Logarithmic spiral is also called equiangular spiral, growth spiral and Bernoulli spiral. Equiangular spiral refers to the spiral in which the distance between arms increases in geometric series. The distance between the two arms of the spiral increases geometrically. One of the greatest characteristics of this curve is self-similarity. Even if the figure is enlarged, the curve is exactly the same.

Spiral and equiangular spiral

Spiral family is huge, such as archimedean spiral, Fermat spiral, equiangular spiral, hyperbolic spiral, interlocking spiral, Fibonacci spiral, Euler spiral and so on. Equiangular spiral, also called logarithmic spiral, is a member of the spiral family.

As early as more than 2000 years ago, the ancient Greek mathematician Archimedes studied the spiral line. 1638, the famous mathematician Descartes first described the logarithmic spiral and listed its analytical formula. This spiral has many characteristics, the most prominent of which is its shape. Whether you enlarge it or shrink it, it won't change. Just like we can't zoom in or out.

Using polar coordinate analysis to analyze the flying trajectory of moths, we know that the angle between the tangent of any point on the trajectory and the connecting line between the point and the origin is fixed, which is the origin of the equiangular spiral. Because logarithm is used in the analysis process, equiangular spiral is also called logarithmic spiral.