The Golden Section
Mathematics · Interactive
- DimensionsSubject to on-site plan
- PresentationInteractive
- PricingQuoted by manufacture spec
Purpose & Scientific Principle
The exhibition item borrows the human body proportion diagram of ancient Roman engineers to vividly interpret the golden ratio discovered by Pylagrass. Through the application and display expansion of the golden ratio, it shows the profound impact this discovery has had on various fields such as architecture and design in later generations.
How to Operate
The polymath Leonardo da Vinci worked hard to draw a perfectly proportioned human sketch "Vitruvian Man" (picture below) around 1485 based on Vitruvius's description in "Ten Books on Architecture" about 1,500 years ago. He embedded the human body into a rectangle and a circle at the same time, perfectly demonstrating the proportions of the human body, which contains the most magical mathematical ratio - the Golden Section. Just take a right triangle, its two right-angled sides are 1 and 1/2 respectively, then the hypotenuse is square root 5 divided by 2, and then subtract 1/2 of the right-angled side length to get AD. Then take AE=AD on AC, then the line segment AC divided by point E is the center-to-outer ratio (golden ratio), which is 0.618.
Application of the golden ratio: The famous ancient Greek statues of Venus de Milo and Apollo, the sun god, were designed with their legs extended, so that the ratio to their height is 0.618; photography taken using the golden ratio is more in line with the physiological structure of the human eye, making it easier for people to discover its beauty; the golden ratio was used in Leonardo da Vinci's works "Vitruvian Man", "Mona Lisa" and "The Last Supper". The golden section principle is also followed in ancient buildings such as the Parthenon in Athens and the pyramids in Egypt. One of the optimization methods popularized by the famous mathematician Mr. Hua Luogeng in his later years is the golden section 0.618 method.
The golden section in nature: The golden section exists a lot in nature, in the proportions of the human body, the structure of animals, and the shapes of plants. For example, the length-to-width ratio of maple leaves, the ratio of body length to wing width of butterflies, the expansion ratio of nautilus, etc. The structure of crystals is also often related to the Fibonacci sequence.
Fibonacci Sequence: Italian mathematician Leonardo Pisano, better known as Fibonacci (Leonardo Pisano, known as Fibonacci, 1170-1250), discovered the famous Fibonacci sequence defined by recursion, in which each term is equal to the sum of the previous two terms. The quotient obtained by dividing adjacent two terms of this magical sequence will approach 0.618 as the number of terms increases. Therefore, the Fibonacci sequence is called the golden section sequence. Expand according to Fibonacci numbers on the plane, and the resulting rectangle is called a golden rectangle. Walking along the diagonal corners of the golden rectangle, we get a beautiful spiral, which is also called a logarithmic spiral (also called an equiangular spiral).
Pythagoras discovered the golden section and expressed it mathematically. Divide a line segment into two parts, so that the ratio of the larger part to the full length is equal to the ratio of the smaller part to the larger part, then this ratio is the golden section, and its ratio is approximately 0.618. In the 1st century BC, Marcus Vitruvius Pollio, the royal architectural engineer of ancient Rome, first proposed applying the natural proportions of the human body to the measurement of buildings, and summarized the proportional laws of the human body structure. The exhibits use the concept of the golden section as a reference to the layout of the human body to demonstrate the application of the golden section.
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