visualizingmath

visualizingmath:

3mbicommission:

The above images are examples of impossible objects. These consist of a two-dimensional figure which is instantly and subconsciously interpreted by the visual system as representing a projection of a three-dimensional object. In most cases the impossibility becomes apparent after viewing the figure for a few seconds. However, the initial impression of a 3D object remains even after it has been contradicted. The intriguing nature of impossible objects occurs because of our natural desire to interpret 2-D drawings as 3 dimensional objects. The images are essentially optical illusions. 

On top is pictured the Blivet, otherwise known as the devil’s tuning fork which appears to have three cylindrical prongs at one end which then mysteriously transform into two rectangular prongs at the other end. The next image is called the Impossible Cube, which was invented by M.C. Escher. Viewed from a certain angle, this cube appears to defy the laws of geometry. This is a example of forced perspective, a technique that manipulates human visual perception to employ an optical illusion.The Klein Bottle and Möbius strip are more of non-orientable surfaces than impossible objects. Whereas a Möbius strip is a surface with a boundary - such as left and right, a Klein bottle has no boundary. The two images are essentially 3-D versions of the infinity symbol, which has been present during the fabrication of my fractals and therefore in my artwork. The final image is the Penrose triangle. It appears to be a solid object, made of three straight beams of square cross-section which meet pairwise at right angles at the vertices of the triangle they form.

Similar to the concept of sacred geometry, imagery that is conceptually infinite like impossible objects are used in religious and sacred sites throughout Europe. Symbols such as the Ouroboros, the tail-devouring snake and the Three Hares, which chase each other perpetually.  

The above images are examples of impossible objects.”  The Mobius strip is very possible and the Klein bottle is possible in the fourth dimension. (I don’t know if the other three objects are possible in higher dimensions, but they are impossible in 3.) I know it later says “The Klein Bottle and Möbius strip are more of non-orientable surfaces than impossible objects”, but I don’t think everybody is going to read that far down.