Square and Compasses Square and Compasses The Square and Compasses (or, more correctly, a square and a set of compasses joined together) is the single most identifiable symbol of Freemasonry. Both the square and compasses are architect's tools and are used in Masonic ritual as emblems to teach symbolic lessons. Some Lodges and rituals explain these symbols as lessons in conduct: for example, Duncan's Masonic Monitor of 1866 explains them as: "The square, to square our actions; The compasses, to circumscribe and keep us within bounds with all mankind". However, as Freemasonry is non-dogmatic, there is no general interpretation for these symbols (or
G-structure on a manifold condition. Without the corresponding integrability condition, the structure is instead called an "almost" structure, as in an almost complex structure, an almost symplectic structure, or an almost Kähler structure. Specifically, a symplectic manifold structure is a stronger concept than a "G"-structure for the symplectic group. A symplectic structure on a manifold is a two-form "ω" on "M" that is non-degenerate (which is an formula_38-structure, or almost symplectic structure), "together with" the extra condition that d"ω" = 0; this latter is called an integrability condition. Similarly, foliations correspond to "G"-structures coming from block matrices, together with integrability conditions so that the