Category: math

fuckyeahphysica: If one remembers this partic…

fuckyeahphysica:

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.

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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.

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But
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:

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Wait.. Hang on a second

This
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
spot.

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

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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.

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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. 


Twitter
, Facebook.  

graftheory:

graftheory:

Trefoil by Dave Whyte | Tumblr

Regular

mathed-potatoes:

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

https://sourceforge.net/projects/groupexplorer/?source=typ_redirect

shadowpeoplearejerks: illustrationinphysics: …

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!

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I have this book. It is very good. 

curiosamathematica:

curiosamathematica:

Math Love by CuteReaper.

curiosamathematica:

curiosamathematica:

By Math with Bad Drawings.

I can’t be the only one. Right? 

I can’t be the only one. Right? 

Pattern

Pattern

Based on Joan Taylor’s wanderer tiling. http://tilings.math.uni-bielefeld.de/substitution/wanderer-refl/