What are the key geometric symbols used in Masonic rituals?

The square is among the oldest symbols used in the Craft, serving as an emblem of morality, uprightness, and human nature 1. In ritual practice, it appears both as an independent instrument symbolizing vertical and horizontal rectitude—such as in meeting upon the level and parting upon the square—and as an old designation for a rectangle, termed the oblong square, which describes the form of the lodge room 1.

The compasses, when combined with the square, form the emblem of brotherhood and a Master Mason's duty to the Craft and himself 1. Dynamically, the combination of straight lines and circular paths is reflected in circumambulation, where movement around the lodge room traces a circuit that is part circle and part square 1.

The triangle, or delta, signifies Deity, active force, and the self-existent, standing in contrast to the square which represents passive matter or humanity 1. When interlaced, two triangles symbolize the union of active and passive forces, as well as light and darkness, wisdom and ignorance 1. A radiated triangle, with rays emanating from its center, symbolizes the divine light of wisdom surrounding the Supreme Architect 1.

The Forty-seventh Problem of Euclid, or the Pythagorean theorem, is adopted in the Master Mason Degree as an emblem represented by a right-angled triangle 12. It illustrates that the square erected on the hypotenuse is equal to the sum of the squares on the other two sides 2. Symbolically, it connects the properties of the triangle and the square, serving as a fundamental emblem of geometry that teaches Masons to cultivate the arts and sciences 12.