Customizable Logarithmic Spiral

thingiverse

As you browse through the realm of mathematics, there exists a fascinating geometric form that showcases a profound connection between geometry and logarithms - the logarithmic spiral. The logarithmic spiral is a remarkable curve that appears in numerous natural patterns, from the shape of galaxies to the configuration of seashells. The defining characteristic of a logarithmic spiral lies in its polar equation, where r equals e to the power of theta. In simple terms, this translates to the radius being directly proportional to the angle theta, which results in an equidistant spacing between each arc of the curve. One key property of logarithmic spirals is that they never touch a rectangular box when wrapped around it. This unusual characteristic can be seen when creating patterns with such curves, where the resulting spiral always emerges as one continuous thread despite traversing multiple boundaries.