Nautilus shell spirals may have phi proportions, but not as you may have heard. The Nautilus shell if often associated with the golden ratio. There is a fair amount of confusion, misinformation and controversy though over whether the graceful spiral curve of the nautilus shell is based on this golden proportion. Some say yes, but offer no proof at all. Some show examples of … [Read more...]
Facial Analysis and the Marquardt Beauty Mask
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 2001 documentary "The Face." Dr. Marquardt, also CEO of Marquardt Aesthetic Imaging, has … [Read more...]
Beauty, the perfect face and the Golden Ratio, featuring Florence Colgate
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 YouTube video and information in this article may give some insight into the answer, with details on the contest, a recap of explanations of beauty … [Read more...]
Amen Break and the Golden Ratio in Music
It's one of the most popular drum loops in music history. The "Amen break" is one of the most frequently used drum loop samples in music. It's only four bars long. It only lasts about six or seven seconds. Even so, this short sampled loop has been used in well over a thousand songs in a wide variety of music, including hip hop, techno, breakbeat and digital. That's pretty … [Read more...]
Facial Beauty and the "New" Golden Ratio (or is it just 1.618 in disguise?)
University study declares a "new" golden ratio for facial beauty but validates Phi, the Golden Ratio, as the basis for perceptions of beauty. A university study (PDF) by Pamela M. Pallett, Stephen Link and Kang Lee at the University of Toronto and University of California, San Diego announced that a "new" golden ratio had been found in perceptions of beauty in the human … [Read more...]
Phi and the Golden Section in Architecture
Phi (Φ) the Golden Section, has been used by mankind for centuries in architecture. Its use started as perhaps early as with the Egyptians in the design of the pyramids. When the basic phi relationships are used to create a right triangle, it forms the dimensions of the great pyramids of Egypt, with the geometry shown below creating an angle of 51.83 degrees, the cosine of … [Read more...]
Car and Auto Industry Design and the Golden Ratio
The Golden Ratio is no stranger in the design circles of the auto industry. Aston Martin gained some great press on its extensive application of the golden ratio in the design of the Rapide S and DB9, with articles appearing in Forbes and the New York Times. This is hardly the first application of the golden ratio by the auto industry. The logos themselves of a number of … [Read more...]
Perfect Golden Ratio Body Proportions for Men
The Golden Ratio and Perfect Proportions for the Male Body Beauty in the the human form is closely correlated to, if not defined by, the golden ratio. It should be no surprise then that the perfect proportions for the male body would also be related to the Golden Ratio. I recently reviewed a new body-building and exercise program called "Adonis Golden Ratio." I was … [Read more...]
Discussion and Comments
Your comments on all topics related to Phi, the Golden Ratio, and Fibonacci series are welcome on this general discussion page or any of the posts on the dozens of topics on the site. Here's what other site visitors and contributors are saying. … [Read more...]
The Parthenon and Phi, the Golden Ratio
Note: See updates to my research on the Parthenon in these articles: My article “Dr. George Markowsky’s “Misconceptions about the Golden Ratio” Reviewed,” published on this site in 2016. My book “The Golden Ratio – The Divine Beauty of Mathematics,” published by The Quarto Group in 2018. See pages 104-108. My article “Donald Duck visits the Parthenon in ‘Mathmagic Land,” … [Read more...]
