On 9/24/06, Ed Pegg Jr <ed@mathpuzzle.com> wrote:
Take any triangle, and trisect the three edges. Connect each corner to the left trisection mark. What is the ratio of the full triangle to the interior triangle?
Draw 3 circles that are tangent to each other, and which are also tangent to a line. Draw a unit circle tangent to the three other circles. What is the distance from the center of the unit circle to the line?
What are some of the other amazing appearances of the number 7?
Ed Pegg Jr
I'm not sure these are 'amazing', but maybe worth a look. (1) there are 7 topologically distinct hexahedra (2) exotic spheres of dimension 7 exist, but not of smaller dimension, except maybe 4?? (3) 7 equal non-overlapping circles fit into a circle twice as large (4) 7 colors are needed to color maps on a torus (5) there is a torus consisting of 7 planar hexagons that requires 7 colors (the Szilassi polyhedron) (6) The minimal finite projective plane has 7 points and 7 lines (the Fano plane) (7) There are 7 deadly sins: pride, envy, gluttony, lust, anger, avarice and sloth. Jim Buddenhagen http://www.buddenbooks.com/jb