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The Yiu triangle DeltaO_AO_BO_C is the triangle formed by the centers of the Yiu circles. It has area where f(a,b,c) is a 12th-order polynomial and Delta is the area of the ...

The semiperimeter on a figure is defined as s=1/2p, (1) where p is the perimeter. The semiperimeter of polygons appears in unexpected ways in the computation of their areas. ...

The simplest dissection of a square into rectangles of the same areas but different shapes, composed of the seven pieces illustrated above. The square is 210 units on a side, ...

The "cannabis" curve is the name given here to the polar curve whose shape resembles that of a cannabis leaf. The cannabis curve encloses an area A=(27619209)/(16000000)pia^2.

What is the sofa of greatest area S which can be moved around a right-angled hallway of unit width? Hammersley (Croft et al. 1994) showed that S>=pi/2+2/pi=2.2074... (1) ...

A pyramidal frustum is a frustum made by chopping the top off a pyramid. It is a special case of a prismatoid. For a right pyramidal frustum, let s be the slant height, h the ...

A column-convex self-avoiding polygon which contains the bottom edge of its minimal bounding rectangle. The anisotropic perimeter and area generating function ...

The Curry triangle, also sometimes called the missing square puzzle, is a dissection fallacy created by American neuropsychiatrist L. Vosburgh Lions as an example of a ...

A polyhedron having two polygons in parallel planes as bases and triangular or trapezoidal lateral faces with one side lying in one base and the opposite polyhedron vertex or ...

The Kakeya needle problems asks for the plane figure of least area in which a line segment of width 1 can be freely rotated (where translation of the segment is also ...