## How to work with Sequences: Part 2

Sequences are all around us. Many of these patterns or sequences are obvious, such as the hexagon! But why is the hexagon used so frequently in nature? Mathematics teaches us that it is incredibly efficient, leaving no wasted space.

The most obvious example is that of the honeycomb. Hard working bees build these structure from wax in order to store honey, pollen and larvae. They produce wax from special glands in their body. Young adults gorge on honey, which activates the glands in their abdomens. The glands convert sugar from the honey into a waxy substance, deposited as flakes on the abdomen. Other bees then collect this wax and chew it, shaping it into honeycomb!

It is not only bees which use hexagons. The compound eyes of the dragonfly contain around 3000 hexagons! This helps provide them with amazing vision. The scutes in the central part of a tortoise shell are also hexagonal.

Snowflakes are hexagonal. The hexagonal structure allows water molecules to form together in the most efficient way. Even volcanic eruptions can produce hexagonal formations, due to the way in which the lava cools. As it cools down, it also contracts, resulting in increasing pressure. This pressure leads to the formation of cracks. Amazingly, the angle at which most tension is released is 120 degrees, the internal angle size in a regular hexagon!

GCSE mathematicians – you need to be able to work with sequences. For help, try our new guide “How to work with Sequences: Part 2”. It includes information about quadratic sequences. In addition there are explanations of how to work out the nth term. As always there are questions to try, and answers to check your understanding.

Click on the picture below to see the guide.

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