Snowflakes

Snowflakes are really awesome, and I realized it when I first saw these amazing pictures by Alexey Kljatov.

The size of these snowflakes is only a few millimeters!

We can make paper snowflakes or kind of snowflakes as shown in this 5 year old video by Vihart. 

I also tried to make some patterns. Not all them were perfect but I made some good ones also! 

Snowflakes have sixfold symmetry that is if you rotate a snowflake by 60 degrees it will look the same as before. 

Here is a paper snowflake with sixfold symmetry!

Happy Mathematics Day!

Mathematics Day

To celebrate the birthday of the famous mathematician Shrinivas Ramanujam or Mathematics Day (22nd December), I would like to share some interesting stuff,

First of all this year, Ramanujam's birth date is more special because 22-12-2017 is a prime number! And it would have been his 130th birthday.

What is shown here is a Magic square. It is an n×n array whose row, column and the diagonal numbers add up to the same number.

The magic square shown above was made by Ramanujam. Its very first row contains his Birth Date. So its also known as Ramanujam's magic square.

If you add the numbers along the row, column or along the diagonal they will add up to 139 (a prime number).

Semi Eulerian Graph

Inspired by this standupmaths video I made some shapes and figured out whether they can be made without taking pen off the paper.

So if a shape has got all odd number of lines going from its every point you can never make it without taking your pen off.

If it has only two such odd points it's called Semi-Eulerian Graph and then you can make the shape by beginning on one odd point and ending on another, as in the very first shape of the following picture.