An investigation how the area of a shape is linked to its parameter.

The journey begins by delving into the concept of compactness for two-dimensional shapes, inviting students to explore and identify the shape that embodies the highest degree of compactness. This exploration then seamlessly transitions into a practical, real-world scenario where the optimal configuration of industrial real estate must be ascertained. In this pursuit, algebraic and numerical methodologies, complemented by Computer Algebra Systems (CAS), prove to be invaluable tools. This task not only encompasses the art of mathematical modeling but also challenges students to exercise their problem-solving prowess, with a touch of investigative curiosity woven throughout the entire process.