40% of the class got this wrong last year. I was so pissed off I wrote a haiku about it.

Science and Math
Science and Math World

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:

whatThis question became known as the

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?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.

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:## 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.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 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.

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 I just read “Visual Complex Analysis” by Tristan Needham, a basic book on complex analysis: lots of historical references, uncompromising explanations, lots of problem solving and plenty of beautiful illustrations!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.

Pattern

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

Reuleaux triangles. These shapes have a very nice property, their width is the same in any direction.