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‘Perfect’ Christmas Tree

January 6, 2016


In the Christmas episode of Wrong, but Useful, Colin (who wasn’t feeling very Christmassy) and I discussed some nonsense about Maths students have the solution for decorating the perfect Christmas tree from the Sheffield University Society of Maths (yes, SUMS).

In our chat, we mocked these formulae heavily and berated the ridiculousness of using them to “get people involved in maths” and have a bit of “good, festive fun”. I mean, seriously, these people even used the pun ‘treegonometry’. Really!

tree formulae

Anyway, I sort of flippantly suggested I might try this out and show them how absurd these formulae are and just how far from ‘perfect’ a Christmas tree would be if decorated in this way.

Well, this is that post. I warn you now: I may well have taken this altogether too seriously. Still, I bet you can’t wait to see what a perfectly decorated tree looks like can you? Well, all good things… you’ll have to wait. It took me ages and I took pictures too. I’m aware we’re a little way past Christmas now but that’s partly because it took a while to calculate and measure everything and there’s no way I’m waiting until next Christmas to post this! Think of this post as a way of reminding you that all the fun you had at Christmas wasn’t really that long ago.

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A tree. (Not usually displayed on a stylish plastic box.) removed from the conservatory for better lighting.

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Christmas tree decorating equipment. (Note the calculator and tape measure.)

I measured the tree making use of  a spare child to ensure accuracy (59.3 cm), and did my calculations. I ready to start but I’ll just check on the University’s website to confirm their approach to rounding:


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Seems to be different answers. This doesn’t bode well but I’ll go with mine. I did check them twice after all!

Lights measured and marked to the precise length using a piece of card. I’m assuming that cutting them to the right length would have issues. Actually, the length of lights seems to look ok – not too many, not too few and worryingly close to ‘just right’. Hmm.

Tinsel measured, cut and applied. Again, this looks worryingly good. I think there’s perhaps a little more tinsel than necessary but I can’t really claim to be much of an expert when it comes to decoration decisions. Oh well, if the lights and tinsel look good, I expect the baubles will make it look ridiculous…

12 carefully counted baubles applied to tree. It’s not looking bad at all. This isn’t what I was expecting. I fear Colin and I have been overly harsh for something that’s working out well.

Sadly, that’s as far as I got. I couldn’t find a star available at 6cm (I promise I looked) and I didn’t want to make my own because it would probably be lacking in the professionalism required for a perfect tree.

In conclusion then, the tree actually looks good. It may well even be perfectly decorated (forgive me the star) for all I know about style. I think I can stand by the claim that these formulae are not likely to get people involved in maths as I think you’ve got to be pretty mathsy to want to bother in the first place.

Other than that, I retract the majority of my claims about these formulae being hopeless and acknowledge that they work very well for this size tree (let me know if you agree or not in the comments). I wonder how they’d hold up for a larger tree? Maybe next year…


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  1. flyingcoloursmaths permalink

    They work for one tree isn’t the same as they work for all trees, or else you can easily ‘prove’ that all even numbers are prime. “I checked an example, 2, and it worked!” That might be how you do things in stats, but mathematicians need a bit more evidence ;o)

    • Hmm. Only one counterexample is required to disprove a claim so this does reject out conjecture that the formulae are complete nonsense.

  2. Peter Rowlett permalink

    I was going to leave a comment, but flyingcoloursmaths has said exactly what I wanted to, especially as I just learned 4 is prime.

    • I can see how Colin’s team mysterious won spoof my proof now.
      Also, don’t listen to Colin. He thinks 4 is prime.

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