vastagons

Vastagons are a hypothetical geometric concept representing a class of shapes with an infinite number of sides, each of a finite length. Unlike a regular polygon where the number of sides is finite and countable, a vastagon theoretically approaches the characteristics of a circle as the number of its sides tends towards infinity. The term itself is a neologism, combining "vast" to suggest immensity and "gon," the common suffix for polygons.

The theoretical properties of vastagons often arise in discussions related to limits and calculus in geometry. For instance, as the number of sides of a regular polygon increases infinitely, its perimeter and area converge to those of a circle inscribed within it or circumscribed around it, depending on the definition. This convergence illustrates how a polygon with an infinite number of infinitesimally small sides can enclose a finite area and possess a finite perimeter, much like a circle.

In practical terms, vastagons are not physically constructible or directly observable in the real world due to limitations of measurement and the discrete nature of matter. Their existence is primarily confined to abstract mathematical thought experiments and theoretical explorations of geometric continua. The concept serves as a useful pedagogical tool for understanding the relationship between discrete and continuous geometric forms.