What are the key geometric symbols used in Masonic rituals?

Craft Masonry incorporates several foundational geometric figures into its instruction and symbolism, notably the square, the triangle, the circle, and the right-angled triangle associated with the Forty-seventh Problem of Euclid.

The square is one of the oldest symbols in the Craft, preserving a primary signification as an emblem of morality and upright conduct 2. In lodge symbolism, it appears in multiple distinct applications. As an instrument, it serves as a working tool 2. Verbally and morally, Masons speak of meeting on the level and parting "upon the square," wherein the square is conceived in a vertical plane with one leg along the level floor and the other standing upright 2. Geometry also defines the structural form of the lodge itself, which is traditionally termed an "oblong square" or rectangle 2.

The circle represents the assembled membership within the lodge 2. The ritualistic practice of circumambulation unites the square and the circle, moving along a path that combines straight lines with circuitous turns around corners 2.

The triangle, or delta, typifies Deity, active force, and Divine Light, standing in symbolic opposition to the square, which represents passive matter and humanity 2. When the triangle and square are combined, they form a pyramid, a structural motif reflected in the flap and body of the Entered Apprentice's apron 2. Interlacing triangles are also used to represent the union of active and passive forces in nature 2.

In the Master Mason degree, the right-angled triangle appears through the emblem of the Forty-seventh Problem of Euclid 21. This theorem states that the square erected upon the hypotenuse of a right-angled triangle equals the sum of the squares erected upon the other two sides 1. Symbolically derived from Pythagorean geometry, it serves as a foundational emblem of mathematical truth and encourages Masons to be lovers of the arts and sciences 1.