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'Maths Is Everywhere!' printed from http://nrich.maths.org/

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We begin by identifying these pictures. From left to right and from top to bottom, they are:

1. Zebra 2. Plagiomnium Affine (plant cells) 3. Honeycomb 4. Pinecone

5. Hemoglobine 6. Gephyrocapsa Oceanica (coccolith) 7. The Earth 8. Snail

9. Beech cell 10. Asterionella Formosa 11. Whale 12. Diatom

13. Pollen 14. Homo vitruvius 15. Snowflake 16. DNA

 

The first thing to identify in these pictures is symmetry. Almost all pictures have at least one axis of symmetry. In particular, we note the perfect symmetry of the Asterionella Formosa, with 4 axis of symmetry along its body, the detailed symmetry of the snowflake, which represents one of the most beautiful structures ever observed, and the symmetry of the Homo Vitruvius, designed by Leonardo Da Vinci to emphasize on the beauty of the human form.

Another mathematical aspect which we can identify are repeating patterns. Of particular interest are the plant cells and the honeycomb, both of which consist of many tiles of hexagons - a shape which considerably helps them carry out their biological functions more easily. We also note the repetitions in the pinecone, whose scales first close to protect the fertilized seeds and afterwards open (a stage that we see now) in order for the seeds to spread.

Curves also appear in some of these pictures. We note for example the spiral in the snail's shell, which helps it grow and protect itself. The DNA also takes various curved forms in order to fit into the small nucleous of the cell.

Spherical structures are also very important in nature. From objects as small as the hemoglobine, a protein found in the red blood cells which helps the transportation of the oxygen, to objects as large as the Earth,  many objects have a spherical form. We also observe a spherical Pollen, and a spherical Coccolith, a shape which mostly helps these species protect themselves from their environment.