What is the significance of geometric figures in Freemasonry?

Geometry is identified as the foundational science upon which the superstructure of the system is erected 2. The Old Constitutions treat geometry and Masonry as synonymous terms 23, while instruction lectures use geometry as a symbol of universal law, order, and Deity 5. Beyond arithmetic, it represents a framework for understanding creation; Wilmshurst reads the term mystically as the measurement of the fundamental soul-stuff or primordial "earth" out of which humanity was formed 4.

Individual geometric figures carry distinct symbolic meanings:

The triangle (or delta) represents Deity, divine force, and the self-existent nature of the Supreme Architect 2. When depicted with rays emanating from its center, it symbolizes Divine Light and wisdom radiating throughout creation 2.

The square represents humanity, passive matter, and the material world in opposition to divine force 2. When the triangle and square are combined, they form the pyramid—as seen on the Entered Apprentice's apron—symbolizing the union of matter and force, and the oneness of man and God 2. Interlaced triangles typify the union of active and passive forces in nature, such as light and darkness or truth and error 2.

The Forty-Seventh Problem of Euclid, featured in the Master Mason Degree, emblemizes a general devotion to the arts and sciences 1 while symbolically expressing cosmic harmony 2. Additionally, the four cardinal directions, referred to as geometric points, symbolize regularity and perfection in alignment with the structure of the lodge 2.