Raphael was one of three Master artists of the Renaissance Raffaello Sanzio da Urbino, known as Raphael, was an Italian painter and architect of the High Renaissance and lived from to He is recognized as one of the three great masters of that period, accompanied by Michelangelo and Leonardo da Vinci.
His work is admired for its form, composition, and visual achievement of the ideal of human grandeur. It captures the spirit of the Renaissance, and is revered as his masterpiece. It was painted between and He found that their durations are grounded in golden ratio relationships.
De Groot took an empirical approach to chart a pattern in the lengths of sub-cycles in GDP growth. Using the Golden Ratio to win at football. The golden ratio is found in many places, but here's one you might not have expected: It can be found in football gaming strategy when making the "point after touchdown" decision as to whether to kick for 1 extra point or go for a 2 point conversion. This applies to the situation when a team is trailing by 14 points late in a football game, and then scores a touchdown to be trailing the other team by 8 points.
So what should you do: Kick for 1 point after touchdown PAT or go for a 2 point conversion? Most football teams kick the PAT in this situation, but in fact it is almost always better to go for 2. Facial golden ratios are simple, clear and abundant. Since my first investigation of human facial proportions in , it seemed clear that the most important features that define a human face are the simplest and most obvious: An oval head and the positions and dimensions of the eyes and the mouth.
As evidence, consider the "smiley face. Let's instead express these same facial markers with normal human proportions, and with the simplest possible representation. This requires a vertical oval, two lines for the eyes and a line for the mouth. The resulting face will look something more like this: This simple facial configuration is easily mapped to very natural human proportions with the use of four simple golden ratio proportions: The next important human … More on Beauty.
A template for human beauty is found in phi, the pentagon and dodecagon Dr. Stephen R. Marquardt is the world's most recognized expert on facial analysis and beauty. He has appeared in many documentaries and been referenced in countless articles, including the Beauty episode of BBC's documentary "The Face. Marquardt, also CEO of Marquardt Aesthetic Imaging, has studied human beauty for decades in his practice of oral and maxillofacial surgery, and now continues his studies full time.
His work includes cross-cultural surveys on beauty, in which he found that all groups had the same perceptions of facial beauty. He also analyzed the human face from ancient times to the modern day. Through his research, he discovered that beauty is not only related to phi, but can be defined for both genders and for all races, cultures and eras with the beauty mask which he developed and patented.
This mask uses the pentagon and decagon as its foundation. Both of these geometric shapes embody … More on Beauty. The human face is based on Phi and Golden Ratio proportions. We'll use a succession of golden ratios to create a golden ruler to understand design in the face: The head forms a golden rectangle with the eyes at its midpoint.
The mouth and nose are each placed at golden sections of the distance between the eyes and the bottom of the chin. The beauty unfolds as you look further. Even when viewed from the side, the human head illustrates the Divine Proportion. The first golden section blue from the front of the head defines the position of the ear opening. The successive golden sections define the neck yellow , the back of the eye green and the front of the eye and back of the nose and mouth magenta.
The dimensions of the face from top to bottom also exhibit the Divine Proportion, in the positions of the eye brow blue , nose yellow and mouth … More on Beauty. What determines the beauty of a perfect face?
We may never answer the question "how many angels can dance on the point of a needle," but how about this one: "How many Divine proportions ratios are there in the face of an angel? The competition drew entries from 8, contestants, who were initially screened by a panel that included … More on Beauty.
Another attempt to debunk the Golden Ratio is fundamentally wrong. In October , Dr. Keith Devlin was interviewed by science writer Julia Calderone in an article titled "The one formula that's supposed to 'prove beauty' is fundamentally wrong. His comments have reach and impact, but his views on the golden ratio are not always accurate, complete, consistent, objective or supported by evidence. A highly regarded NYC designer, Darrin Crescenzi, described the article as "dangerous" and "under-informed nonsense," motivating him to write a … More on Beauty.
Best practice techniques for facial and beauty analysis. Surprising few get it right, so the results of many of these studies are inaccurate and misleading. There are four important keys to selecting photographs that are suitable for facial measurements. Next, it is critical to understand and measure the facial markers that commonly reflect golden ratio proportions. In this article I'll cover these key points, the common mistakes made and the best practices to yield results that are both accurate and meaningful.
Orientation of the head, and eliminating the impacts of perspective. As simple as it sounds, one of the most important aspects of any image used for facial analysis is that the subject be looking directly into the camera. The front of the face must be parallel to the lens of the camera. There must be no tilt of the head either up, down, left or … More on Beauty. Unlike pi, which is a transcendental number, phi is the solution to a quadratic equation.
Phi, like Pi, is a ratio defined by a geometric construction Just as pi p is the ratio of the circumference of a circle to its diameter, phi is simply the ratio of the line segments that result when a line is divided in one very special and unique way. Divide a line so that: the ratio of the length of the entire line A to the length of larger line … More on Phi.
Leonardo Fibonacci discovered the sequence which converges on phi. In the AD, Leonardo Fibonacci wrote in his book "Liber Abaci" of a simple numerical sequence that is the foundation for an incredible mathematical relationship behind phi. This sequence was known as early as the 6th century AD by Indian mathematicians, but it was Fibonacci who introduced it to the west after his travels throughout the Mediterranean world and North Africa.
He is also known as Leonardo Bonacci, as his name is derived in Italian from words meaning "son of the Bonacci". Starting with 0 and 1, each new number in the sequence is simply the sum of the two before it.
This sequence is shown in the right margin of a page in Liber Abaci, where a copy of the book is held by the Biblioteca Nazionale di Firenze. Click to enlarge. The relationship of the Fibonacci sequence to the golden ratio is this: The ratio of each successive pair of … More on Phi. Kalana Dido of France made a very insightful discovery in May that unites the visual spectrum of light, the proportions of the human body, the chakras i. This integrates four separate concepts, making it one of the more fascinating discoveries of Golden Ratio appearances I've seen in recent years.
Let's explore each topic and then see how they then relate. The Golden Ratio is a mathematical ratio you can find almost anywhere, like nature, architecture, painting, and music. When specifically applied to design specifically, it creates an organic, balanced, and aesthetically pleasing composition. The ratio itself comes from the Fibonacci sequence, a naturally occurring sequence of numbers that can be found everywhere, from the number of leaves on a tree to the shape of a seashell.
The Fibonacci sequence is the sum of the two numbers before it. It goes: 0, 1,1, 2, 3, 5, 8, 13, 21, and so on, to infinity. From this pattern, the Greeks developed the Golden Ratio to better express the difference between any two numbers in the sequence. How does this relate to design? This formula can help you when creating shapes, logos, layouts, and more. You can also take this idea and create a golden rectangle.
Take a square and multiple one side by 1. If you lay the square over the rectangle, the relationship between the two shapes will give you the Golden Ratio. If you keep applying the Golden Ratio formula to the new rectangle on the far right, you will end up with an image made up of increasingly smaller squares.
Now that the math lesson is over, how can you apply this knowledge to the work you do on a daily basis? Here are four ways to use the Golden Ratio in design:. The Golden Ratio can help you figure out what size font you should use for headers and body copy on a website, landing page, blog post, or even print campaign. A full set of permanent teeth, for instance, is 32—not a Fibonacci number.
Your heart has four chambers—not a Fibonacci number. The audio, illustrations, photos, and videos are credited beneath the media asset, except for promotional images, which generally link to another page that contains the media credit. The Rights Holder for media is the person or group credited. Caryl-Sue, National Geographic Society. For information on user permissions, please read our Terms of Service.
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