Bowerbirds as a group are some of the most fascinating of all birds because of their incredible and elaborate architectural abilities. Well known is the fact that male bowerbirds create the most elaborate displays to attract females for mating, putting untold effort into designing, crafting, and displaying the perfect "love nest" to attract females of the species. But less well known is the amount of thought and calculation put into the creation of the perfect bower. Depending on the species, bowerbirds will get extremely detailed about the colors used, how the colors are displayed, and even more interesting, the geometry of the displays.
Found in Australia and New Guinea, bowerbirds use different materials and tricks depending on the species, but all are particular about exactly how their bower is created. And math is part of the process.
For the great bowerbird, it's all about perspective. Discovery Magazine reports on the use of forced perspective, "a trick of the eye that makes objects seem bigger or smaller, further or closer than they actually are. These illusions were used by classical architects to make their buildings seem grander, by filmmakers to make humans look like hobbits, and by photographers to create amusing shots. But humans aren’t the only animals to use forced perspective. In the forests of Australia, the male great bowerbird uses the same effect to woo his mate."
This species creates a courtyard with large objects placed toward the back and smaller objects placed toward the front, nearer to where the female approaches. The overall effect is that the courtyard looks smaller overall than it actually is. The male great bowerbird very specifically designs and arranges his bower in such a manner, though why it works to woo the females is still unknown.
Even more interesting, this is the only species of animal known to build something that creates perspective. But the talent of bowerbirds doesn't stop with geometry. There is also color coordination.
In a special on bower birds, PBS NATURE explains some birds' particular preference for color:
Some, like the iridescent blue Satin bower bird, the star of Bower Bird Blues, even “paint” the walls of their structures with chewed berries or charcoal. For the male Satin, which builds a U-shaped bower from parallel walls of twigs, the favored color is blue. To decorate its “avenue,” as scientists call it, he collects blue feathers, berries, shells, and flowers. While some of these decorations are found in the forest, others are stolen from the bowers of other males; young males, in particular, are prone to this petty thievery. However obtained, the precious knickknacks are then scattered around the bower. The male then waits, passing time by constantly fine-tuning his structure and rearranging the decorations.
Here is more detail in a segment of bowerbirds in Discovery's LIFE:
And here is the always iconic David Attenborough on the subject: