Comment décorer un sapin de Noël mathématiquement parfait

Un sapin de Noël.

Un sapin de Noël. SUPERSTOCK/SIPA

SCIENCES – Guirlandes, boules... Des étudiants de l'université de Sheffield ont calculé les quantités optimales...

Votre sapin est trop dépouillé, ou au contraire, trop chargé? Pas de problème, les mathématiques sont là pour vous sauver. Des étudiants de l'université de Sheffield se sont penchés sur l'optimisation des décorations et ont déterminé les formules suivantes:

  • nombre de boules de Noël = (racine carrée (17) / 20 ) x (hauteur de l'arbre en cm)
  • longueur des guirlandes = 13π/8 x hauteur de l'arbre
  • longueur des guirlandes électriques = π x hauteur de l'arbre
  • diamètre de l'étoile = (hauteur de l'arbre) / 10

Pour un sapin de 150 cm, cela donne: 31 boules, 7,6m de guirlandes, 4,7m de guirlandes électriques, une étoile de 15 cm.

Pour un sapin de 200 cm: 41 boules,  10,2m de guirlandes, 6,3m de guirlandes, 20 cm pour l'étoile

Pour le reste, voir leur simulateur ici

Les deux étudiants de 20 ans et leur professeur jurent que la formule marche pour tous les types d'arbres. On la trouve un peu trop simple, car elle ne prend pas en compte la surface couvrante du cône qu'est le sapin. Pour cela, il faudrait utiliser le diamètre des branches à la base de l'arbre. Allez, on leur met 14/20 quand même, pour avoir inventé la treegonometry.


Treegonometry creates perfect Christmas tree

Festive maths students from the University of Sheffield have created formulas for the perfect Christmas tree.



Members of the University’s Maths society, called SUMS, have put an end to bare branches, by calculating the amount of baubles, tinsel and lights needed, as well as the size of the essential star on top.

Department store Debenhams set the University the Christmas themed challenge to create the formulas for the perfectly decorated Christmas tree and it is also available below as a calculator.

If you've found your ideal Christmas tree but want to ensure you use the appropriate amount of decorations then the calculator will have the answer.

The formulas – which are being rolled out for use by Debenhams personal shoppers nationwide – are as follows:


For example, a 180cm (6ft) Christmas tree would need 37 baubles, around 919 cms of tinsel and 565 cms of lights and an 18cm star or angel is required to achieve the perfect look.



Number of baubles: 29

Height of star or fairy (cm): 14

Length of tinsel (cm): 715

Length of lights (cm): 440

Students Nicole Wrightham and Alex Craig, both aged 20, from the University of Sheffield, created the formulas.

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

The formula allows customers to be savvy when buying the Christmas decorations, as they can calculate exactly how much they need to create a beautifully decorated tree.

Debenhams Christmas decorations buyer Sarah Theobold added: “The formula is so versatile it will work for a tree large enough for the Royal Family at Balmoral but also on trees small enough for the most modest of homes.

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.
  • This year's Trafalgar Square tree is 21 meters tall, meaning it would need 433 baubles, over 100 meters of tinsel, 65 meters of lights and a two meter tall star.

"Customers are often making the error of buying too large or small an angel; however this simple formula means you’ll have the tree to star ratio correct."

Additional information

The University of Sheffield

With nearly 25,000 students from 125 countries, the University of Sheffield is one of the UK’s leading and largest universities. A member of the Russell Group, it has a reputation for world-class teaching and research excellence across a wide range of disciplines. The University of Sheffield was named University of the Year in the Times Higher Education Awards 2011 for its exceptional performance in research, teaching, access and business performance. In addition, the University has won four Queen’s Anniversary Prizes (1998, 2000, 2002, and 2007).

These prestigious awards recognise outstanding contributions by universities and colleges to the United Kingdom’s intellectual, economic, cultural and social life. Sheffield also boasts five Nobel Prize winners among former staff and students and many of its alumni have gone on to hold positions of great responsibility and influence around the world. The University’s research partners and clients include Boeing, Rolls-Royce, Unilever, Boots, AstraZeneca, GSK, ICI, Slazenger, and many more household names, as well as UK and overseas government agencies and charitable foundations.

The University has well-established partnerships with a number of universities and major corporations, both in the UK and abroad. Its partnership with Leeds and York Universities in the White Rose Consortium has a combined research power greater than that of either Oxford or Cambridge.


Debenhams is a leading international, multi-channel brand with a proud British heritage which trades out of 240 stores across 28 countries. Debenhams gives its customers around the world a unique, differentiated and exclusive mix of own brands, international brands and concessions.

In the UK, Debenhams has a top four market share in womenswear and menswear and a top ten share in childrenswear. It leads the market in premium health and beauty.

Debenhams is the eleventh biggest UK online retailer by traffic volume and in March 2012 was awarded "Multichannel Retailer of the Year" at the Oracle Retail Week Awards.


For further information please contact:

Paul Mannion
Media Relations Officer
University of Sheffield
0114 2229851

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