# Carnival of Mathematics 187

Welcome to Carnival of Mathematics 187. As is tradition, we going to start off with some interesting facts about the number 187. Firstly, 187 is an odd number. That isn’t a very interesting fact because anybody can tell you that. Getting more interesting, 187 is a composite number. This means that it is the product of two or more primes. 187 is also a deficient number. This means that the sum of the divisors of the number is less than two times the number. While we are here, I might as well say some properties of these new numbers:

1. Deficient numbers have an infinite cardinality, meaning that there are an infinite number of them.
2. If an odd number has one or two distinct prime factors, it is deficient (as 187 is).
3. Most interestingly, the divisors of deficient perfect numbers are deficient.

187 is also a self number. A self number is a number that can’t be made from taking a number and adding it’s digit sum, 20 is another self number, as if we take n < 15 we get numbers less than 20 (14+1+4=19) and bigger and inlcuding 15 are larger than 20 (15+1+5=21). 187 is square free. This means that no square number divides 187. This is very useful for definitions in prime number theory, as anybody that has come to one of my prime talks would know. Talking about primes, we can find the prime factors of 187 are 11 and 17. I also have some other interesting facts about primes and 187. It is the sum of three consecutive prime numbers; 59, 61 and 67. If you thought that was amazing, let me tell you something more astounding. I can write 187 as the sum of nine consecutive prime numbers; 7, 11, 13, 17, 19, 23, 29, 31 and 37. Finally, to end the torment of number theory for now, I have two more facts about 187. The difference of two square numbers can be made up to 187. These are 142−32 and 942−932 and 187 is a centred 31-gonal number.

Onto the actual submissions this month! First up is a podcast by Sophie Maclean (The Mathmo), one which I have had a little listen of myself (it totally isn’t because Sophie is a friend of mine ). The podcast is all about what you can do with a degree in Mathematics. A topic which we can all agree is important for any prospective Mathematics student. The podcast is well structured with new guests each episode and a plethora of games and facts to keep the interest piqued. It is hosted on Spotify at this link: The Maths Aftermath

Next is a tweet by Francisco Martinez,

Let's take a look at how pi came to be. All things were made by him; and without him was not any thing made that was made...All things created He... #pi #maths #geometry pic.twitter.com/eZpBJpWS7w

— Francisco Martinez (@TheFranc) December 24, 2019

He shows the 47th problem of Euclid with its link to Pythagoras theorem. It shows the three concentric circles drawn on the diagram and where π can be calculated from that.

Following that we have Mark Dominus, with an interesting take on Newton’s Method in, ‘Newton’s Method but without calculus — or multiplication’. Newton’s method can solve all sorts of nonlinear equations but requires calculus. For special cases, like extracting square roots, you can get away with not using calculus. Instead you get something called the “Babylonian method”, which is at least 2000 years old! But you can make it simpler still. Here’s a stripped-down version of the Babylonian method for extracting square roots that not only doesn’t require calculus, it doesn’t even require multiplication! The post can be found here, Newton Mediants.

As an aspiring differential geometer, I take great enjoyment in Topology out in the wild and this is no exception. Before you look at the tweet below, let me ask you this; how many holes do donuts, coffee cups and straws have? Well, we finally have definitive answers. Below is the results of a survey on those and similar questions:

Someone surveyed 1,600 people about how many holes certain objects have. The answers are... perplexing. #dataviz