Final answer:
A vertex in mathematics is a point where two or more lines or edges meet, such as the corners of a polygon or the points in a three-dimensional shape.
Step-by-step explanation:
In mathematics, a vertex refers to a point where two or more lines or edges meet. It is a significant concept in various branches of mathematics, including geometry and graph theory. For example, in a polygon like a triangle or a square, each corner point is known as a vertex. In graph theory, a vertex is one of the fundamental units used to model relationships; it can represent an entity such as a city in a network of roads where the roads themselves are the edges connecting the vertices.
Vertices also play a crucial role in the representation of three-dimensional shapes, such as cubes and pyramids, where they are the points where the edges of the shape meet. Moreover, in the context of vectors, which are typically drawn as arrows having a magnitude and direction, the starting point of the vector is called the tail, and the endpoint is known as the head. Although the term 'vertex' isn't typically used in direct conjunction with vectors, understanding the concept is vital as vertices are the fundamental building blocks for complex structures represented in a mathematical form.