We are excited to host 176-th and 177-th Carnival of Mathematics in a single blog post for December 2019 and January 2020. And perhaps this is happening for the first time in the history of Carnival of Mathematics. Carnival of Mathematics is a monthly blogging round up that is organised by The Aperiodical. We choose to host Carnivals in December 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.

The following posts together makes the 176-th and 177-th Carnival.

Ari Rubin has provided us with a great article titled "Optical Control Of A Lunar Lander" where he has shown how the optimal control problem of lunar landing can be converted into a boundary value problem using calculus of variation.

Another illuminating article authored by Ari Rubin on optical control is "An Introduction to Direct Methods in Optimal Control". This post describes the basics of setting up an indirect method in optimal control and as well provides a code example for MatLab.

We have found the post "The Anti-Calculator Puzzle" in Math with Bad Drawings and the post is very fascinating.

We loved this thought-provoking tweet https://twitter.com/divbyzero/status/1196908517531299841 by Dave Richeson who is a Mathematics professor at Dickinson College and author of Tales of Impossibility.

For all twitter usres, this is an innocent question indeed to find out "Does anyone know the largest prime that fits in a tweet with all digits written out?". This important question has been asked by applied mathematician Tamás Görbe.

Every parent wants to see their little girl to smile and the obvious choice to make them smile is to gift them Barbie Doll. But, the crochet spiral dresses, that Barbie Dolls wear can help your little ones to get interested in Maths too, when they are little grown up. We are thankful to Katie Stecks for providing us with this beautifuland insightful post with title Barbie Spirals.

How to calculate an average when you are indecisive? In other words, which mean to use - Arithmetic Mean or Geometric Mean, and which situations or circumstances are best suited for which mean. When these are the questions to answer, let us take a look into this throughtful article "The Ditherer's Mean" by Evelyn Lamb.

Kaprekar Numbers are an interesting family of numbers and here is a beautiful exposition on the topic by Vaibhav Sawhney. The article ends with some interesting questions on Kaprekar numbers which are worth trying.

We, as teachers, always require to provide with our students food for thought so that they can mathematically challenge themselves. Here is an ecstatically beautiful example

"The Number Column Puzzle" for everyone to try out.

Thomas Lu has shared with us a giant glossary featuring approximately 100 of the most fundamental jargons used in higher mathematics. The title of the post is The Definitive Glossary of Higher Mathematical Jargon. Each and every explanation given here for the jargons are clearly articulated with examples.

John D. Cook has provided us with his article "Determining Fundamental Frequency" where he has explained the nuances of finding out the fundamental frequency when input data are not ideal.

Ben Leis has pointed us to his own written article "Tilted Parabolas (Or all the stuff they didn't tell you in school about them)" which provides fascinating insight about parabolas.

We stumbled upon on this 12 year old post titled "Indians predated Newton 'discovery' by 250 years" which is amazingly interesting.

Dr Neena Gupta is the youngest awardee of Shanti Swarup Bhatnagar Prize of India for solving the 70-year-old Zariski Cancellation Problem in Mathematical Sciences. We whole-heartedly congratulate her on her success and also encourage readers to go through https://researchmatters.in/news/mathematician-dr-neena-gupta-shines-youngest-shanti-swarup-bhatnagar-awardee.

With this we close 176-th and 177th Carnivals and the next Carnival of Mathematics (#178) will be hosted by Stormy at Storm Bear World.

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