How do the numbers in Freemasonry relate to geometry?

How do the numbers in Freemasonry relate to geometry?

In Freemasonry, numbers such as 3, 5, and 7 are deeply intertwined with geometric principles and hold significant symbolic meaning. For instance, the 47th Proposition of Euclid, which is a cornerstone in Masonic symbolism, illustrates the relationship between geometry and these numbers. This proposition involves the Pythagorean theorem, where the sides of a right triangle can be expressed as 3, 4, and 5, leading to the ratio of 3:4:5, which is fundamental in geometry and Masonic teachings【4:7†source】.

Moreover, the sequence of numbers starting from the Monad (1) and progressing to 4, 9, and 16 reveals that subtracting each square from the next yields 3, 5, and 7. These numbers are emblematic of the three degrees of Masonry: Entered Apprentice (3), Fellowcraft (5), and Master Mason (7)【4:1†source】.

Additionally, Freemasonry emphasizes the importance of geometry, stating that masonry and geometry were originally synonymous terms. The study of geometry is said to reveal the wonderful properties of nature, linking life and nature to the principles of geometry【4:4†source】【4:6†source】. The Winding Stair symbol, central to the Fellowcraft degree, further illustrates this connection, as it invites candidates to explore the hidden mysteries of nature and geometry【4:12†source】.