The learning guide “Discovering the Art of Mathematics: Geometry” lets you, the explorer, investigate connections between mathematical ideas and concepts and the many-dimensional world around you. Starting in the imaginary world of "Flatland", you will investigate in a playful way how we see what we see. Analyzing and building your own three-dimensional piece of art will have you think more deeply about space and how our mind makes sense of it. Building on your insights into the mathematical structures, you will be able to reach into the worlds of the fourth and higher dimensions as well as the intricate worlds of the $1.5^{th}$ and other fractured dimensions.