"The golden ratio in particular is seen in the proportions of the Parthenon in Greece and the Great Pyramid of Giza, indicating that ancient architects might have employed these as sacred proportions to mirror the harmony found in nature."
"The golden ratio refers to a specific mathematical principle which is present across art, architecture, and much of the natural world."
"The ratio between terms in the Fibonacci sequence tends towards the golden ratio."
"The golden ratio may be the fundamental constant of nature."
"The golden ratio is always such a cool little tool for you to use."
"Golden ratio. Put your point of interest in the little hole of the spiral, align the rest of the image with a rule of thirds type grid, and you're pretty much there."
"The golden ratio is basically a term that describes the way specific elements can be placed within a piece of artwork in the most aesthetically pleasing way possible."
"Some suggest that the reason we're drawn to this particular artwork can be explained using a mathematical quandary known as the golden ratio."
"The Fibonacci sequence is life's way of creating the golden mean."
"While no designer in their right mind would swear by one single rule, the golden ratio has seemingly become a mainstay in graphic design."
"The golden ratio... it can be defined by taking a line and breaking it into two separate pieces."
"Now we have created an amazing thing, a rectangle that has these proportions is something that we call a golden rectangle."
"The Golden Age... the golden ratio... civilization at its height."
"The golden ratio is defined as A plus B is to A as A is to B."
"Every one of these rectangles has the golden ratio on it. Fascinating!"
"The ratio of a to B is Phi, so the ratio of Y to X is also Phi."
"If you have one of these golden ratio calipers, you actually have the key to the universe."
"The Turtle's shell has a rectangle with a ratio of 1.618 to 1."
"How you make a golden ratio out of 60 seconds is to have a 23-second half and a 37-second half."
"The golden ratio is the unique ratio of lengths where the hole divided by the larger is the same as the larger divided by the smaller."
"The geometry of beauty is written in the golden ratio, the sacred harmonic proportions existent in all living things."
"This overlay, this golden ratio, actually exists in nature."
"The golden ratio turns up all the time whenever you're doing pentagons or pentagrams."
"The Golden Ratio occurs in the human body, most notably in the relation of the height of a person’s navel from the floor, to the height at the top of the head."
"It's absolutely remarkable that Bach depicted the golden spiral musically."
"Golden ratio is a mathematical ratio which you can find almost anywhere... it creates an organic, balanced, and aesthetically pleasing composition."
"All trees, plants, flowers, humans, everything's based on what's called the golden ratio."
"A correct love hug reaches its maximum pressure much later, creating a ratio called the golden mean ratio."
"The diagonal of a regular pentagon is precisely the golden number phi."
"For many landscape photographers, and me included, I actually prefer to put a horizon line on the lower horizontal line of the golden ratio rather than the rule of thirds."
"The music of Beethoven is so immense, it is created with so much love, care, and dignity, the absolute golden ratio of the form."
"The Fibonacci spiral can be seen throughout nature."
"The golden ratio is found in a lot of Nature and tends to be very appealing to our eyes."
"The golden ratio... is the well-known phi."
"The golden ratio plays a very important role throughout mathematics and theory of tilings and partitions, continued fractions, approximation, all kinds of geometry, entropy, and more."
"The aesthetically pleasing proportion of 1 to 1.618 is often known as the golden ratio."
"Everything in nature and in life is just built based on this Fibonacci sequence."
"The Fibonacci numbers are also used to find the divine proportion, the perfect shape, the one used by classical architects which is still commonly used by designers today."
"The Fibonacci sequence and the golden section... it's about a ratio, and that ratio is simply this: it breaks down into the 1:2 1.618."
"This number is a special number in math or a number theory, this is called the golden ratio."
"The proportion of 0.618 to 1 is a mathematical basis for the shape of playing cards, the Parthenon in Greece, sunflowers, snail shells, Greek vases, and the spiral of galaxies from outer space."
"The golden ratio, 1 plus square root of 5/2, is the solution of the characteristic equation of the Fibonacci series."
"Golden ratio, mathematics in mathematics, monstrous moonshine theory is the unexpected connection between the monster group M and modular functions."
"It gives you that reference of 1/2 1.618 the golden ratio Fibonacci scale so you know you get this ratio versus this ratio and it gives you a feel for where you want to put a design on a bowl how where you want to put the lid on a box."
"The golden ratio follows the geometry and symmetry of life and the divine."
"Rotating it by 137.5 degrees, and this is an absolutely crucial number."
"These sequences have existed and they're called the golden ratio or the golden mean."
"If you divide any number in the sequence by the previous number, the ratio is always 1.618, known as the golden ratio."
"The same ratio that we find as beautiful is made from the square root of two." - Speaker
"What is it about this number 1.618 that makes it so prevalent in nature?"
"The golden ratio is where we optimize our finances, where we ensure that we're getting maximum out of what we are doing in our business financially."
"61.8% is found throughout the world and not just the stock market."
"...the interesting thing about Fibonacci sequences is that as you go off to infinity, the ratio of successive Fibonacci integers actually converges to the golden ratio."