World PhiloMathematics & Design Society

Golden Ratio & Fibonacci Sequence There is a special relationship between the Golden Ratio and the  Fibonacci Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... (The next number is found by adding up the two numbers before it.) And here is a surprise: when we take any two successive  (one after the other)  Fibonacci Numbers,  their ratio is very close to the Golden Ratio . In fact, the bigger the pair of Fibonacci Numbers, the closer the approximation. Let us try a few: A B B/A 2 3 1.5 3 5 1.666666666... 5 8 1.6 8 13 1.625 ... ... ... 144 233 1.618055556... 233 377 1.618025751... ... ... ... We don't even have to start with  2 and 3 , here I chose  192 and 16  (and got the sequence  192, 16, 208, 224, 432, 656, 1088, 1744, 2832, 4576, 7408, 11984, 19392, 31376, ... ): A B B / A 192 16 0.08333333... 16 208 13 208 224 1.07692308... 224 432 1.92857143... ... ... ... 7408 11984 1.6

Golden Ratio Phi, like Pi, is a ratio defined by a geometric construction In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a > b > 0, where the Greek letter phi  (  or  )  represents the golden ratio. Its value is: We find the golden ratio when we divide a line into two parts so that: Just as pi ( p ) is the ratio of the circumference of a circle to its diameter, phi ( ) is simply the ratio of the line segments that result when a line is divided in one very special and unique way. Divide a line so that: the ratio of the length of the larger line segment (B) to the length of the smaller line segment (C). is the same as the ratio of the length of the larger line segment (B) to the length of the smaller line segment (C). This happ

Additive Sequence Fibonacci was instrumental in propagating Indo-Arabic Numerals (0,1,2,3,4,5,6,7,8,9) in Western world in favor of  cumbersome Roman Numerals (I, II, III, IV, V, etc).  A very well known sequence which is vaguely found in nature is the series of numbers where the next number is found by summing up the two numbers before it.  0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 ... Though mathematicians of earlier period are aware of this sequence yet it is attributed to Italian guy  known as Fibonacci because of his introducing it in Europe.

Japanese Puffer Fish These "mystery circles" are about 7 feet wide and are made by a 5 inch fish. It takes about seven to nine days for the pufferfish to construct the circles. Males laboriously flap their fins as they swim along the seafloor, resulting in disrupted sediment and amazing circular patterns. Although the fish are only about 12 centimeters (5 inches) long, the formations they make measure about 2 meters (7 feet) in diameter. But this new pufferfish's geometric patterns have three features never seen before. First, they involve radially aligned ridges and valleys outside the nest site. Second, the male decorates these ridges with fragments of shells. Third, the male gathers fine sediments to give the resulting formation a distinctive look and coloring. Strangely enough, the male "gathers" the fine sediments using the circular pattern itself, Kawase said. A fluid dynamics test using a half-size model of one of these circles found th

WPMD aims at understanding of universe , world and its constituent elements. The awareness and the understanding of the basic questions provide solid base for a rational and a balanced approach  in ever changing world that in turn needs adaption for successful solution. Objectivity is always the goal yet the subjective aspect can not be avoided. Position of part in relation to whole; absolute versus dynamic; a priori & a posteriori ; Knowledge of possibilities, limitations, variables and calculations are prime requirements for attaining excellence, progress and order resulting in gratifying outcomes and actualization . Pursuit of truth and beauty are the very cores on which it is founded.