We are glad to host the $153$rd Carnival of Mathematics in December $2017$ after last months Carnival of Mathematics 152 by TD Dang & Matthew Scroggs at Chalkdust Magazine. Carnival of Mathematics is a monthly blogging round up that is organised by The Aperiodical.

We choose to host $153$rd Carnival in December because $22$nd of this month is celebrated as National Mathematics Day of India. Indian legendary Mathematician Srinivasa Ramanujan was born on $22$nd December $1887$. In order to recognize his immense contribution towards Mathematics the Government of India has declared Ramanujan's birthday to be celebrated every year as the National Mathematics Day of India.

To start with let us first take a look into some interesting facts about number $153$.We choose to host $153$rd Carnival in December because $22$nd of this month is celebrated as National Mathematics Day of India. Indian legendary Mathematician Srinivasa Ramanujan was born on $22$nd December $1887$. In order to recognize his immense contribution towards Mathematics the Government of India has declared Ramanujan's birthday to be celebrated every year as the National Mathematics Day of India.

1. $153$ is a Harshad Number in base 10. Remember that, Harshad number in any base is an integer which is divisible by the sum of its digits. Here $153$ is divisible by 1 + 5 + 3 = 9. Number $351$ which is the reverse of the number $153$, is also a Harshad number, so $153$ is also a reversible Harshad number.

2. $153$ can be expressed as the sum of the cubes of its digits. Therefore, $153 = 1^{3} + 5^{3} + 3^{3}$.

3. Since, $153 = 1 + 2 + 3 + \ldots + 16 + 17$, is a triangular number. Reverse of $153$, i.e., $351$ is also a triangular number.

4. A crazy sequential representation of $153$ written in terms of $1$ to $9$ in increasing as well as

decreasing order (taken from http://arxiv.org/abs/1302.1479) is as follows $$153 = 1 + 23 + 45 + 67 + 8 + 9 = 9 + 8 + 76 + 54 + 3 + 2 + 1$$

We will now move on to the posts that make up this months carnival.

$153$ is an interesting number. There are many other properties of $153$ as has been nicely explained and described in Curious Properties of 153.

Mark Dominus shared with us a nice article titled Testing for divisibility by 99. This demonstrates the test for

divisibility by 99, which is analogous to the test for divisibility by $9$, except that we are required to do it in chunks of two digits. This is interesting and we hope

that middle schoolers will enjoy it.

Mark Dominus has shared with us another nice blog post of his own with title Mathematical pettifoggery and pathological examples. The post is a discussion of why mathematicians are so interested in pathological examples, and even in trivial examples. Author has described this in the context of a particular general topology exercise.

Mark Dominus has provided another interesting article titled Wasteful and frugal proofs in Ramsey theory. This post compares two different theorems in the same area of mathematics. One achieves essentially the best result possible; the other is a paragon of profligate waste, achieving an upper bound of 325 for a quantity that is actually equal to 9. Author thinks that this will be interesting to people at all levels. High-schoolers will understand the examples and may learn something from them. More advanced readers may find the metaquestion interesting: what is different about the two proofs?

Sayudh Shamik Jana has shared with us a very interesting YouTube video titled The hardest problem on the hardest test.

Zor Shekhtman has directed us to an interesting YouTube video with title System of Equations for Special Relativity. This video is an example of how a system of equations can be used to derive formulas of special theory of relativity. Albert Einstein has derived these formulas in his "Electrodynamics" in a more physical, more intuitive way. This is pure mathematics and, as such, causes much less problems in understanding, as long as basic assumptions are agreed upon. The article containing the same derivation as in this video can be found at http://www.unizor.com/Doc/zor_math_teen_algebra_EU_sys_linear_equations_relativity.

Shecky R has provided us with a brainteaser titled Elusive Conversation (brainteaser).

Shivani Mishra has shared with us his article titled Sudoku where she has written about Sudoku puzzle in general and about many of its variants like binary puzzle and stair step sudoku.

Shivani Mishra has directed us to a nice blog post Topology vs. "A Topology" (cont.) authored by Tai-Danae Bradley. In this blog post the definition or the axioms behind a Topological Space has been explained nicely.

Anthony Bonato has shared with us the title Survivor: Did math predict the big win?. This post explores how network science can be used to predict winners of the social game show Survivor. Post has analyzed the current season and has matched up the outcomes with what has been predicted by theory.

Two other nice posts we would like to make a mention of is Math Hats and On The Christmas Cracker 'Mystery Calculator' Trick.

This brings to an end of this edition of Carnival of Mathematics. Next Carnival of Mathematics will be hosted by Rachel at The Math Citadel.

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