Cúspide

Cúspide is a Spanish noun meaning a pointed tip or apex. The term derives from the Latin cuspis, “spear point,” and is used across different fields to denote a sharp point, tip, or summit. In general usage it can refer to the highest point of a structure, the tip of a blade, or a sharp projection such as a mountain crest.

In mathematics, a cusp (cúspide) is a type of singular point on a plane curve where the curve has a sharp point and is not differentiable at that point. At a cusp, the left and right tangents coincide, but the parameterization slows to zero velocity, creating a pointed extremity. A classic example is the semi-cubical parabola described by y^2 = x^3, which has a cusp at the origin. In parametric form, x = t^2 and y = t^3 illustrates how the curve behaves near the cusp.

In dentistry, a cúspide is the pointed projection on the crown of a tooth, especially on molars and premolars, that participates in occlusion and grinding. Cusp height and number vary by tooth type, and wear from chewing or abrasion can reduce their prominence over time.

Other uses of the term can include references to sharp summit features in geology or topography, where a ridge or peak presents a distinct, pointed end. The word is commonly used in Spanish-language texts, with English equivalents including cusp, apex, or tip depending on the context.