13 December 2021

Maths students have the solution for decorating the perfect Christmas tree

If you've gone overboard while decorating the Christmas tree this year and it's more gaudy than great then maths students from the University of Sheffield may have the answer.

Christmas tree

Members of Sheffield University Maths Society (SUMS) have created a festive formula to ensure just the right ratio of lights, tinsel and baubles are used to give your Christmas tree the perfect look.

Using their 'treegonometry' calculations they say a 152cm (5ft) Christmas tree would need 31 baubles, around 776 cms of tinsel and 478 cms of lights with a 15cm star or angel to top it off.

Their calculations look like this:

  • Length of tinsel in cm: (13 x pi) divided by 8, then multiply by tree hight in cm
  • Number of baubles: (17 x pi) then multiply by tree hight in cm
  • Length of lights in cm: pi multiplied by tree hight in cm
  • Height of star in cm: tree height in cm divided by 10

Formula for the perfect Christmas tree

Number of baubles: 29

Height of star or fairy (cm): 14

Length of tinsel (cm): 715

Length of lights (cm): 440

    Sophie Chong, president of SUMS said: "Being interested in maths can be a struggle for a lot of people but this is a brilliant way of showing an applicable side of maths.

    "This equation - which was created by two former students and SUMS members a few years ago - is a nice and easy equation to get people involved in maths, as well as a bit of good, festive fun."

    Christmas tree facts

    • The world's tallest Christmas tree would, at 2,600ft tall, need more than 16,000 baubles, over 4,000 meters of tinsel, almost 2,500 meters of lights, and an 80 meter tall star.
    • The Trafalgar Square tree is usually about 25 meters tall, meaning it needs 515 baubles, over 100 meters of tinsel, 78 meters of lights and a 2.5 meter tall star.

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