In mathematics, a curve or a curved line is a shape or an object similar to a path which does not have to be straight. Without a specific reason, a curve may be considered as the mark left by a moving point. Curiosity in curves started long before as they were the topic of mathematical study. This can also be seen in many numerous examples and their decorative application in art and on common objectives from ancient times. The graphical representation of curves is simple to create; for instance, these can be drawn just by using a stick or hand in the sand on beaches.

The Greek geometers had analysed many other types of curves. One purpose was their curiosity and interest in solving geometric problems which were not able to be solved even with the help of a regular compass and straightedge constructions. These curves include conic sections, archimedean spiral, spiral sections and so on. All these topics are used in different fields of study which in turn provide a large number of benefits to lead our life conveniently.

Uses of curves in real life and education have always determined when looking back at history. They are used in the visualization of art and decoration in various scenarios. However, the exact definition of curves has been rewritten in later times. In the earlier days, Mathematicians were used to staying very interested related to curved lines. In current mathematics, the curved lines are useful for graphical representation of different types of functions.

A curve is a continuous and smooth moving line without any sharp corners. One of the best ways to identify a curve is that it twists and changes its direction at least once. A curve may be an upward, downward, open or closed in shape. In real life, race tracks, roads, and some bridges look like curves. Besides, the items or things that we use in each and every incident may contain the shape of a curve. There are some specific reasons behind any construction which is in the shape of a curve.

Different types of curves exist in mathematics, namely, parabola, hyperbola, ellipse, and so on. We can observe all these types in some of the other situations in everyday life. The long cables strung between pillars of a suspension platform, such as a parabola can be observed from the Golden Gate Bridge in San Francisco. Connection to the roadway of the bridge is essential in forming the large cables in the shape of a parabola.

A telephone wire appears like curves most of the time. The reason could be its weight and is not a parabola but is a catenary. Suppose when a dense liquid like mercury is placed in a large can and the lavatory rotated.  In this situation, the surface of the liquid will form a paraboloid.  Thus, we can say that every vertical cross-section over the centre of the can form a parabola. Also, we can observe that many logos which are related to the company or an educational institution have curves in their designs.