Maths Bite: Impossible cube

The impossible cube was invented by M.C. Escher for his 1958 print Belvedere. It is based on the Necker cube, and seems to defy the rules of geometry; on the surface resembles a perspective drawing of a 3D cube, however its features are drawn inconsistently from the way they would be in an actual cube.

The impossible cube draws upon the ambiguity present in a Necker cube illustration, in which a cube is drawn with its edges as line segments, and can be interpreted as being in either of two different three-dimensional orientations. – Wikipedia


Source: kidsmathgamesonline

How would this cube look like in real life? The below video attempts to demonstrate that.

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Art and Maths: Connected Throughout History

For thousands of years, artists have used mathematical concepts in their work. In this post, I will quickly reveal some connections between these two fields throughout history.

Golden Ratio

The golden ratio is roughly equal to 1.618. The special nature of this ratio appealed to the Greeks, who thought that objects in this proportion were particularly aesthetically pleasing. It has been said that they used this ratio in their architecture and statues to ensure their beauty, for example the dimensions of the Parthenon. In fact, throughout history there have been a number of pieces of art that exhibit the golden ratio: Leonardo Da Vinci’s paintings or Michelangelo’s David. However, it has been debated whether Ancient or Renaissance artists consciously used this ratio, or whether it is simply a numerological coincidence.

Geometric Patterns

Geometric patterns – simple arrangements of mathematical shapes and figures – have been widely used in decoration throughout history. For example, the ‘Flower of Life’ pattern was used on the Temple of Osiris at Abydos in Egypt. Dating back about 5000 years, it consists of circles positioned in rows, each one centred on the circumference of circles in neighbouring rows.

Additionally, Mosques throughout the world are embellished with elaborate geometrical patterns, which symbolize the divine order of the Universe. The use of the geometrical patterns is due to the fact that Islamic art traditionally does not depict people and animals.



Popularised by Maurits Escher, tessellations are one of the more well-known and direct forms of mathematics in artwork. A tessellation is a tiling of a geometric shape with no overlaps or gaps. Escher made an art form out of colourful patterns of tessellating shapes, including reptiles, birds and fish.


Origami originated from Japan and is the craft of creating three-dimensional shapes solely by folding paper (usually only one sheet). These shapes range from paper cranes to flowers. If you unfold the piece of paper, there will be a complex geometrical pattern of creases that are made up of triangles and squares. Many of these will be congruent due to the fact that the same fold produced them, revealing the deep links between geometry and ancient art.


Fractals are mathematical structures that have the property of ‘self-similarity’, meaning that if you zoom in on one, the same type of structure will keep appearing. I have already talked about extensively in a previous blog post; check it out if you’re interested! (Personally, I find them beautiful).


Mathematics as Art

The mathematician Jerry King stated, “the keys to mathematics are beauty and elegance and not dullness and technicality”. In ‘A Mathematician’s Apology’ by G.H. Hardy, Hardy explores this idea by explaining his thoughts on the criteria for mathematical beauty: “seriousness, depth, generality, unexpectedness, inevitability, and economy”. Furthermore, Paul Erdos agreed that mathematics had beauty by explaining: “”Why are numbers beautiful? It’s like asking why is Beethoven’s Ninth Symphony beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful.”

If this topic interests you, I would highly recommend reading this article in AMS’s Feature Column. M x