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.
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:
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!
👌👌😄
Toyota Matrix (matrix)
Essa animação é o mesmo modelo descrito na publicação abaixo 👇👇👇
Semi-regular polyhedra transformations.
These transformations are same as the models in this post.
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
It’s a serious issue!
The regular hexagon hidden in a cube unfolds to a straight line on a net of the cube.
New Geometrically-Inspired Pastries, Cakes, and Sweets by Dinara Kasko
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!
Transit Across a Purple Sun. What’s the total shaded area?
Shearer’s Emerald. Four squares. What’s the shaded area?
The Pyramid with Two Tombs. Two squares inside an equilateral triangle. What’s the angle?
Setting Sun, Rising Moon. What fraction of the rectangle is shaded?
Hex Hex Six. Both hexagons are regular. How long is the pink line?
Four, Three, Two. What’s the area of this triangle?
The Trinity Quartet. All four triangles are equilateral. What fraction of the rectangle do they cover?
The Falling Domino. This design is made of three 2×1 rectangles. What fraction of it is shaded?
Slices in a Sector. The three colored sections here have the same area. What’s the total area of the square?
Disorientation. The right-angled triangle covers ¼ of the square. What fraction does the isosceles triangle cover?
Sunny Smile Up. What fraction of the circle is shaded?
Bruno Munari, (1960), The Square, Translation by corrainiStudio, Corraini Edizioni, Mantova, (2006-)2011, pp. 62-63
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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