# Coincidence

48 If you ever want to incorporate Jupiter, Saturn and Uranus orbits into a window or floor design the diagram opposite might help. An equilateral triangle and an octagram proportion the outer, mean and inner orbits of the three largest planets. Tiny inaccuracies are visible but the fit is excellent overall, memorable, and adequate for many practical purposes. It is a spiky inversion of the touching circles solution for the first three planets see page 29, lower right. One way of depicting the musical octave a halving or doubling of frequency or wavelength is by an equilateral triangle, as the inscribed circle has a diameter half that of the containing circle. Another rule of thumb is to remember that if Jupiters orbit is 6, then Saturns is 11 99.9, twice the MoonEarth size ratio page 30. Saturns orbit also happens to invoke or pi twice below Its radius is the circumference of Mars orbit 99.9 and its circumference is the diameter of Neptunes orbit 99.9. threes and eights again