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Mathematical formula for the perfect Christmas tree

By Darren Quick
December 10, 2012
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A tree that could benefit from the formulas devised by students at the University of Sheffield (Photo: Shutterstock)
A tree that could benefit from the formulas devised by students at the University of Sheffield (Photo: Shutterstock)

For those who prefer something more traditional than the Treeasy, members of the University of Sheffield’s Maths society have devised a formula for the perfect Christmas tree in response to a challenge by U.K. department store Debenhams.

The formula, which was created by students Nicole Wrightman and Alex Craig, uses the height of a tree to calculate the ideal number of baubles, length of tinsel, length of lights and even the height of the star, fairy or angel sitting atop the tree required to give the tree that catalog-perfect look.

“The formulas took us about two hours to complete,” said Wrightman. “We hope the formulas will play a part in making Christmas that little bit easier for everyone.”

The "treegonometric" formulas are as follows:

  • Number of baubles = √17 / 20 x (tree height in cms)
  • Length of tinsel (cms) = 13 x π / 8 x (tree height in cms)
  • Length of lights (cms) = π x (tree height in cms)
  • Height of star/fairy/angel (cms) = height of tree in cms /10

    • For those without a calculator at hand, an online calculator can be found via the source link.

    Source: University of Sheffield

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    Darren Quick
    Darren's love of technology started in primary school with a Nintendo Game & Watch Donkey Kong (still functioning) and a Commodore VIC 20 computer (not still functioning). In high school he upgraded to a 286 PC, and he's been following Moore's law ever since. This love of technology continues as Managing Editor of New Atlas.
    2 comments
    Jamie Smith
    The first three formulae are linear functions of the tree height. This means for instance that if the height doubles, the spacing between the baubles will also double, so a larger tree might look a tad sparse. However, if the formulae were to use the square of the height, the spacing would remain the same, which would definitely make a larger tree look cluttered. I would have thought that using something like the 1.5 power (h^1.5) might be preferable.
    Marcus Carr
    Jamie, I'm no mathematician, but would a better way to overcome this not be to specify the size of the baubles, tinsel and lights as a proportion of the height of the tree? I agree that it would look sparse as it got bigger - imagine it at ten metres tall?
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