This is the third installment of my ‘Pictures of Maths’ series. Hope you enjoy!

The structure of honeycomb displays symmetry.

The complex folding patterns that arise when layered paper is put into a test machine and squashed.

A sample image generated by Lawrence Ball’s harmonic maths.

Geometric art is often used as decoration in the ceilings of buildings.

‘Vitruvian Man’, drawn in 1487 by Leonardo Da Vinci, showed the relationship between the human body and geometry. It is a piece of art that represents how closely connected science and art are.

The *421 polytope* is believed to be the most geometrically complex and aesthetically beautiful structure in mathematics. It is the algebraic form at the centre of a Universal Theory of Everything. It was originally describe in the late 19th century and models all interactions and transformations between known and theorised sub-atomic particles. The theory is an attempt to unify quantum physics and gravitation in hopes of ultimately explaining the fabric of the universe. The visualisation was hand drawn in illustrator to an accuracy of 1/10,000 of a millimetre.

The Klein Bottle: an object with no boundaries, no inside or outside. It is a one sided, non-orientable surface. That’s topology for you!

Fractal patterns are visible throughout nature, for example in ferns as displayed above.

Let me know which one is your favourite! Mx

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Regarding the folding paper, I used to work part time at a local business and every time we had to swap out the bins in the massive room-sized box crusher I was the first one to volunteer. It was always interesting to me how the boxes folded and collapsed, especially the bigger stacks that came off the trucks.

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It amazing that something so simple could be so interesting and beautiful!

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