Mathematical patterns are regularities or sequences that can be observed in numbers, shapes, or other mathematical concepts. These patterns can help identify relationships and make predictions. For example, the Fibonacci sequence is a famous pattern where each number is the sum of the two preceding ones, starting with 0 and 1. Patterns can also be found in geometry, such as in the arrangement of triangles in a hexagon or the symmetry of shapes. Recognizing these patterns is essential in various fields, including algebra, calculus, and even in nature, where they can describe phenomena like the growth of plants.