#Ratio math illustrations windows

It is believed that Martin Ohm (1792вЂ“1872) was the first person to use the term вЂњgoldenвЂќ to describe the golden ratio. The first we may compare to a measure of gold the second we may name a precious jewel.вЂќ The вЂњGolden RatioвЂќ was coined in the 1800вЂ™s вЂњGeometry has two great treasures: one is the theorem of Pythagoras the other, the division of a line into extreme and mean ratio. Johannes Kepler (1571-1630), discoverer of the elliptical nature of the orbitsВ of the planets around the sun, also made mention of the вЂњDivine Proportion,вЂќ saying this about it:

#Ratio math illustrations windows

Leonardo Da Vinci, for instance, used it to define all the fundamental proportions of his painting of вЂњ The Last Supper,вЂќ from the dimensions of the table at which Christ and the disciples sat to the proportions of the walls and windows in the background.

The Renaissance artists used the Golden Mean extensively in their paintings and sculptures to achieve balance and beauty. Leonardo Da Vinci provided illustrations for a dissertation published by Luca Pacioli in 1509 entitled вЂњ De Divina ProportioneвЂќ (1), perhaps the earliest reference in literature to another of its names, the вЂњDivine Proportion.вЂќ This book contains drawings made by Leonardo da Vinci of the five Platonic solids. It was first called the вЂњDivine ProportionвЂќ in the 1500вЂ™s

The contributions of Pingala and Fibonacci are important, but itвЂ™s not apparent that anyone even realized its connection to the Golden Ratio until the 1600вЂ™s by Johannes Kepler and others. The sequence itself though had been described as early as the 2nd or 3rd century BC in the works of Acharya Pingala, an Indian mathematician who enumerated the possible patterns of Sanskrit poetry that could be formed from syllables of two lengths. Liber Abaci became a pivotal influence in adoption by the Europeans of the Arabic decimal system of counting over Roman numerals. He learned of it though while being educated in North Africa with an Arab master, where he was exposed to the much earlier knowledge of Indian mathematicians. His book Liber Abaci, published in 1202, introduced this sequence to Western European mathematics in the form of a math problem on the breeding of rabbits. What we now as the Fibonacci sequence is named after Leonardo Pisano Bonacci (aka Bigollo) of Pisa, an Italian born in 1175 AD, who later became known as Leonardo Fibonacci. The Fibonacci Sequence was written of in India in about 200-300 BC and brought to the Western world around 1200 AD He also linked this number to the construction of a pentagram. Plato (circa 428 BC вЂ“ 347 BC), in his views on natural science and cosmology presented in his вЂњTimaeus,вЂќ considered the golden section to be the most binding of all mathematical relationships and the key to the physics of the cosmos.Д®uclid (365В BC вЂ“ 300В BC), in вЂњElements,вЂќ referred to dividing a line at the 0.6180399вЂ¦ point as вЂњdividing a line in the extreme and mean ratio.вЂќ This later gave rise to the use of the term mean in the golden mean. Phidias (500 BC вЂ“ 432 BC), a Greek sculptor and mathematician, studied phi and applied it to the design of sculptures for the Parthenon. The Greeks are thought by some to have based the design of the ParthenonВ on this proportion, but this is subject to some conjecture. It appears that the Egyptians may have used both pi and phi in the design of the Great Pyramids. Uses in architecture potentially date to the ancient Egyptians and Greeks It is reasonable to assume that it has perhaps been discovered and rediscovered throughout history, which explains why it goes under several names. While the proportion known as the Golden Mean has always existed in mathematics and in the physical universe, it is unknown exactly when it was first discovered and applied by mankind.