Sothic Cycle, Six‐Fold Symmetry, Golden Ratio, Square Root Two, A440 My work has lead to approximations to the square root of two over two, which is the ratio of a side of a square to its hypotenuse, and the golden ratio conjugate which is 0.618. I call the former Manuel’s number and the latter Levinson’s number. I have found that Manuel’s number, M, and Levinson’s number, L, together with standard concert pitch (A440) relate the important square root of two over two and the golden ratio conjugate to the Sothic Cycle of The Egyptian calendar. The Sothic Cycle is a cycle of the Egyptian Calendar, which is the time between helical risings of the brightest star, Sirius, when it coincides with the annual inundation of the Nile River. It is 1,460 Julian Years (365.25 days). Here is how it is done: I say six‐fold symmetry is 11/6. I relate six‐fold symmetry to standard concert pitch (A440), Levinson’s number, Manuel’s number, and the 240 seconds in which time the earth rotates through one degree. Then we show that is 4 minutes and 4 minutes times the 365 day year is the Sothic cycle. This says while a star rises four minutes earlier each day, that is 240 seconds earlier each day. However notice: 360 360 ! 11 6 +1 = 6 360 L = 621; M = 0.708534622
2 2 A440 ML 11 = = 240 240 6 24hr 60 min year 1440 year = = 4 min/ day day hr 360! day 360 240sec 1min = 4 min/ day deg 60sec ! = 0.618 4 min 365day = 1, 460 = sothic _ cycle day year Ian Beardsley January 07, 2014 L " 1000! ; M "