This repetitive pattern involves a simple technique called numeric reduction in which all the digits of a number are added together until only 1 digit remains. “The Fibonacci sequence also has a pattern that repeats every 24 numbers. We have seen this before in the Platonic solids, Sacred Number Canon and reducing to 9.įor example: 25920 = 2+5+9+2+0 = 18 = 1+8 = 9.Īs we saw in the previous article, the digital roots in the Fibonacci sequence repeat infinitely with a period of 24. See page 7 in Quantification by Scott Onstott and Construction Lesson #62.Įight equally sized circles having diameters that are a term in the Fibonacci sequence will fit snugly around a central ninth circle if the ninth circle’s diameter is the next higher term in the sequence.įor example, eight circles with a diameter of 34 can fit around a central circle with diameter of 55, the next highest term in the Fibonacci sequence.ĭigital roots are a single-digit value obtained through an iterative process of summing digits. These proportions of circles reveal interesting things. The above circles are all in Fibonacci proportions. Growth by accretion is also used by crystals, as it is the simplest law of growth. This allows the center of gravity to remain the same throughout the course of its life. They grow in size, increasing length and width, but maintain the same proportions. This is seen in the way bones, teeth, horns, and shells grow. “Contemplation of the gnomon leads to an understanding of one of nature’s most common principles, growth by accretion.”2 Staring with a square we build new squares to create a spiral of squares which grows and grows by the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34 and 55. Starting with a square side = 1, each successive rectangle is built on the diagonal of the previous one to create squares of area 2, 3, 4 and 5.Īnd this is also found with the Fibonacci spiral. Gnomonic growth is also seen with square root rectangles. This concept is also seen in square and triangular numbers (as well as rectangular and cubic numbers): In geometry, a gnomon is a plane figure formed by removing a similar parallelogram from a corner of a larger parallelogram or, more generally, a figure that, added to a given figure, makes a larger figure of the same shape. This concept was discovered by Aristotle, as far as we know.Ī gnomon is any figure, which, when added to another figure, leaves the resultant figure similar to the original. Gnomons are things that suffer no change other than magnitude when they grow. Reference Construction Lesson #62: Phi Scaling Angle & Fibonacci Circles. This is seen in the growth of a spruce tree sea shells v-shaped flocks of birds sand patterns left by waves weave patterns in some tree bark, and other natural phenomenon. The center angle that intersects each circle’s center point is 13.75 (1/10 of 137.5). When a set of circles (or spheres) with diameters expanding by Fibonacci values, are placed tangential to one another in a straight line the angle between the horizontal line at the bottom of each circle and the line that touches each circle’s “upper” surface point is the phi scaling angle.1 The Phi Scaling angle is the angle of expansion. We will now discuss the Phi Scaling Angle, Fibonacci Circles and Roots, the Golden Triangle, Golden Rectangles and the Golden Angle.
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