The purple box shows what we would see if we were looking at the screen head on. We call this image of our cube on the screen its ‘projection’. If we think of the xy-plane (the plane spanned by the red and blue axes) as our screen, the black lines show what we see of our green cube on the screen. We want to look at this object on a 2D screen. On the canvas, there is a set of 3 axes (x, y, and z) representing 3D space. When thinking about how to visualise a higher dimensional cube, it will help to first think about how we look at a 3D cube on a 2D screen. In fact, we shall find that if we first take a step back and break down the process through which we view three dimensional objects, we can extend our method to four or more dimensions. We can all conjure up a clear image in our head when we are told to think about a three dimensional cube, but what about a four dimensional one? It seems strange, perhaps even illogical that there should be such an abrupt cut-off point between three and four dimensions. However, the idea of a higher dimensional object is less tangible. ![]() ![]() We find it natural to do so, since we are able to relate these concepts to the world we live in. Thinking about two and three dimensional objects is commonplace to everyday life. The project works towards understanding how to create a simple visual representation of the hypercube, while also teaching the importance of abstraction in mathematics! This inspired me to write and create in Desmos an accessible discussion for how we can think about higher dimensions. ![]() I recently showed my friends a Desmos (online graphing calculator) project of a hypercube that I made, and I was met with confusion about how it is possible for us to visualise 4D. Richard Zhang – winner of the 2020 Teddy Rocks Maths Essay Competition
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