5/31/2023 0 Comments Oe goldenratioBut modern investigations (for example, G. Throughout history many people have tried to attribute some kind of magic or cult meaning as a valid description of nature and attempted to prove that the golden ratio was incorporated into different architecture and art objects (like the Great Pyramid, the Parthenon, old buildings, sculptures and pictures). Phi is the first Greek letter in the name of the Greek sculptor Phidias. The symbol (phi) for the notation of the golden ratio was suggested by American mathematician M. Chrystal (1898) first used this term in a mathematical context. Sulley (1875) first used the term "golden ratio" in English and G. Ohm (1835) gave the first known use of the term "golden section", believed to have originated earlier in the century from an unknown source. Simson (1753) gave a simple limit representation of the golden ratio based on its very simple continued fraction. Kepler (1608) showed that the ratios of Fibonacci numbers approximate the value of the golden ratio and described the golden ratio as a "precious jewel". Mästlin (1597) evaluated approximately as. Cardano (1545) mentioned the golden ratio in his famous book Ars Magna, where he solved quadratic and cubic equations and was the first to explicitly make calculations with complex numbers. Pacioli published the book De Divina Proportione, which gave new impetus to the theory of the golden ratio in particular, he illustrated the golden ratio as applied to human faces by artists, architects, scientists, and mystics. Therein Euclid showed that the "mean and extreme ratio", the name used for the golden ratio until about the 18th century, is an irrational number. Specifically, in book VI of the Elements, Euclid gave the following definition of the golden ratio: "A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less". 265 BC), the Italian mathematician Leonardo of Pisa (1170s or 1180s–1250), and the Renaissance astronomer J. The properties of the golden ratio were mentioned in the works of the ancient Greeks Pythagoras (c. For example, the Greek sculptor Phidias (490–430 BC) made the Parthenon statues in a way that seems to embody the golden ratio Plato (427–347 BC), in his Timaeus, describes the five possible regular solids, known as the Platonic solids (the tetrahedron, cube, octahedron, dodecahedron, and icosahedron), some of which are related to the golden ratio. It is possible that the magical golden ratio divisions of parts are rather closely associated with the notion of beauty in pleasing, harmonious proportions expressed in different areas of knowledge by biologists, artists, musicians, historians, architects, psychologists, scientists, and even mystics. The concept of golden ratio division appeared more than 2400 years ago as evidenced in art and architecture. The two ratios are both approximately equal to 1.618., which is called the golden ratio constant and usually notated by : The division of a line segment whose total length is a + b into two parts a and b where the ratio of a + b to a is equal to the ratio a to b is known as the golden ratio.
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