Wait.. Hang On A Second

If One Remembers This Particular Episode From The Popular Sitcom ‘Friends’ Where Ross Is Trying To

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.

image

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.

image

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:

image

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.

image

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.

image

Have a good one!

More Posts from Matematicaulysses and Others

3 years ago

👌👌😄

6 years ago
Toyota Matrix (matrix)
Toyota Matrix (matrix)
Toyota Matrix (matrix)

Toyota Matrix (matrix)

6 years ago

Essa animação é o mesmo modelo descrito na publicação abaixo 👇👇👇

Semi-regular Polyhedra Transformations.
Semi-regular Polyhedra Transformations.
Semi-regular Polyhedra Transformations.

Semi-regular polyhedra transformations.

These transformations are same as the models in this post.

6 years ago

Um belo gráfico 3D com a frequência das teclas mais usadas no inglês.

Só acho que o "espaço" é que seria uma das maiores.

Frequency Of Keyboard Key Usage

Frequency of keyboard key usage

4 years ago
It’s A Serious Issue!

It’s a serious issue!

4 years ago

The regular hexagon hidden in a cube unfolds to a straight line on a net of the cube.

6 years ago
New Geometrically-Inspired Pastries, Cakes, And Sweets By Dinara Kasko
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2 years ago

Shearer’s geometry puzzles

On his blog MathWithBadDrawings, Ben Orlin reposted a couple of geometrical sangaku-like puzzles by math teacher Catriona Shearer. These are eleven of her personal favorites. If you dare, definitely give them a try!

Shearer’s Geometry Puzzles

Transit Across a Purple Sun. What’s the total shaded area?

Shearer’s Geometry Puzzles

Shearer’s Emerald. Four squares. What’s the shaded area?

Shearer’s Geometry Puzzles

The Pyramid with Two Tombs. Two squares inside an equilateral triangle. What’s the angle?

Shearer’s Geometry Puzzles

Setting Sun, Rising Moon. What fraction of the rectangle is shaded?

Shearer’s Geometry Puzzles

Hex Hex Six. Both hexagons are regular. How long is the pink line?

Shearer’s Geometry Puzzles

Four, Three, Two. What’s the area of this triangle?

Shearer’s Geometry Puzzles

The Trinity Quartet. All four triangles are equilateral. What fraction of the rectangle do they cover?

Shearer’s Geometry Puzzles

The Falling Domino. This design is made of three 2×1 rectangles. What fraction of it is shaded?

Shearer’s Geometry Puzzles

Slices in a Sector. The three colored sections here have the same area. What’s the total area of the square?

Shearer’s Geometry Puzzles

Disorientation. The right-angled triangle covers ¼ of the square. What fraction does the isosceles triangle cover?

Shearer’s Geometry Puzzles

Sunny Smile Up. What fraction of the circle is shaded?

4 years ago
Bruno Munari, (1960), The Square, Translation By CorrainiStudio, Corraini Edizioni, Mantova, (2006-)2011,
Bruno Munari, (1960), The Square, Translation By CorrainiStudio, Corraini Edizioni, Mantova, (2006-)2011,

Bruno Munari, (1960), The Square, Translation by corrainiStudio, Corraini Edizioni, Mantova, (2006-)2011, pp. 62-63

6 years ago

Basic definition of a tangent line.

image
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matematicaulysses - Profº Ulysses Bueno
Profº Ulysses Bueno

Blog do profº Ulysses TDBueno destinado a curiosidades, demonstrações, links, trabalhos, artigos, imagens e tudo que possa mostrar a matemática no mundo.

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