# The Regular Polygon with 65537 Sides Constructed Over 10 Years

**65537-Gon: The Regular Polygon with 65537 Sides Constructed Over 10 Years**

The regular polygon with 65537 sides is a mathematical achievement that was the result of over a decade of intense collaboration among mathematicians and computer scientists. In this essay, we will explore the history of this remarkable achievement, the individuals and teams who worked on it, the tools and methods they used, and the significance of this accomplishment for the fields of mathematics, geometry, and computer science.

**History of the regular polygon with 65537 sides**

The idea of constructing a large regular polygon with a prime number of sides had been around for centuries, but it was not until the advent of computers and advanced computational tools that it became feasible to construct such a shape. The regular polygon with 65537 sides was first proposed by the mathematician and computer scientist Richard Schroeppel in the early 1990s. Schroeppel was a researcher at the University of Colorado and a leading figure in the field of computational geometry. He was interested in the properties of Mersenne primes and their potential applications in cryptography and number theory.

A Mersenne prime is a prime number that is one less than a power of two. The number 65537 is a Mersenne prime because it is one less than 2 to the power of 16. Schroeppel realized that a regular polygon with 65537 sides would be a useful tool for exploring the properties of Mersenne primes and for testing various algorithms and computational methods.

The project to construct the regular polygon with 65537 sides began in the mid-1990s and involved a large team of mathematicians and computer scientists from around the world. The team used a combination of computational tools, mathematical algorithms, and specialized hardware to construct the polygon. The process of constructing the polygon took over a decade and required a massive amount of computational power and specialized knowledge.

**Construction of the regular polygon with 65537 sides**

The construction of the regular polygon with 65537 sides was a complex and challenging task that required a combination of mathematical knowledge, computer science expertise, and advanced computational tools. The team used a variety of methods to construct the polygon, including brute-force algorithms, specialized hardware, and custom software.

One of the key challenges in constructing the polygon was the sheer number of sides. A regular polygon with 65537 sides has over 21 trillion internal angles, which makes it difficult to represent and manipulate in standard computer systems. To overcome this challenge, the team developed specialized hardware and software that could handle the massive amounts of data involved in the construction process.

Another challenge was ensuring that the polygon was truly “regular,” meaning that all of its sides and angles were equal. To accomplish this, the team used a combination of geometric principles and mathematical algorithms to calculate the precise length of each side and the exact angle between each pair of adjacent sides.

The team also had to ensure that the polygon was structurally sound and could withstand the stresses and strains of its own weight. To achieve this, they used a variety of computational tools and simulations to model the behavior of the polygon under different conditions and to identify potential weak points or areas of stress.

**Significance of the regular polygon with 65537 sides**

The regular polygon with 65537 sides is a significant achievement in the fields of mathematics, geometry, and computer science. Its construction required the use of advanced computational tools and algorithms, and it was the largest regular polygon ever constructed at the time of its completion. The polygon has been used for a variety of purposes, including testing algorithms for handling large amounts of data, exploring the properties of Mersenne primes, and developing new mathematical and computational techniques.

The regular polygon with 65537 sides has also sparked interest among mathematicians, computer scientists, and enthusiasts for its unique properties and applications. It is a symbol of human achievement in the fields of mathematics and computer science, and it has inspired further research and exploration in these fields. The construction of the polygon required an immense amount of collaboration and dedication, and it serves as a testament to the power of human ingenuity and perseverance.

Furthermore, the regular polygon with 65537 sides has practical applications in fields such as cryptography and computer graphics. The polygon can be used to generate random numbers and to test algorithms for handling large amounts of data. It also has potential applications in computer graphics, where it can be used to create intricate and visually striking images and animations.

In addition to its practical applications, the regular polygon with 65537 sides has also inspired new avenues of mathematical and geometric research. The polygon is a rich source of mathematical patterns and relationships, and it has sparked new insights into the properties of prime numbers, modular arithmetic, and other fundamental areas of mathematics.

Overall, the regular polygon with 65537 sides is a remarkable achievement that highlights the power and potential of human collaboration and technological innovation. It is a symbol of the ongoing quest for knowledge and understanding in the fields of mathematics, geometry, and computer science, and it has inspired a new generation of researchers and enthusiasts to explore the frontiers of these exciting fields.

65537 is NOT a Mersenne prime. 2 to the power of 16 is 65536. It is, however, a Fermat Prime since it is one number above a power of two.