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Illustration showing the golden angle. The golden angle is the smaller of two angles created by dividing the circumference of a circle according to the golden section. The ratio of the length of the larger arc to the smaller arc is equal to the ratio of the entire circumference to the larger arc. The golden angle is approximately 137.51°.

Golden Angle

Illustration showing the golden angle. The golden angle is the smaller of two angles created by dividing…

Illustration showing the construction of a golden rectangle. Beginning with a unit square, a line is then drawn from the midpoint of one side of the square to its opposite corner. Using that line, an arc is drawn that defines the length of the rectangle. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi.

Construction Of A Golden Rectangle

Illustration showing the construction of a golden rectangle. Beginning with a unit square, a line is…

Illustration showing how the golden ratio in a regular pentagon (inscribed in a circle) can be found using Ptolemy's theorem. The lines that are bolded form a quadrilateral. Ptolemy's theorem says the square of b equals the sum of a squared and ab, which in turn gives the golden ratio.

Golden Ratio In A Pentagon

Illustration showing how the golden ratio in a regular pentagon (inscribed in a circle) can be found…

Illustration showing the golden rectangle. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi.

Golden Rectangle

Illustration showing the golden rectangle. Two quantities are considered to be in the golden ratio if…

Illustration showing a nesting of 2 golden rectangles. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. The large rectangle shown is divided to show the a golden rectangle. The smaller portion is then divided into the golden ratio again.

Golden Rectangles

Illustration showing a nesting of 2 golden rectangles. Two quantities are considered to be in the golden…

Illustration showing a nesting of 3 golden rectangles. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. The large rectangle shown is divided to show the a golden rectangle. The smaller portion is then divided into the golden ratio again, and so on.

Golden Rectangles

Illustration showing a nesting of 3 golden rectangles. Two quantities are considered to be in the golden…

Illustration showing a nesting of 4 golden rectangles. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. The large rectangle shown is divided to show the a golden rectangle. The smaller portion is then divided into the golden ratio again, and so on.

Golden Rectangles

Illustration showing a nesting of 4 golden rectangles. Two quantities are considered to be in the golden…

Illustration showing a nesting of 5 golden rectangles. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. The large rectangle shown is divided to show the a golden rectangle. The smaller portion is then divided into the golden ratio again, and so on.

Golden Rectangles

Illustration showing a nesting of 5 golden rectangles. Two quantities are considered to be in the golden…

Illustration showing a nesting of 6 golden rectangles. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. The large rectangle shown is divided to show the a golden rectangle. The smaller portion is then divided into the golden ratio again, and so on.

Golden Rectangles

Illustration showing a nesting of 6 golden rectangles. Two quantities are considered to be in the golden…

Illustration showing a nesting of 7 golden rectangles. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. The large rectangle shown is divided to show the a golden rectangle. The smaller portion is then divided into the golden ratio again, and so on.

Golden Rectangles

Illustration showing a nesting of 7 golden rectangles. Two quantities are considered to be in the golden…

Illustration showing succession of golden rectangles that are used to construct the golden spiral. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. Each rectangle shown is subdivided into smaller golden rectangles. The golden spiral is a special type of logarithmic spiral. Each part is similar to smaller and larger parts.

Golden Rectangles

Illustration showing succession of golden rectangles that are used to construct the golden spiral. Two…

Illustration showing succession of golden rectangles that are used to construct the golden spiral. Two quantities are considered to be in the golden ratio if (a+ b)/a = a/b which is represented by the Greek letter phi. Each rectangle shown is subdivided into smaller golden rectangles. The golden spiral is a special type of logarithmic spiral. Each part is similar to smaller and larger parts.

Golden Rectangles

Illustration showing succession of golden rectangles that are used to construct the golden spiral. Two…