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Golden Ratio | Silver Ratio | Plastic Number | Square Root of Two | Square Root of Three | Doubling the Cube | Pi | e

# Calculate the Golden Ratio

The golden ratio is

## a / b = φ ≈ 1.6180339887498948

Enter one value for the lengths a or b or for the total a+b. The other two values will be calculated.

 a: b: a+b: (total length)

Example: if the total length, i.e. a + b, should be one hundred, be it centimeters or percent, then the length of a is about 61.8 and the length of b is about 38.2.

The golden ratio occurs naturally in the arrangement of the leaves of many plants, such as the sunflower. Its most famous occurrence in geometry is the pentagram. It has been frequently used as a stylistic device in art and architecture since the Renaissance because it is considered particularly aesthetic. For example, it often appears in a landscape painting in the ratio of the height of the earth and sky above the lower edge of the picture.

Other ratios that can be calculated on this page are as follows:
The rarely used silver ratio with a longer long distance.
The plastic number that describes when two objects are subjectively assigned to different size classes. It is sometimes used specifically in architecture.
Root of two, the length of the diagonal of the square.
Root of three, the length of the diagonal in the cube.
The cube doubling constant, the third root of two by which the side length of a cube must be multiplied to obtain a cube with double the volume.
Finally, the two most important constants in mathematics, pi and Euler's number e.
For each of these constants, the value is represented as a ratio of two lengths.

Calculate special ratios - Tool for design and architecture

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German: Goldener Schnitt, Silberner Schnitt, Plastische Zahl, Wurzel aus Zwei, Wurzel aus Drei, Würfelverdoppelung , Pi, e

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