What is the square of PHI?

The large yellow square has sides of length phi, so its area is phi2. The sides of a red rectangle are of length phi and 1-phi=phi2 so each has an area of phi3! The small blue square has sides of length 1-phi=phi2 so its area is phi4!!

In what way is the Golden Ratio related to the Fibonacci sequence?

There is a special relationship between the Golden Ratio and Fibonacci Numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, etc, each number is the sum of the two numbers before it). So, just like we naturally get seven arms when we use 0.142857 (1/7), we tend to get Fibonacci Numbers when we use the Golden Ratio.

Is a square a Golden Ratio?

Take a square and multiple one side by 1.618 to get a new shape: a rectangle with harmonious proportions. If you lay the square over the rectangle, the relationship between the two shapes will give you the Golden Ratio.

Why is 1.618 special?

The Golden Ratio (phi = φ) is often called The Most Beautiful Number In The Universe. The reason φ is so extraordinary is because it can be visualized almost everywhere, starting from geometry to the human body itself!

What’s the inverse of Phi?

The inverse of Phi, 1/Phi, is commonly referred to as the “lowercase phi” (Both symbols for Phi and phi are at top of page). Any division of two quantities that results in Phi or phi yields the Golden Ratio. This can be explained by considering the nature of ratios.

What is the relation between the golden ratio and Golden Rectangle?

Approximately equal to a 1:1.61 ratio, the Golden Ratio can be illustrated using a Golden Rectangle. This is a rectangle where, if you cut off a square (side length equal to the shortest side of the rectangle), the rectangle that’s left will have the same proportions as the original rectangle.

What mathematician discovered the golden ratio?

The ancient Greeks recognized this “dividing” or “sectioning” property, a phrase that was ultimately shortened to simply “the section.” It was more than 2,000 years later that both “ratio” and “section” were designated as “golden” by German mathematician Martin Ohm in 1835.