Logarithmic Spiral Equiangular Geometry
Inspect a spiral’s constant radial–tangent angle, curvature and scaling law.
Free theory articleInspect a spiral’s constant radial–tangent angle, curvature and scaling law.
Concept & interpretation
A logarithmic spiral, also known as an equiangular spiral, is a special class of spiral curve that appears frequently in nature and applied mathematics. Unlike an Archimedean spiral where the spacing between turns is constant, the distances between turns of a logarithmic spiral increase in geometric progression.
Experiment
You can investigate the equiangular property of the logarithmic spiral using the Logarithmic Spiral Equiangular Geometry module.
- Set the Initial radius to
1. - Set the Growth b to
0.5. - Set the Angle radians to
1and then2. Observe that while the curvature and position change, the Outward radial tangent angle remains exactly the same. - Try setting the Growth b to
0. The spiral degenerates into a circle, the tangent angle becomes exactlyπ/2, and the radius multiplier becomes1.0.