New – Irregular Pentagon that can tile the Plane

Some time ago, I have written a post about tiling: Floors of Derelict Buildings with Tile-like Patterns and after that I have been looking for more information about tiling and recently I got to this really interesting article: With Discovery, 3 Scientists Chip Away at an Unsolvable Math Problem. The article tells the story of 3 scientists: McLoud-Mann, along with her husband, Casey Mann, and David Von Derau and the discovery of a new type of irregular pentagons that can tile the plane. 

Moreover, I have found some interesting gifs that help you understand tiling better. First of all, some regular polygons can tile the plane nicely and easily to visualize:

But for regular pentagons the problem transforms and becomes more complicated:

Thought it sounds easy to find a way to tile the plane, the practice shows it is not that easy. For me it sounds like using just pen, paper and imagination you can solve the problem. But (as you can read in the article mentioned above) it is not that easy:

But it gets a lot more complicated when dealing with pentagons — specifically convex, or nonregular pentagons with the angles pointing outward. The number of convex pentagons is infinite — and so is the number that could potentially tile the plane. It’s a problem that’s almost unsolvable because, as McLoud-Mann put it, it has “infinitely many possibilities.”

In other words: It’s possible that that there are dozens — hundreds, thousands even — of these convex pentagon shapes waiting to be discovered.

And this is why, I love the new pattern so much:

Thank you for your support.Hope you are all having fun this summer, don’t forget to check my Facebook event: Mathematics and Summer ^_^ Thank you for your help and support. Thank you for reading. You can find me on FacebookTumblr, Google+,  TwitterInstagram and Lettrs, I will try to post there as often as possible. Don’t forget that maths is everywhere! Enjoy! 


5 thoughts on “New – Irregular Pentagon that can tile the Plane

Add yours

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Blog at

Up ↑

%d bloggers like this: