[math-fun] Amazing appearances of 7

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