Centoid

Centoid is not a standard mathematical term. In formal geometry and related fields, the correct and widely used term is centroid. Occurrences of centoid are typically typographical errors or nonstandard coinages, and readers should treat it as centroid unless the author explicitly defines a different meaning. Because of its similarity to centroid, centoid can appear in informal writing, proofreading errors, or when the concept is referenced without the proper terminology.

If you encounter centoid in a text, check the surrounding definitions to determine the intended meaning. In contexts involving polygonal shapes, computer graphics, or finite-element methods, the intended concept is usually the centroid. In geometry, the centroid is the point that serves as the center of mass for a shape with uniform density and often as the intersection of the figure’s medians.

For a triangle, the centroid is located at the average of its vertex coordinates: ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3). For general polygons or sets of points with equal masses, the centroid is the mean position of the points, with area-weighted means used for polygons with nonuniform densities. The centroid is also known as the center of mass for uniform density shapes and is a fundamental reference point in many geometric and physical computations.

Etymology wise, centroid comes from Latin centrum meaning center; centoid would be a nonstandard coinage, combining center with the suffix -oid. Related terms include center of mass, medians, and geometric centers.