The Golden Ratio: The Divine Beauty Of Mathematics EXCLUSIVE
Gary B. Meisner is the creator of www.goldennumber.net, a popular website dedicated to the mathematics, prevalence, and design applications of the golden ratio. In 2004, he led the development of his PhiMatrix Golden Ratio Design and Analysis software, which is used by thousands of artists, architects, designers, and photographers in over seventy countries, as well as in cosmetic medical and stock market analysis applications. After earning accounting and MBA degrees from two top business schools, he spent most of his career in CFO/CIO roles with operating units of five Fortune 1000 public companies. Gary is now a self-employed technology/systems consultant conducting ongoing research and collaboration on the golden ratio, and his work has been featured in Da Vinci The Exhibition at the Venetian Hotel in Las Vegas. Providing an online community in which new findings can be shared and discussed, he helps others to appreciate the incredible beauty and design in the world around us and to applying these same principles of design to their own creative works.
The Golden Ratio: The Divine Beauty of Mathematics
In the book, Pacioli writes about mathematical and artistic proportion, particularly the mathematics of the golden ratio and its application in art and architecture. The book contains dozens of beautiful illustrations of three-dimensional geometric solids and templates for script letters in calligraphy.
The golden ratio, also known as the divine proportion, is a special number (equal to about 1.618) that appears many times in geometry, art, an architecture. The golden ratio is found when a line is divided into two parts such that the whole length of the line divided by the long part of the line is also equal to the long part of the line divided by the short part of the line.
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. Expressed algebraically, for quantities a \displaystyle a and b \displaystyle b with a > b > 0 \displaystyle a>b>0 ,
The golden ratio appears prominently in the Penrose tiling, a family of aperiodic tilings of the plane developed by Roger Penrose, inspired by Johannes Kepler's remark that pentagrams, decagons, and other shapes could fill gaps that pentagonal shapes alone leave when tiled together. Several variations of this tiling have been studied, all of whose prototiles exhibit the golden ratio:
The psychologist Adolf Zeising noted that the golden ratio appeared in phyllotaxis and argued from these patterns in nature that the golden ratio was a universal law. Zeising wrote in 1854 of a universal orthogenetic law of "striving for beauty and completeness in the realms of both nature and art".
The Great Pyramid of Giza (also known as the Pyramid of Cheops or Khufu) has been analyzed by pyramidologists as having a doubled Kepler triangle as its cross-section. If this theory were true, the golden ratio would describe the ratio of distances from the midpoint of one of the sides of the pyramid to its apex, and from the same midpoint to the center of the pyramid's base. However, imprecision in measurement caused in part by the removal of the outer surface of the pyramid makes it impossible to distinguish this theory from other numerical theories of the proportions of the pyramid, based on pi or on whole-number ratios. The consensus of modern scholars is that this pyramid's proportions are not based on the golden ratio, because such a basis would be inconsistent both with what is known about Egyptian mathematics from the time of construction of the pyramid, and with Egyptian theories of architecture and proportion used in their other works.
The golden ratio, also known as the golden number, golden proportion, or the divine proportion, is a ratio between two numbers that equals approximately 1.618. Usually written as the Greek letter phi, it is strongly associated with the Fibonacci sequence, a series of numbers wherein each number is added to the last. The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on, with the ratio of each number and the previous number gradually approaching 1.618, or phi.
Does phi, the golden ratio, the divine proportion, whatever grand name you wanna give it, really show up everywhere in nature, or is it our pattern-sensing brains making us think that we see it everywhere?
The name of Fibonacci is connected with the Fibonacci sequence, which hooks up with rabbits and the golden ratio.Most of this knowledge is only partially correct.The man was born around 1175 in Pisa, and died somewhere around the middle of the 13th century.His name was Leonardo of Pisa (Leonardo Pisano), andFibonacci is a nickname invented by historian Guillaume Libri in 1838 because Fibonacci in hismost famous work Liber abbaci (1202) he announced himself asfilius Bonaci although his father's name was Guilielmo Bonacci.So instead of "son" he may have meant to say "of the Bonacci family".The rabbit story is only one of the hundreds of examples he uses to illustrate the strength ofcalculating with the Hindu-Arabic number system as we know it today worldwide.This Liber abbaci, written in Latin, is a true work of mathematics following theEuclidean approach of logic derivation.It also explains many techniques to solve problems like the rule of three,the rule of false position, and so many algebraic recipes we are quitefamiliar with today.And, most importantly, it contains also many illustrative examplesand whole chapters with practical applications from commerce and finance.The rabbit example is only one of them. It was known for centuries by Indiansin connection with Sanskrit poetry long before Fibonacci. The name Fibonacci sequence was coined byÉdouard Lucas in the 19th century.And Fibonacci never connected the sequence with the golden section φ.Luca Pacioli in 1509 called φ the divine ratio and the news was spreadthat this number appearing in nature so often should represent perfectionand beauty.Devlin debunks also this myth. 041b061a72