No two of these circles are linked together

These are Borromean rings.

The name "Borromean rings" comes from the use of these rings, in the form of three linked circles, in the coat of arms of the aristocratic Borromeo family in Northern Italy. The link itself is much older and has appeared in the form of the valknut, three linked equilateral triangles with parallel sides, on Norse image stones dating back to the 7th century. The Ōmiwa Shrine in Japan is also decorated with a motif of the Borromean rings, in their conventional circular form. A stone pillar in the 6th-century Marundeeswarar Temple in India shows three equilateral triangles rotated from each other to form a regular enneagram...

The Borromean rings have been used in different contexts to indicate strength in unity. In particular, some have used the design to symbolize the Trinity. A 13th-century French manuscript depicting the Borromean rings labeled as unity in trinity was lost in a fire in the 1940s, but reproduced in an 1843 book by Adolphe Napoléon Didron. Didron and others have speculated that the description of the Trinity as three equal circles in canto 33 of Dante's Paradiso was inspired by similar images, although Dante does not detail the geometric arrangement of these circles. The psychoanalyst Jacques Lacan found inspiration in the Borromean rings as a model for his topology of human subjectivity, with each ring representing a fundamental Lacanian component of reality (the "real", the "imaginary", and the "symbolic").

The rings were used as the logo of Ballantine beer, and are still used by the Ballantine brand beer, now distributed by the current brand owner, the Pabst Brewing Company. For this reason they have sometimes been called the "Ballantine rings"