The diagram shows a regular pentagon with sides of unit length.
Find all the angles in the diagram. Prove that the quadrilateral
shown in red is a rhombus.
Weekly problem 52 - 2006
Show that it is rare for a ratio of ratios to be rational.
Robert managed to solve this
Find the ratio corresponding to B.
Also compare the D-A ratio with the ideal fifth (3/2):
"B's ratio is calculating by use of
the fact that the interval from E to B is a perfect fifth, and a
perfect fifth's ratio is 3/2. Also E's ratio is 5/4. Therefore B =
The ideal fifth ratio=81/54.Therefore
if we were to tune two adjacent keys to two different A's, the
first being in the ratio A/D, and the second a perfect fifth above
D (in the ratio 3/2). The second A would be higher than the first
by a ratio of 81/80."