Golden ratio in venation patterns of dragonfly wings

The vein pattern in insect wings allows this lightweight structure to carry multiple biological functions. An investigation of the angular distribution of the vein struts in dragonfly wings revealed that the golden angle or golden ratio dominates the venation patterns in two closely related ways. First, the golden angle dominates the intervein angles in regions where thin veins and membranes demand strength reinforcement. Second, a golden ratio partition method has been developed to explain a set of preferred intervein angles in distorted polygon-shaped venation cells throughout the venation pattern in dragonfly wings. These observations provide new evidence that the wing structure is spatially optimized, by the golden rule in nature, for supporting biomechanical functions of dragonfly wings.