The Latin word *curvilineus* came to our language as curvilinear. This adjective is used to qualify that formed by curved lines. A curve, on the other hand, is something that continuously moves away from the straight direction, without creating an angle.

In this context, the angle formed by curved lines is called a curvilinear angle. This means that its sides are not straight, but curved. If the angle has a curved line and a straight line, it is qualified as mixtilinear.

A curvilinear motion, on the other hand, is a circular, oscillatory, or parabolic displacement. A competition vehicle disputing a race on an oval-shaped circuit performs a curvilinear movement.

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If the path along which a particle moves is known to the observer, it is considered appropriate to describe the movement using the coordinate axes *n* (which acts as normal to the path) and *t* (is tangent to the path), and at the instant considered they have their origin located in the particle. If the trajectory is curved, then we can speak of an elliptical movement.

If we consider a particle that moves in a plane on a fixed curve, at any instant it will be in position *s*, which is measured taking into account the point *O*. For a coordinate system whose origin is a fixed point on the curve and at the observed instant this coincides with the position of the particle, the following will occur:

* the t-axis will be tangent to the curve and positive in the direction in which s increases (the positive direction of the particle ‘s displacement );

* said axis is perpendicular to n in its positive direction pointing towards the center of the curve;

* the plane that contains them both is called *osculating* or *embracing*. In a case like this, it would be fixed in the plane of displacement.

Since the particle is in motion, the position is a function of time. The direction of the velocity is always tangent to its path, and to calculate its magnitude it is necessary to derive the time from the path function.

If we have a curvilinear motion on an XY plane, with the corresponding axes and the determined origin, the magnitudes that describe it are a position vector at a given instant, and can be represented by the letters *r* and *t*, respectively. Let’s not forget that along the entire trajectory of the particle, it will pass through a set of points; at each instant, one of them can be identified in relation to the instant.

In short, everything that has curves, or is characterized by them, can be mentioned as curvilinear. For example: *“The curvilinear layout of the circuit means that cars cannot reach a high speed”*, *“The Finnish company surprised by presenting a curvilinear telephone”*, *“The curvilinear container of the soft drink is very easy to grip”*.

The idea of curvaceous is often used with respect to feminine forms. When a woman has marked curves in her figure, it is said that she is curvaceous. This is an aesthetic feature that is usually considered attractive: *“The Italian actress dazzled on the beach with her curvaceous body”*, *“The model’s curvaceous figure captivated the leading man, who as soon as he saw her approached to talk to him”*, *“I like women curvaceous silhouette*.

The measures that are usually mentioned as the ideal of feminine beauty (36 inches bust, 24 inches waist, and 36 inches hips) are linked to curvaceous women. These different measurements suppose the existence of pronounced curves in the silhouette.