Erect means build or upright. If you erect a house, you build it. If you stand erect, you hold your body as tall as possible.
A mathematical model is a description of a system using mathematical concepts and language.The process of building a mathematical model is termed mathematical modeling.Mathematical models are used in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (e.g. computer science, artificial intelligence). mathematical model is a description of a system using mathematical concepts and language.
In mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic approach to the study of geometry by focusing on groups of geometric transformations, and the properties of figures that are invariant under them.