Calculating with the Golden Angle
Calculator for multiples of the golden angle and the resulting direction angle. The golden angle divides a circle according to the golden ratio. This creates two circular arcs, with the ratio of the circumference of the complete circle to the length of the longer arc being the same as the ratio of the longer arc length to the shorter arc length. The value of the golden ratio φ is (1+√5)/2 and is calculated here as 1.6180339887498948. The golden angle is obtained by dividing 360 degrees by φ and then taking the supplementary angle to obtain 360 degrees, or by dividing 360 degrees by φ². This golden angle is 137.50776405003783... degrees.
The calculation here is what is resulting if several golden angles one after the other occur. Please enter one of the three values to calculate the other two values and the direction angle.
Example: 3 times the golden angle equals 412.52 degrees, which corresponds to 1.15 rotations. The resulting angle points toward 52.52 degrees, roughly to the upper right.
The golden angle divides the circle into two different sized pieces in the ratio of the golden ratio.
The golden ratio is considered the most irrational of all numbers because it is the most difficult to be approximated by a fraction of natural numbers. Therefore, if several directional arrows are arranged concentrically at intervals of the golden angle, they will maintain the greatest possible distance from each other and never overlap. Many flowers, for example, use this principle in the arrangement of their petals, because overlapping here creates shading, which is of course to be avoided. Examples of these flowers include roses, sunflowers, daisies, and artichokes.