With apologies to 1990s alt-rock fans, a perfect circle cannot exist outside the realm of mathematics.
From subatomic particles to carefully built structures, nothing in the physical world passes the perfect circle test, where every point on the circumference is exactly equidistant from the circle’s center.
That said, some notable natural forms and human-made buildings get pretty close.
Occurring either by happenstance or designed to pay homage to the shape that the Greek scholar Proclus called “the first, simplest and most perfect form,” these sites highlight the singular symmetry and symbolism the circle embodies.
A fascination and interest in circles predate recorded history, with many ancient cultures finding approximations for pi—the ratio of a circle’s circumference to its diameter—thousands of years before mathematicians gave it that name with the tasty homophone.
Because of their symmetry, circles were seen as representations of the “divine” and “natural balance” in ancient Greece. Later on, the shape would become a vital foundation for the wheel and other simple machines.
A focus on circles is evident among structures built throughout history.
Although the meaning of its design is still being deciphered, Gobekli Tepe, a series of stone circles in Turkey, is the oldest known temple, built 6,000 years prior to Stonehenge (another famous circle).
The shape marks many more important gathering places used by diverse cultures as centers of worship, governance, and even spectacle.
Roman amphitheaters, including the Colosseum, for example, were designed as circles or ellipses to place the focus on one main event, such as gladiatorial battles.
St. Peter’s Piazza, the square leading up to the main Vatican building, features two semicircles that enclose the space, meant to personify “the motherly arms of the church” welcoming people into the area.
In addition to the physical purposes they serve, circular structures have also been built to act as more abstract symbols.
In Beijing, the Temple of Heaven is a conical structure that sits adjacent to a three-tiered circular marble altar used for imperial sacrifices during the Ming and Qing Dynasties.
The circle represented the heavens, while a neighboring square depicted the Earth. The design of the Indian Parliament’s Central Hall building is circular to represent the Ashoka Chakra, a Hindu symbol that literally translates to “wheel of the law,” which is also on the country’s flag.
In a case of modern practicality, the Large Hadron Collider underneath the Switzerland-France border takes the form of a 16.7-mile-long circular tunnel.
The round shape forces particles to constantly change direction and accelerate—colliding with great enough force to shake loose new types of matter.
In nature, the appearances of major circular areas are often thought to offer some secondary meaning.
Crop circles are intricate, bewildering patterns that have long confounded people, even igniting speculation about extraterrestrial activity, although more reasonable explanations cite wind patterns and human interference.
Fairy circles in Africa embody a similar degree of mystery. Bare areas of earth surrounded by circular rings of grass, fairy circles’ origins and distribution remain unexplained, with some terming them the “footprints of the Gods.”
It seems that even thousands of years after Egyptians first approximated the value of pi, the intrigue of circles lives on.
Author Bio: Li Zhou is the digital editorial intern for Smithsonian.com. She has previously written for The Boston Globe, PolicyMic and Interview Magazine.