Visual representation of my thoughts about dimension

A few expressions of dimension through art...

Dimension and Art - Slideshow

Flatland the film

Flatland the film is an adaptation of the book 'Flatland' written by A. Abbott in 1984. The main character of the book is a square living in Flatland, the two-dimensional world. The book is divided into two parts. The first consists of an exploration of Flatland and its inhabitants, while the second part describes how the square meets other worlds and other people such as Monarch in Pointland, King in Lineland and, a Sphere in Spaceland.

more about "YouTube - Flatland: The Movie - Offic...", posted with vodpod

What is dimension?

The word 'dimension' comes from the Latin word 'dimensus' and means "measured out".

In mathematics, no definition of dimension adequately captures the concept in all situations where we would like to make use of it. All mathematical definitions on dimension, however, are inspired by the notion of the dimension of Euclidean n-space E ⁿ. The point E ⁰ is 0-dimensional. The line E ¹ is 1-dimensional. The plane E ² is 2-dimensional. And in general E ⁿ is n-dimensional. Figure 1 consists of examples of objects in various dimensions presented as 2-dimensional renderings: 

Figure 1: 2-dimensional renderings (ie. flat drawings) of a 0-dimensional point, a 1-dimensional line segment, a 2-dimensional square, a 3-dimensional cube, and a 4-dimensional tesseract

More definitions on the Web:  Wikipedia, Wolfram MathWorld

Welcome to this dimension!

When you hear the word 'dimension' what is the first thing that comes to your mind?

How many different meanings of the word can you think of?

I bet you will find a lot! Indeed, 'dimension' is a word mentioned quite often in a variety of settings. Dimension as a term is used in many disciplines such as Geography and Physics. This blog however focuses on the different definitions of dimension in Mathematics: What do we mean by 'dimension'? And more specifically, what do we mean by 'spatial dimension'?

Please feel free to post anything you consider relevant to the above questions. Any suggestions or questions are always welcomed!