#### Applications for Better Art, Design and Composition

The Parthenon has long been associated with the golden ratio. The lack of clear evidence to support this though has led some to conclude in error that this is just a myth. This article will provide the best evidence Ive found to date to illustrate appearances of golden ratios in the design of the Parthenon. In my analysis, Ill use the golden ratio grids created with pixel-level accuracy by my PhiMatrix software. These include golden rectangles and/or rectangles with a dividing line at the golden ratio point of their height or width. Ill apply these to the best photos and illustrations of the Parthenon available. This requires that the images be very high resolution, and taken from directly perpendicular to the Parthenon to avoid distortions from perspective. As a quick background, the golden ratio is defined by dividing a line at the one point at which the ratio of the larger segment (a) to the small segment (b) is equal to the ratio of the line (a+b) to the larger segment (a). Note … More on Art and Design

In November 2019, Samantha James of Carwow published a very interesting article titled Best-looking cars of the last decade. What made it more interesting yet is that their review applied golden ratio analysis techniques used for human faces to the front end view of automobiles. Headlights became eyes. Emblems became noses. Grills became mouths. Makes good sense, right? Ive been showing the golden ratio in human faces since the late 1990s. London plastic surgeon Dr. Julian Silva is recognized for giving a golden ratio score of famous celebrity faces, as shown below left. Carwow used a very similar approach, as shown on the right: Carwow is UK company that helps consumers to make choosing and buying their perfect car easy and enjoyable. Stefanie Finch of their PR agency, Propellernet.co.uk, contacted me on behalf of Carwow to ask if Id be interested in covering their story on this site. I of course said YES! She and the Carwow team were kind enough to provide me with the … More on Art and Design

Governments around the world commemorate the Golden Ratio, Phi and Fibonacci sequence. Stamp collecting is one of the worlds most popular educational hobbies, and is enjoyed by people of all ages and nationalities. The most popular stamp ever is US 1993 Elvis stamp, with over 124 million collected. So, the Golden Ratio and Fibonacci sequence may not compete with Elvis in popularity anytime soon, but they too have been recognized with commemorative stamps issued by governments around the world. In addition to adding some phi to philately, they offer some interesting expressions of golden ratio concepts, as well as its application in design. Liechtenstein 2013 Commemorative Fibonacci Sequence and Phi Stamp set: The Principality of Liechtenstein, a landlocked micro-state bordered by Switzerland and Austria, issued a set of three stamps in 2013 that illustrate the Fibonacci sequence and its relationship to the golden ratio. Note that interesting presentation of concepts: The first … More on Art and Design

The golden ratio is Stephen Silvers secret weapon of character design. Stephen Silver is a character designer and art teacher who has designed characters for Disney Television Animation, Sony Feature Animation and Nickelodeon Animation. In this role he has designed the style of the shows such as Kim Possible, Kevin Smiths Clerks the animated series, Danny Phantom and many others. He is also the author and artist of seven books on the art of character design, caricature, sketching and life drawing. In addition to his freelance work and lectures, he owns an art school called Silver Drawing Academy in Simi Valley, CA. He has two online character design courses online at www.schoolism.com. Those are some great credentials. And what does he say is his secret weapon for character design? Yes, its the golden ratio. The golden ratio is flawless because it gives the small, medium and large that design is built upon. He describes the golden ratio is just perfect, flawless, … More on Art and Design

Overview: Analysis of the site of the Great Pyramid of Giza reveals that the positions and relative sizes of the pyramids may be based on the golden ratio. Evidence of the Golden Ratio in the Great Pyramid complex. There are many pyramid theories and questions as to who built the pyramids in ancient Egypt. Its commonly known though in Egyptology that the proportions of the Great Pyramid of Egypt are within inches of a golden ratio-based pyramid. This is discussed in detail in my article Phi, Pi and the Great Pyramid. Some say, however, that this single piece of evidence is just a simple coincidence. The primary rationale given to deny this claim is that there is no written historical evidence that the ancient Egyptians had any knowledge of the golden ratio. Thats a reasonable objection, but what if the evidence showed that the application of the golden ratio at Giza was not limited to the Great Pyramid? That evidence is presented in this article. The golden ratio connection … More on Art and Design

New study unveils Michelangelos extensive use of the golden ratio in the Sistine Chapel. In 2013, I reported that Michelangelo used the golden ratio in his painting The Creation of Adam in the Sistine Chapel. This Divine Proportion appears at the point at which Adams finger is touched by the finger of God, as God breathes life into Adam. In July 2015, Clinical Anatomy published an article by a team from Brazil titled More than a neuroanatomical representation in The Creation of Adam by Michelangelo Buonarroti, a representation of the Golden Ratio. (PDF here.) The article claimed, incorrectly, that there was no previous association of Michelangelos works with the golden ratio. It identified the very same golden ratio touch point as the one reported here two years earlier. It also claimed, however, a new finding. It claimed that the fingers touched at the golden ratio point of the length of all the paintings on the ceiling of the Sistine Chapel. My analysis of this claim … More on Art and Design

New Google logo design finds visual harmony using the Golden Ratio. Googles design follows in the footsteps of Leonardo da Vinci and other masters When Luca Pacioli published The Divine Proportion in 1509 (with illustrations by Leonardo da Vinci), he described his work on this golden ratio of 1.618 as a very delicate, subtle and admirable teaching that would delight in diverse questions touching on a very secret science. Johannes Kepler later called it a precious jewel of geometry. The designers at Google have apparently found its value too, as we see when we study and appreciate the underlying design of Googles new logo, iconic G, the microphone icon and even the layout of the Google search page. This is the kind of thoughtful design work that follows in the footsteps of Leonardo, Michelangelo, Raphael, Botticelli, Seurat, Le Corbusier and other masters of design, and that would make Pacioli proud. Heres a version without the arrows for a clearer … More on Art and Design

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 1483 to 1520. 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. One of his most famous works is The School of Athens, a fresco in the Apostolic Palace in the Vatican. It captures the spirit of the Renaissance, and is revered as his masterpiece. It was painted between 1509 and 1511. The School of Athens: Inspired by a union of art and mathematics It was also in 1509 that Luca Pacioli published the book De Divina Proportione (The Divine Proportion), with illustrations by Leonardo da Vinci. MonaLisa.org reports that The School of Athens incorporates many of the mathematical theories of Luca and Leonardo. Civilisation author Kenneth … More on Art and Design

#### Stock Market and FOREX Trading Analysis

In 2021, Bert de Groot, Professor of Governance and Strategic Investment Policy at Erasmus School of Economics, published a paper in “Technological Forecasting and Social Change” titled “Disentangling the enigma of multi-structured economic cycles - A new appearance of the golden ratio.” In his paper, De Groot examines the economic cycles of GDP growth in over two dozen countries. 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. Understanding the interrelationships between the length of economic sub-cycles then allows their cycles and their fluctuations to be detected … More on Markets/Gaming

Using the Golden Ratio to win at football. The golden ratio is found in many places, but heres 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. The reason is related to … More on Markets/Gaming