Moving sofa problem

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The moving sofa issue or sofa problem is a two dimensional idealization of real moving furniture issues and requests a rigid two-dimensional form of the largest area A that can maneuver through an L-shaped planar region with a unit-wide foot. The acquired A area is referred to as sofa constant . The exact value of sofa constants is an open problem.

Video Moving sofa problem

Histori

The first official publication was by Austrian-Canadian mathematician Leo Moser in 1966, although there were many informal mentionings before that date.

Maps Moving sofa problem

Lower and upper limit

Lower limit

Pekerjaan telah dilakukan untuk membuktikan bahwa konstanta sofa tidak dapat berada di bawah atau di atas nilai-nilai tertentu (batas bawah dan batas atas). Satu batas bawah adalah $            {\displaystyle         A        >\; =        ?                  /                2        ?        \mathrm{1,57079}      }        \{\backslash \; displaystyle\; A\; \backslash \; geq\; \backslash \; pi/2\; \backslash \; approx\; 1.57079\}\;  ÂÂ$ . Ini berasal dari sofa yang merupakan setengah-disk unit radius, yang bisa berputar di sudut.

John Hammersley memperoleh batas bawah ${\ displaystyle A \ geq \ pi/2 2/\ pi \ approx 2.2074}  ÂÂ$ berdasarkan bentuk yang menyerupai handset telepon, yang terdiri dari dua seperempat-disk radius 1 di kedua sisi 1 oleh 4/? persegi panjang dari mana setengah-disk radius ${\ displaystyle 2/\ pi}  ÂÂ$ telah dihapus.

Joseph Gerver found the sofa described by 18 parts of each curve taking a smooth analytic form. This further increases the lower limit for sofa constants to around 2.2195.

Calculations by Philip Gibbs produce an indistinguishable form with a Gerver couch that gives the value for the same area with eight important figures. This is proof that the Gerver sofa is the best but still not proven.

Upper limit

Hammersley juga menemukan batas atas pada konstanta sofa, menunjukkan bahwa itu paling banyak ${\ displaystyle 2 {\ sqrt {2}} \ kira-kira 2.8284}  ÂÂ$ .

Yoav Kallus dan Dan Romik membuktikan batas atas baru pada Juni 2017, membatasi konstanta sofa pada ${\ displaystyle 2.37}  ÂÂ$ .

src: www.3ders.org

Sofa Ambidextrous

The variant of the sofa problem asks the shape of the largest area that can rotate to the left and right angles of 90 degrees in the wide corridor of the unit. The lower boundary area around 1.64495521 has been described by Dan Romik. The couch is also explained by 18 parts of the curve.

src: fjellkjeden.net

See also

• Mountain climbing problem
• Moser worm issue

src: www.3ders.org

References

src: stemantics.files.wordpress.com

External links

• Romik, Dan (March 23, 2017). "Moving Sofa Problem" (video) . YouTube . Brady Haran . Retrieved March 24 2017 .

Source of the article : Wikipedia