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Given a regular tetrahedron of unit volume, the mean triangle area of a triangle picked at random inside it is approximately A=0.1811+/-0.0012, and the variance is ...

The mean triangle area of a triangle picked inside a regular hexagon with unit area is A^_=289/3888 (Woolhouse 1867, Pfiefer 1989). This is a special case of a general ...

The mean triangle area A^_ is the average area of a triangle in triangle picking within some given shape. As summarized in the following table, it is possible to compute the ...

The mean triangle area of a triangle picked inside a regular n-gon of unit area is A^__n=(9cos^2omega+52cosomega+44)/(36n^2sin^2omega), (1) where omega=2pi/n (Alikoski 1939; ...

Square line picking is the selection of pairs of points (corresponding to endpoints of a line segment) randomly placed inside a square. n random line segments can be picked ...

A point which lies on at least one ordinary line is called an ordinary point, or sometimes a regular point.

The problem of finding the mean triangle area of a triangle with vertices picked inside a triangle with unit area was proposed by Watson (1865) and solved by Sylvester. It ...

If g is a continuous function g(x) in [a,b] for all x in [a,b], then g has a fixed point in [a,b]. This can be proven by supposing that g(a)>=a g(b)<=b (1) g(a)-a>=0 ...

A point at the intersection of two or more grid lines in a point lattice.

A point which is a member of the set closure of a given set S and the set closure of its complement set. If A is a subset of R^n, then a point x in R^n is a boundary point of ...