#spaceland

From Flatland to Hypergraphics: Interacting with Higher Dimensions

Thomas F. Banchoff Department of Mathematics, Brown University, Providence, Rhode Island, USA

Flatland is over one hundred years old (1884), and it has never been more popular than it is now, with five new English editions in the past six years, and translations into eight foreign languages. Much of its social satire is still pertinent today, and it is only now with the advent of modern computer graphics that we can begin to appreciate the challenge of seeing phenomena from higher dimensions which so baffled the two-dimensional protagonist of Edwin Abbott Abbott's little masterpiece. In this review we begin to answer the questions: "Who was the author of this book?" and, "How did he come to write it?"

The book: A two-dimensional narrator 'A Square' interacts with a 3-dimentional Spaceland observer that appears as an intersection (slice) of the hyper-solid shape always changing form and measurements. Explaining is sheer fun...

The article appeared in substantially the same form in the British journal Interdisciplinary Science Reviews, in 1990

A hypercube is a multi-dimensional geometric figure that acts as a generalized extension of a 3D cube into n-dimensions. It is also known as an n-cube. In four dimensions, a hypercube is specifically called a tesseract

beyond pure geometry, "hypercube" refers to several real-world concepts:

Data & Statistics: Used in algorithms like Latin Hypercube Sampling (LHS) to accurately select random variables for statistical models.

Computer Networking: A network topology where nodes are connected in a multidimensional mesh to route data.

https://www.math.brown.edu/tbanchof/abbott/Flatland/ISR/