Search Results for ""

The theorem of Möbius tetrads, also simply called Möbius's theorem by Baker (1925, p. 18), may be stated as follows. Let P_1, P_2, P_3, and P_4 be four arbitrary points in a ...

The dual of Brianchon's theorem (Casey 1888, p. 146), discovered by B. Pascal in 1640 when he was just 16 years old (Leibniz 1640; Wells 1986, p. 69). It states that, given a ...

Two lines, vectors, planes, etc., are said to be perpendicular if they meet at a right angle. In R^n, two vectors a and b are perpendicular if their dot product a·b=0. (1) In ...

Bubbles can meet only at angles of 120 degrees (for three bubbles) and cos^(-1)(-1/3) approx 109 degrees28^'16^('') (for four bubbles), where cos^(-1)(-1/3) is the ...

A configuration of 12 planes and 12 points such that six points lie in every plane and six planes pass through every point. Alternatively, the configuration consists of 16 ...

The second Brocard circle is the circle having center at the circumcenter O of the reference triangle and radius R_B = sqrt(1-4sin^2omega)R (1) = (2) where R is the ...

Let c_1, c_2, and c_3 be the circles through the vertices A_2 and A_3, A_1 and A_3, and A_1 and A_2, respectively, which intersect in the first Brocard point Omega. ...

Guy's "strong law of small numbers" states that there aren't enough small numbers to meet the many demands made of them. Guy (1988) also gives several interesting and ...

The study of figures on the surface of a sphere (such as the spherical triangle and spherical polygon), as opposed to the type of geometry studied in plane geometry or solid ...

The first strong law of small numbers (Gardner 1980, Guy 1988, 1990) states "There aren't enough small numbers to meet the many demands made of them." The second strong law ...