The Golden Ratio is a strange ratio that scientists have found all throughout nature, architecture, art, and various other places. Some say that the Golden Ratio could only have been made possible by God while others believe it is merely a coincidence. This “Golden Number” has been thought of as the most pleasing to the eye and many tests have been done to see whether humans’ perception of beauty is affected by the appearance of this phenomenon.
Fibonacci was born in approximately 1175 AD with the birth name of Leonardo in Pisa, Italy. During his life he went by many names, but Leonardo was the one constant. Very little is known of his early life, and what is known is only found through his works. Leonardo’s history begins with his father’s reassignment to North Africa, and that is where Fibonacci’s mathematical journey begins. His father, Guilielmo, was an Italian man who worked as a secretary for the Republic of Pisa. When reassigned to Algeria in about 1192, he took his son Leonardo with him. This is where Leonardo first learned of arithmetic, and was interested in the “Hindu-Arabic” numerical style (St. Andrews, Biography). In 1200 Leonardo ended his travels around the Mediterranean and returned to Pisa. Two years later he published his first book. Liber Abaci, meaning “The Book of Calculations”.
The Fibonacci sequence was introduced as a problem involving population growth based on assumptions. Fibonacci got the idea from early Indian and Arabian Mathematics. He grew the theory and introduced it to the western world. The sequence is explained by starting at 1, 2 then adding the two t...
The first person who is believed to have used the Golden Ratio is Phidias when he used it to design the statues inside of the Parthenon. This happened between 490 and 430 BC. In the early 300’s BC Plato used the Golden Ratio when he described the five platonic solids which are the tetrahedron, cube, octahedron, dodecahedron, and the icosahedron. Later in the 300’s Euclid gave the first written definition of the Golden Ratio which is an extreme and mean ratio. Then between 1170 and 1250 Fibonacci discovered a numerical series which had sequential elements that approaches the Golden Ratio asymptotically. Between 1445 and 1517 Luca Pacioli defined the Golden Ratio as the “divine proportion”. Then in between 1550 and 1631 Michael Maestlin published the first known approximation of the inverse golden ratio as a decimal fraction which is 1.61803398875. Very soon afterwards Johannes Kepler proved that the golden ratio is the limit of the ratio of consecutive Fibonacci numbers. Then in between 1842 and 1891 Edouard Lucas named the numerical sequence the Fibonacci sequence. In 1974 Roger Penrose discovered Penrose tiling which is a pattern that is related to the golden ratio both in the ratio of areas of its two rhombic tiles and in their relative frequency within the pattern.
Lamb, Robert. "How are Fibonacci numbers expressed in nature?" HowStuffWorks. Discovery Communications, 24 June 2008. Web. 28 Jan. 2010. .
The recursive sequence of numbers that bear his name is a discovery for which Fibonacci is popularly known. While it brought him little recognition during the course of his life, is was nearly 100 years later when the majority of the mathematicians recognized and appreciated his invention. This fascinating and unique study of recursive numbers possess all sorts of intriguing properties that can be discovered by applying different mathematical procedures to a set of numbers in a given sequence. The recursive / Fibonacci numbers are present in everyday life and they are manifested in the everyday life in which we live. The formed patterns perplex and astonish the minds in real world perspectives. The recursive sequences are beautiful to study and much of their beauty falls in nature. They highlight the mathematical complexity and the incredible order of the world that we live in and this gives a clear view of the algorithm that God used to create some of these organisms and plants. Such patterns seem not have been evolved by accident but rather, they seem to have evolved by the work of God who created both heaven and
Nevertheless, that day followed me, and I tried to understand more about fractals through the resources I already had at my disposal-- through courses I was taking. Sophomore year, through my European History and Architecture courses, I learned about many ancient architectural feats-- Stonehenge, the Pyramids of Giza, the Parthenon, many Gothic Cathedrals, and the Taj Mahal-- and that they all somehow involved the use of the golden ratio. I will come back to how this relates to fractals later in the article, but for now know that each of these buildings use different aspects of their design to form the golden ratio. I was intrigued by the fact that fractals, what seemed to be something only formed by the forces of nature, were being constructed by human hands. Although I wanted badly to find out more, I waited until that summer, when I discovered a YouTube account by the name of Vihart. Vihart’s videos are not tutorials on how to do math, however Vihart’s ramblings about the nature and the concepts of the mathematical world have a lot of educational value, especially on topics that are more complicated to understand then to compute. Her videos on fractal math and their comparability to nature, helped to show me that...
Leonardo Da Vinci was born April 15 1452, to Caterina Da Vinci and Piero Frusino di Antonio Da Vinci. He was a popular Italian Renaissance polymath. A polymath is someone that has mastered several different subject areas. His interest included invention, painting, sculpting, architecture, science, music, mathematics, engineering, and literature; just to name a few. He has been variously called father of palaeontology, which is the study of life that once existed. He is widely considered one of the greatest painters of all time, and was often credited with the invention of the parachute, helicopter and the tank.
Leonard Da Vinci was born on April 15, 1452 in a Tuscan Hamlet near Vinci which today is called Italy. Leonardo was originally born Leonardo di ser Piero da Vinci this mean “Leonardo (son) of (Mes)ser Piero from Vinci.” Leonardo was born out of wedlock to a wealthy notary named Piero da Vinci, and a peasant woman Caterina in Vinci. After his mother left his father, Leonardo spent the first five years of his life with his mother in the hamlet of Anchiano. In 1457, Leonardo moved to live with his father, grandparents, and his uncle in the small town of Vinci. Leonardo da Vinci was an Italian Renaissance man who areas of interests included painting, sculpting, invention, architecture, science, music, mathematics, engineering, literature, anatomy,
Leonardo da Vinci was a well-known artist, engineer, and mathematician in the 14th and 15th centuries, who created and assisted in some of the most well known works of art, mechanical ingenuity, and theoretical mathematics. His works were equally important in his fields of study, with him discovering and portraying many different methods of his profession to increase realism, efficiency, and integrity. He had influences over many modern day technologies, like the parachute, steam turbines, and even thermal engines. Leonardo’s life was full of changes and moments of blatant curiosity, his childhood was an experience when he abandoned traditional education in search of answers, his adult years were used to develop his skills as an artist and