The 100 Sided Polygon: Hectogon, Centagon, and Beyond

Imagine a shape with 100 sides. What is that called? It's a fascinating question that leads us into the world of geometry and the names given to polygons with a large number of sides. A 100-sided polygon is known as a hectogon or occasionally a centagon. Both terms are used, but they all refer to the same geometric shape. Mathematicians would likely recognize it as a circle if the sides are smooth and the angles are close enough, similar to how we often use polygons to approximate circles in computer simulations.

Understanding 100-Sided Polygons

Hectogon (also spelled as hectagon) is a term derived from the Greek words "hecto-" meaning "100" and "-gon" for polygon. While this term is accurate, it may not be as commonly used as centagon, which comes from the Latin "centum," meaning "100." However, both terms refer to the same shape. Interestingly, in some languages, the term "100-gon" can be read in their native alphabet and language barriers.

Curious about other large-sided polygons? Here are a few more:

A 1000-sided shape is called a chiliagon. A 10,000-sided shape is called a myriagon. A 100,000-sided shape is called a regular megagon. A 1,000,000-sided shape is called a megagon.

While a megagon is incredibly close to a circle, it still retains the properties of a polygon. The sum of any hectogon's interior angles is exactly 17,640 degrees, a value that underscores its unique geometric properties.

Common Notations and Names

For smaller polygons, we use Greek or Latin-based prefixes to name them. Here are some examples:

A 5-sided polygon is a pentagon. A 6-sided polygon is a hexagon. A 7-sided polygon is a heptagon. A 10-sided polygon is a decagon.

These names are fancy and elegant, but you can also refer to any polygon with n sides as an n-gon. For instance, a 100-sided polygon can be simply called a 100-gon. This term is more practical and easier to remember, especially in everyday contexts.

Real-World Applications of Polygons with Many Sides

Understanding polygons with a large number of sides can be quite useful. In computer simulations and design, a 30-sided polygon (triacontagon) or a 20-sided polygon (icosagon) is often used to approximate a circle. This helps in faster rendering and reducing computational complexity.

One can even create polygons with much larger numbers of sides, but these are rarely used in practical applications due to their extreme complexity. They are more of a theoretical concept rather than something we encounter in day-to-day situations.

Conclusion

A 100-sided polygon, or hectogon (or centagon for that matter), is a fascinating shape that bridges the gap between regular polygons and circles. Understanding the terminology and properties of these shapes can provide a deeper insight into the world of geometry. Whether you use the term hectogon, centagon, or simply 100-gon, the importance of these shapes in mathematics and technology cannot be underestimated.