We are excited to host 189-th Carnival of Mathematics for January 2021. Carnival of Mathematics is a monthly blogging round up that is organised by The Aperiodical. We choose to host Carnivals in December / January because 22nd of December is celebrated as National Mathematics Day of India. Indian legendary Mathematician Srinivasa Ramanujan was born on 22nd 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. That is why we celebrate Carnival of Mathematics during December/January and we are doing it for last six consecutive years including this one.Earlier versions that we have celebrated are 129^{th}, 141^{th}, 153^{rd}, 165^{th}, 176^{th}/177^{th}.

We start by writing an interesting property of the integer 189. 189 can be written as sum of two cubes in 2 ways and they are $4^{3} + 5^{3}$ and $6^{3} + (-3)^{3}$. There are two types of numbers which we can think of after seeing this and they are TaxiCab and CabTaxi numbers. $TaxiCab(n)$ is defined as the smallest number which can be expressed as sum of cubes of $2$ distinct positive integers in $n$ different ways. $CabTaxi(n)$ is defined as the smallest number which can be expressed as sum of cubes of $2$ distinct integers (positive or negative) in $n$ different ways. We must mention here that 189 is not a CabTaxi number, because CabTaxi(2) is 91. We should also mention that TaxiCab(2) is 1729. Interested readers who want to know little more about these numbers can refer 'A Short Note on TaxiCab and CabTaxi Numbers'.

Kartik has shared with us a beautiful thought-provoking post titled Public Time and the Privacy of Time where he has described how the math behind interference patterns can let one tune guitars just by watching the strings vibrate!

Peter Lynch has provided us with a light hearted, aesthetic post titled Decorating Christmas Trees with the Four Colour Theorem which has got seasonal application of the four colour theorem.

A very interesting post titled Pen-and-Paper Arithmetic Is Useful When You're Selling Textiles has been forwarded to us by the author of the post Virginia Postrel.

Sam Hartburn has shared with us a beautiful post titled Swirled Series: The Result which exhibits a wonderful example of collaborative mathematical art. The post was written by Craig S. Kaplan.

On a lighter note, we would like to share the post titled Playing Cards – Extraordinary Ordinary Things which attempts to justify why playing cards is an ''Extraordinary Ordinary Things''.

Abhik Jain has forwarded us with a nice post written by John Pavlus titled Super Slow Computer Programs Reveal Math's Fundamental Limits which illuminates on some connections of “busy beavers” game with mathematics and the recent advances on the topic. In 1962, hungarian mathematician Tibor Radó asked the question “How long can a simple computer program possibly run before it terminates?” which was popularly known as “busy beavers” game.

We have been shared by Katie Steckles a nice post titled Menger-Sierpinski which is very illuminative and can help us to know surprising findings of the fractals Menger Sponge and Sierpinski Carpet.

We have found out a illuminating preprint titled COVID-19: Risks of Re-emergence, Re-infection, and Control Measures – A Long Term Modeling Study which has tried to modify SIER model to assess the risks of re-emergence and re-infection of Covid-19 on a long term perspective.

A class VII student, Priyadarshini Mukhopadhyay, of a Kolkata based school has shared with us some hand drawn beautiful images of Sierpinski Triange and Sierpinski Square. We appreciate her efforts and as per her this is a nice activity to do at liesure time.

With this we end the 189th version of Carnival of Mathematics. Next version of Carnival will be hosted by Sophie the Mathmo.

We start by writing an interesting property of the integer 189. 189 can be written as sum of two cubes in 2 ways and they are $4^{3} + 5^{3}$ and $6^{3} + (-3)^{3}$. There are two types of numbers which we can think of after seeing this and they are TaxiCab and CabTaxi numbers. $TaxiCab(n)$ is defined as the smallest number which can be expressed as sum of cubes of $2$ distinct positive integers in $n$ different ways. $CabTaxi(n)$ is defined as the smallest number which can be expressed as sum of cubes of $2$ distinct integers (positive or negative) in $n$ different ways. We must mention here that 189 is not a CabTaxi number, because CabTaxi(2) is 91. We should also mention that TaxiCab(2) is 1729. Interested readers who want to know little more about these numbers can refer 'A Short Note on TaxiCab and CabTaxi Numbers'.

Kartik has shared with us a beautiful thought-provoking post titled Public Time and the Privacy of Time where he has described how the math behind interference patterns can let one tune guitars just by watching the strings vibrate!

Peter Lynch has provided us with a light hearted, aesthetic post titled Decorating Christmas Trees with the Four Colour Theorem which has got seasonal application of the four colour theorem.

A very interesting post titled Pen-and-Paper Arithmetic Is Useful When You're Selling Textiles has been forwarded to us by the author of the post Virginia Postrel.

Sam Hartburn has shared with us a beautiful post titled Swirled Series: The Result which exhibits a wonderful example of collaborative mathematical art. The post was written by Craig S. Kaplan.

On a lighter note, we would like to share the post titled Playing Cards – Extraordinary Ordinary Things which attempts to justify why playing cards is an ''Extraordinary Ordinary Things''.

Abhik Jain has forwarded us with a nice post written by John Pavlus titled Super Slow Computer Programs Reveal Math's Fundamental Limits which illuminates on some connections of “busy beavers” game with mathematics and the recent advances on the topic. In 1962, hungarian mathematician Tibor Radó asked the question “How long can a simple computer program possibly run before it terminates?” which was popularly known as “busy beavers” game.

We have been shared by Katie Steckles a nice post titled Menger-Sierpinski which is very illuminative and can help us to know surprising findings of the fractals Menger Sponge and Sierpinski Carpet.

We have found out a illuminating preprint titled COVID-19: Risks of Re-emergence, Re-infection, and Control Measures – A Long Term Modeling Study which has tried to modify SIER model to assess the risks of re-emergence and re-infection of Covid-19 on a long term perspective.

A class VII student, Priyadarshini Mukhopadhyay, of a Kolkata based school has shared with us some hand drawn beautiful images of Sierpinski Triange and Sierpinski Square. We appreciate her efforts and as per her this is a nice activity to do at liesure time.

With this we end the 189th version of Carnival of Mathematics. Next version of Carnival will be hosted by Sophie the Mathmo.

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