Category: math

fuckyeahphysica: If one remembers this partic…


If one remembers this particular episode from the popular sitcom ‘Friends’ where Ross is trying to carry a sofa to his apartment, it seems that moving a sofa up the stairs is ridiculously hard.

But life shouldn’t be that hard now should it?

The mathematician Leo Moser posed in 1966 the following curious mathematical problem: what
is the shape of largest area in the plane that can be moved around a
right-angled corner in a two-dimensional hallway of width 1?
This question became known as the moving sofa problem, and is still unsolved fifty years after it was first asked.


The most common shape to move around a tight right angled corner is a square.

And another common shape that would satisfy this criterion is a semi-circle.


what is the largest area that can be moved around?

Well, it has been
conjectured that the shape with the largest area that one can move around a corner is known as “Gerver’s
sofa”. And it looks like so:


Wait.. Hang on a second

sofa would only be effective for right handed turns. One can clearly
see that if we have to turn left somewhere we would be kind of in a tough

Prof.Romik from the University of California, Davis has
proposed this shape popularly know as Romik’s ambidextrous sofa that
solves this problem.


Although Prof.Romik’s sofa may/may not be the not the optimal solution, it is definitely is a breakthrough since this can pave the way for more complex ideas in mathematical analysis and more importantly sofa design.


Have a good one!

Triangulating a circle. How to do a drawing li…

Triangulating a circle. 

How to do a drawing like this? Start with a circle and divide it into n equal parts. I choose n=100 for this drawing. There is an easy formula for this, the i-th point is (radius*cos(i*2*PI/n),

radius*sin(i*2*PI/n)). Then for each i connect the i-th point to the point  (radius*cos(PI-2*i*2*PI/n), radius*sin(PI-2*i*2*PI/n)). This might not be one of the original points, but it is on the circle. And that is it 🙂    

Why is this mathematically interesting?  This way we get a set of nonparallel  lines such that there are a lot of triple intersections between them.  

Shifting lines.  Twitter, Facebook.  

Shifting lines. 

, Facebook.  



Trefoil by Dave Whyte | Tumblr



I’m having a blasty-bast with Group Explorer today. How have I never played with this before!?

shadowpeoplearejerks: illustrationinphysics: …



Complex analysis – the perfect subject for combining visual and analytic thinking. I just read “Visual Complex Analysis” by Tristan Needham, a basic book on complex analysis: lots of historical references, uncompromising explanations, lots of problem solving and plenty of beautiful illustrations!


I have this book. It is very good. 



Math Love by CuteReaper.



By Math with Bad Drawings.

I can’t be the only one. Right? 

I can’t be the only one. Right? 



Based on Joan Taylor’s wanderer tiling.