Parametrise

Parametrise is a term used in mathematics and computer science to describe the process of expressing a function, curve, or surface in terms of one or more parameters. This technique is particularly useful in various fields, including geometry, physics, and engineering, where it allows for a more flexible and intuitive representation of mathematical objects.

In geometry, for example, a curve can be parametrised by expressing its coordinates as functions of a single parameter, often denoted as t. This parameterisation can simplify the study of the curve's properties, such as its length, curvature, and tangents. Similarly, surfaces can be parametrised using two parameters, typically denoted as u and v, which can be used to describe the surface's shape and properties.

In computer science, parametrisation is commonly used in the context of algorithms and data structures. For instance, a parametrised algorithm is one that takes one or more parameters as input, allowing it to be adapted to different situations or data sets. Similarly, a parametrised data structure is one that can be customised using parameters, enabling it to store and manipulate data more efficiently.

Overall, parametrisation is a powerful tool that can simplify the study and manipulation of mathematical objects, as well as the design and implementation of algorithms and data structures. By expressing these objects in terms of parameters, it becomes easier to analyse their properties, adapt them to different situations, and optimise their performance.