Sprucing up

People playing in hexagonal dust-based ice crystals, also known as snowDan Nguyen

Decorating the Christmas tree is a frequent family tradition. Some will adorn it gradually; others dedicate one special afternoon to it. Ribbons, embellishments, stars and angels: there are many ways to decorate a Christmas tree.

But were you ever discontented with your Christmas tree: was it asymmetrical, too full, or too strange-looking? Two maths students found the solution in 2012, calling it ‘Treegonometry’. Nicole Wrightham and Alex Craig, members of the University of Sheffield Maths Society, created a formula to decorate the perfect Christmas tree:

  • To calculate the number of baubles to use, do the square root of 17, divide the result by 20 and multiply by the height of the tree in centimetres
  • For the length of the tinsel, multiply 13 by Pi, then divide the result by eight and multiply by the height of the tree in centimetres
  • For the length of the lights, Pi must be multiplied by the height of the tree in centimetres
  • For the size, in centimetres, of the star or angel to top the tree, just divide the height of the tree by 10.

And now there is no chance of buying too many Christmas decorations!

Stuffing yourself

Besides the Christmas tree in the room, many dinner tables will have a turkey on Christmas Day. And since Christmas only happens once a year, many eat too much food at once. Consequently, at the end of the night they become sleepy and tired. Many believe that it is the turkey which gives us this sleepy feeling, but why?

The turkey’s proteins contain tryptophan, an essential amino acid for the human body. Our body does not synthesize tryptophan, instead needing to ingest it from our food. Tryptophan is used to make serotonin, a neurotransmitter responsible for feelings of relaxation and well-being and also, weirdly, pain (in the case of some bites). Serotonin is used to make melatonin, a hormone that helps control sleep cycles. Hence it is thought that the tryptophan of the turkey is responsible for drowsiness after the holiday meal, or any meal with a lot of meat.

However, according to the American Chemical Society, this is probably a myth since tryptophan levels in turkey are too low to cause drowsiness, with 64mg per 33g serving.
At certain doses, the ingestion of tryptophan on an empty stomach can make you sleep, but not in this case. One of the more likely explanations for drowsiness is that when we eat too much, the blood is directed to the stomach, leaving the blood flow and oxygenation of the brain impaired, hence we feel tired and sleepy.

Let it snow

Everyone loves a white Christmas. Think no two snowflakes are alike? Yes, the large ones are unique, but this is not true of the simplest crystals which fall before they develop.

A snowflake begins by being a grain of dust floating in a cloud. The water vapour surrounds the grain of dust and, from that particle, a tiny drop is formed which soon turns to ice due to the low temperatures.  First, the small ice crystal becomes hexagonal. This form originates from the chemistry of the water molecule, which consists of two hydrogen atoms attached to an oxygen atom.

Because of the angle of the water molecule and its hydrogen bonds, the water molecules in an ice flake bind chemically to form a six-sided flake. After the drop crystallises, a small cavity arises on each face, because the ice forms faster at its ends. Thus, the cavities make the corners of each face increase in size more quickly, giving rise to the traditional six arms of the snowflakes. Each of these arms grows to form laterals in a direction and shape influenced by minute changes in temperature as the flake falls from the clouds. Thus, each snowflake looks unique.

Scientists’ interest in snowflakes lies in what these ice crystals may mean for global climate change.
Researchers believe that ice crystals also play a role in ozone degradation. In the atmosphere, these crystals contribute to the electric charge of clouds and are believed to influence lightning production, although the mechanism is still unclear.

Snow business

One may also wonder why snow is white if solid water and ice are transparent. Snowflakes have many surfaces reflecting the light which disperse it multiple times in all directions and colours, making the snow appear white. It’s same process that make milk and powdered sugar look like they do.

Typical Christmas snow globes can be made with benzoic acid crystals in water. The benzoic acid does not dissolve readily in water, but because its solubility increases with temperature, crystals similar to snowflakes form when the solution cools.
If you are unlucky and wit does not snow where you spend your Christmas, you just need to do a quick search on YouTube to find the many ways of making fake snow. For example, simply add water to sodium polyacrylate, a superabsorbent polymer found in disposable nappies.

For coloured snow, just add a dye. But beware, if you play with fake snow for too long, your hands may dry out due to the absorbant properties of the polymer. It should not be dangerous, but of course, try at your own risk!