A dot has no dimensions – it has no length, width, or depth. If you were to draw another dot and connect them with a line, this would have one dimension. If you were to then connect three lines to make a triangle shape, this would have two dimensions – it would be a flat shape, ‘two dimensional’ as it has length and width. In maths, we call these two dimensional shapes polygons. A triangle, circle, square or rectangle are all two-dimensional shapes. We use dots, lines and shapes as the basis of art and design.
If you add depth to a two-dimensional shape you add another dimension – so it becomes a three-dimensional shape. Adding depth to a square makes it a cube, and a cube is three-dimensional. If you add depth, you also create volume – which is the space inside the shape. Three dimensional shapes with flat sides (like cubes and pyramids) are called polytopes.
We live in a three-dimensional world. Things we can touch and hold are three-dimensional.
We can only imagine the fourth dimension, but Mathematicians and physicists are exploring this more all the time.
An example of a four-dimensional shape would be a cube within a cube – also known as a tesseract.
The exhibition “And She Built a Crooked House” explored the fourth spatial dimension in art - watch the YouTube video in which artist explains her artwork (see Supporting Links).
You can also make your own exploded fourth-dimensional shape using the activity sheet here!