Tuesday, March 21, 2017

The Sofa Problem Takes Man to the Stars - Science

The Sofa Problem is one all of us know since this is determining the size of the largest sofa we can get around a ninety-degree turn when we're moving.  Most of us probably get it wrong and the sofa consequently gets stuck but mathematicians have formalized study of the problem to discover the actual limits.  Presumably they have been stuck as well when they tried moving.  (Science Daily:  New twist on sofa problem that stumped mathematicians and furniture movers)

The Moving Sofa problem asks, what is the largest shape that can move around a right-angled turn? UC Davis mathematician Dan Romik has extended this problem to a hallway with two turns, and shows that a 'bikini top' shaped sofa is the largest so far found that can move down such a hallway.

Credit: Dan Romik, UC Davis

There you have it, Davis, California, one of my ex-hometowns, is in the science news again.

Ed:  do they have sofas looking like that in Davis?

I don't think they have sofas like that anywhere, mate.

"It's a surprisingly tough problem," said math professor Dan Romik, chair of the Department of Mathematics at UC Davis. "It's so simple you can explain it to a child in five minutes, but no one has found a proof yet.

The largest area that will fit around a corner is called the "sofa constant" (yes, really). It is measured in units where one unit corresponds to the width of the hallway.

Inspired by his passion for 3-D printing, Romik recently tackled a twist on the sofa problem called the ambidextrous moving sofa. In this scenario, the sofa must maneuver around both left and right 90-degree turns. His findings are published online and will appear in the journal Experimental Mathematics.

- SD

Maybe you ask if they take it seriously and apparently they take it extremely seriously.

Romik decided to tackle the problem of a hallway with two turns. When tasked with fitting a sofa through the hallway corners, Romik's software spit out a shape resembling a bikini top, with symmetrical curves joined by a narrow center. "I remember sitting in a café when I saw this new shape for the first time," Romik said. "It was such a beautiful moment."

Finding Symmetry

Like the Gerver sofa, Romik's ambidextrous sofa is still only a best guess. But Romik's findings show the question can still lead to new mathematical insights. "Although the moving sofa problem may appear abstract, the solution involves new mathematical techniques that can pave the way to more complex ideas," Romik said. "There's still lots to discover in math."

- SD

Well, we can't really tell what he discovered this time but the source article is linked and the interested student is invited ...

1 comment:

Anonymous said...

What a waste of time since sectional sofa solved this decades ago