Math meets game mechanics in Marc ten Bosh's 2010 IGF finalist, the insanely brilliant mind-bender Miegakure. Miegakure presents a series of three-dimensional puzzles that are solved by flipping between the third and fourth dimension, engaging players to think about spatial geometry in a new and unfamiliar way.
Our world is three-dimensional: width, depth, and height. But what if there was a fourth physical dimension that we cannot see, in addition to the other three?
This game is about exploring the consequences of being able to move in four spatial dimensions. It plays like a regular three-dimensional platformer, but at the press of a button one of the dimensions is exchanged with the fourth dimension, allowing for four-dimensional movement.
Think about a two-dimensional character living on a horizontal, flat two-dimensional plane. To this character, height would be a foreign concept. A number of actions we three-dimensional beings take for granted feel like absolute magic to this two-dimensional character.
For example, if there is a wall in the shape of a circle around an object in 2D, it is essentially closed-off, since to reach it one would have to leave the 2D plane. It is also impossible for an outsider to know what is inside.
But us 3D beings can see the object from above, and also simply lift it off the ground to move it outside, essentially teleporting it. Now by analogy a four-dimensional being could perform many similar miracles to us living in only three-dimensions. This game allows you to perform these "miracles."
The game medium makes the mathematical concept of a fourth dimension easier to understand by allowing to experience it first-hand, using trial and error, as opposed to being told about it.