Is there a mathematical formula for the perfect Christmas tree?

Decorating the Christmas tree is one of the most beloved traditions surrounding this festive period. In some homes it is almost a ritual with strict, measured steps and an order that you have to follow so that your fir tree becomes the most ornate and eye-catching being in the whole house. For others this ritual is less important and choose to turn it into a social convention rather than a decorative tradition. Be that as it may, it is rare to find a place where a Christmas tree is missing.

In 2012, a team of students from the University of Sheffield (UK) developed a system that formulated the perfect way to decorate a Christmas tree. The team developed a calculator that, from four mathematical formulas, predicted the perfect number of balls, garland and lights needed to optimally decorate a tree according to height. Thus, to decorate a tree of 180cm you would need: 37 balls, 565 centimetres of Christmas lights and 919 centimetres of garland. As for the size of the star that crowns it, it is calculated by dividing the height of the tree by ten centimetres.

"We hope that our formulas will make Christmas easier for everyone," declared the creators of this original mathematical application they have dubbed ‘Treegonometry’. In addition to being useful for domestic use, the formula will also be of great help to public administrations and private companies that want to give a touch of Christmas spirit and place the huge trees that are usually seen in the squares of cities around the world. For example, the Christmas tree that is usually placed in Trafalgar Square (London) has an average height of 21 metres, so you would need 433 balls in order for it to be perfectly decorated.


This tradition of decorating trees comes, like almost all ancient traditions, from the Celtic peoples of northern and central Europe. Many of their gods used to be represented and worshipped through trees and, in winter, a festival was celebrated in honor of the birth of the God of sun and fertility, Frey. During this festival a tree was adorned representing Yggdrasil, the tree-world of Nordic mythology where the kingdoms of men, gods and other creatures are found.

It was also common for fir trees to be kept inside houses because, as their leaves never fall or lose their color, they were considered a symbol of life and rebirth. The most widespread belief is that it was Saint Boniface, the evangelizer of Germany, who took advantage of this pagan tradition in order to give it a new meaning and to adapt it to Christian beliefs. He substituted worship of Odin through a tree for a pine tree that represented God and was also decorated with apples (symbol of original sin) and candles (symbol of Jesus' light).


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