow. Moreover, if you are interested in more number facts you can check the book Numbers: Facts, Figures and Fiction by Richard Phillips, which has some interesting number facts for the numbers from 0 to 156 and also some other big numbers.

Have a nice day. Thank you for your help and support. Thank you for reading. You can find me on Facebook, Tumblr, Google+,  Twitter  and  Instagram, I will try to post there as often as possible. Don’t forget that maths is everywhere! Enjoy!