A polygon with 10000000000000000000000000000000000000 (or $10^{36}$) sides is most accurately referred to as a 10^36-gon.
For polygons with an exceptionally large number of sides, a specific Greek or Latin prefix is often not established or universally recognized. In such instances, the standard mathematical convention is to name the polygon by its exact number of sides, followed by the suffix "-gon." Therefore, a shape with $10^{36}$ sides is precisely known as a $10^{36}$-gon.
Understanding Polygon Naming Conventions
The naming of polygons typically follows a systematic pattern derived from Greek numeral prefixes. Common examples include:
- Triangle: A polygon with 3 sides.
- Quadrilateral: A polygon with 4 sides.
- Pentagon: A polygon with 5 sides.
- ...and so forth.
However, for shapes possessing a very large, yet specific, quantity of sides, unique names have sometimes been coined to denote their scale. A prime example of this is the megagon.
The Megagon: A Polygon with a Million Sides
A megagon is a polygon specifically defined as having exactly one million ($1,000,000$, or $10^6$) sides. This distinct naming sets it apart from polygons with an even greater number of sides, such as the $10^{36}$-gon, for which no comparable, widely accepted single-word name exists.
A regular megagon, like other regular polygons, possesses specific geometric properties:
| Feature | Description |
|---|---|
| Number of Sides | 1,000,000 ($10^6$) |
| Symmetry Group | Dihedral ($D_{1,000,000}$), indicating an order of $2 \times 1,000,000$ |
| Internal Angle | Approximately 179.99964° |
| Properties | Convex, cyclic, equilateral, isogonal, isotoxal |
In practical geometry, as the number of sides in a regular polygon increases significantly, its shape progressively approximates that of a circle. For instance, the internal angle of a regular megagon is already remarkably close to 180 degrees, which is the internal angle of a straight line, illustrating how it approaches the smooth curvature of a circle. A $10^{36}$-gon would be visually indistinguishable from a perfect circle, even when viewed under high magnification.
