Given the theme, "festive mathematics" proposed by Mau for this Carnival of Mathematics # 114 , I remembered having read some time ago about a "decision tree" proposed by Dr. Gordon Hunter , of Kingston University of London , for the choice of 'tree, and some formulas by a team from Britain's University of Sheffield to determine the perfect decorations.
Mathematics would thus have provided an answer to those who strive to create.
The 2017 Christmas tree of 30 m. that Sky has set up in Piazza Duomo in Milan
(photo Annalisa Santi)
(photo Annalisa Santi)
 |
| Dr. Gordon Hunter (Credit Kingston University London ) |
Dr Gordon Hunter, who works in the University of London's Faculty of Science, Engineering and Computer Science, has created a "decision tree for Christmas," based on a scientific method most commonly used to help solve business and personal problems.
Dr. Hunter hopes his statistical sparkler will help people solve the puzzle of choosing their ideal Christmas tree, paying particular attention to key factors such as smell, color, style and size (as seen in the image, however, they are excluded or better. little considered "fake" trees).
Indeed, he accepted the challenge in 2013, after being asked if it was possible to create a "Christmas decision tree" for the industry-leading chain of garden centers Dobbies.
The company, which has branches across the UK, was keen to help its customers find a solution for their "trees" by choosing the variety of pine or spruce (Fraser spruce, Nordic spruce, Norway spruce or spruce). red blue) more suited to their tastes.
These are the words of Gordon who underlined his collaboration: "It was an interesting change to be given the opportunity to take a method I use in my research and give it a quirky, seasonal application, accessible to everyone. My Christmas decision tree will hopefully help people decide what type of tree is best for them and their home. " "It has been an interesting change to have the opportunity to take a method I use in my research and give it an unusual seasonal application, accessible to all. I hope my Christmas decision tree will help people decide which type of tree is best for them. them and their home ".
"The Christmas Decision Tree" by Dr. Gordon Hunter (Credit Kingston University London )
As you can read in the image:
Artificial tree
Available with a lot of sizes, colors and shapes, it can fit everyone's preferences, you can have a tall and sparkling silver one, a traditional green one or a small one. What you want!
Fraser fir
With a slimmer shape, its branches with soft needles are suitable for being less decorated, giving maximum elegance to the house and has a good citrus scent
Nordic Fir
With its rich dark green foliage, light scent and soft leaves , it's an ideal tree for the family!
Norway Spruce
It is considered the classic traditional Christmas tree with its pyramid shape, good holiday scent and dark green foliage.For the traditionalists or the perfectionists among us!
Blue Spruce
A larger tree with naturally blue foliage. This tree fits a myriad of fabulous decorations!Go wild and wonderful! After all, it's Christmas!
Hunter's "Christmas Decision Tree" then helps a person find a suitable answer to multifaceted questions.
It contains questions like "do you like a big tree", "do you like a thick tree?" and "Do you want a tree to smell Christmas too?" ......
The yes or no answers lead to follow-up questions until they lead to the best possible tree for each one. "Now, with the help of the 'Christmas decision tree', our customers will spend less time reviewing the many wonderful varieties available and will have more time to think about how to make them shine," said Steve Guy, an expert on the Christmas tree of the Dobbies chain.But another challenge, besides the choice of the tree, was also accepted by the Maths Society of Britain's University of Sheffield .
In fact, the University accepted the challenge of finding a formula, later called " treegonometry ", which would allow a tree to be decorated in such a way that the tree and sumptuous decorations were in harmonious proportion, thus solving the problem of not creating a tree that was too poor or too flashy.
Members of the Sheffield University Maths Society (SUMS) have created a "festive" formula to ensure the right balance of lights, filaments and balls, to give the Christmas tree the perfect look.
Their calculations look like this:
Here are the formulas for determining the number of balls, the length of the tinsels (long pieces of thin, shiny material used as decoration) and lights, as well as the height of the star, angel or spire to put on top of the tree:
- Number of balls = take the square root of 17, divide it by 20 and multiply it by the height of the tree (in centimeters)
- Length of the tinsel (in centimeters) = consider the number 13, multiply it by π (3.145 ....), divide it by 8 and then multiply it by the height of the tree
- Length of the tree lights wire (in centimeters) ¹ = take Ï€ (3.145 ....) and multiplied by the height of the tree
- Height (in centimeters) of star or angel above the tree = take the height of the tree and divide it by 10 notes¹ The density of the lights on the wire has not been clarified, but it could be assumed a density of 4 to 10 lights for meter based also on their brightness (if led or not)
To be clearer let's consider, for example, a 180 cm Christmas tree. and, with the help of a simple calculator or with the immediate solution found on the site , we could calculate the decorations.
For this tree it will therefore take 37 balls, about 919 cm of tinsel (30 feet), 565 cm (19 feet) of lights and an 18 cm (seven inches) star or angel and so, as the University claims, the appearance will be perfect!
Number of balls
√17 = 4.123
4.123: 20 = 0.206
0.206 x 180 = 37.10 -> 37
Length of tinsel
13 x π (3.145 ...) = 40.84
40.84: 8 = 5.10
5.10 x 180 = 918.91 -> 919 cm.
Length of lights
Ï€ (3.145 ...) x 180 = 565.48 -> 565 cm.
Star or angel or spire height
180: 10 = 18 cm.
 |
| Spiral tree |
Particularly aroused my interest, or rather my curiosity, in the formula for calculating the length of tinsel, the factor 13/8.
I didn't find any files explaining in detail how these formulas were found, so I don't know if it was intentional or not, but it's interesting to note that 8 and 13 are consecutive Fibonacci numbers .
Why is this interesting?
Because the Fibonacci sequence is closely related to spirals and, usually, the tilsen are arranged in a spiral.
In particular this thing is also seen in nature and if, for example, you look at the spirals on a pineapple, the spirals that go in one direction could be 13 and the number in the opposite direction could be 8. Or the numbers could be 21 left and 13 right .... The fact is that pineapple spiral numbers are always consecutive Fibonacci numbers (or sometimes Lucas numbers ).
And you notice the same effect on other things, like the seed spirals in the head of a sunflower, or the seeds on a strawberry, or the spirals on a pinecone, or a cauliflower, or all sorts of things.
Is it therefore necessary to deduce that the tinsel for a Christmas tree must form Fibonacci spirals?
But will these formulas be really reliable?
Incidentally I would like to mention that Britain's University of Sheffield , with around 26,000 students from 125 countries, is one of the UK's leading and largest universities. A member of the Russell Group, he has a reputation for world-class teaching and research excellence across a broad range of disciplines.
The University of Sheffield was named University of the Year at the 2011 Times Higher Education Awards for its outstanding research, teaching, access and business performance. Additionally, the University has won four Queen's Anniversary Prizes (1998, 2000, 2002 and 2007).
These prestigious awards recognize the outstanding contribution of universities and colleges to the UK's intellectual, economic, cultural and social life.
Sheffield also boasts five Nobel Prize winners among former employees and students and many of its alumni have held 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 other family names, as well as overseas and overseas government agencies and government agencies and foundations of charity.
The University has established partnerships with a number of universities and large companies, both in the UK and overseas. Its partnership with the universities of Leeds and York in the White Rose consortium has a combined research power superior to that of Oxford or Cambridge.
These equations were created by two former students and SUMS members a few years ago, commissioned by the Debenhams department store, and are easy, easy equations also made to sympathize people with math.
Staying on the subject and speaking of universities, I would like to recall the Milanese initiative, linked to the large Christmas tree in Piazza Duomo in Milan, which sees a collaboration between Sky Academy and the Milan Polytechnic - School and Department of Design.
It is not a question of mathematical formulas in this case, but of an activity that has the common objective of developing the culture of innovation and sustainability, in which about 50 young designers supported by teachers will participate.
In fact, for the upcoming Christmas holidays Sky Italia - thanks to the operational support of Live by IGPDecaux and the promo & activation agency Integer - pays tribute to the city of Milan with a very special gift.
From 6 December to 7 January it is in fact possible to admire, in Piazza Duomo, a majestic Christmas tree, chosen in full respect of the environment.
The spruce, selected in collaboration with the Trentino Alto-Adige Forestry Corps (I don't think with Dr. Gordon Hunter's "decision tree"), was in fact already destined for felling, since it was higher than the maximum height allowed for ensure the safety of nearby roads.
The Christmas tree that Sky has set up in Piazza Duomo in Milan has an imposing height of over 30 meters and is the tallest tree ever for Christmas in the most famous Milanese square.
Click here
But let's see if it's perfect?
According to the formulas, having a height of 30 meters (3000 cm.), It should in fact be adorned with:
618 balls
15315 cm. of tinsel (shiny threads)
9425 cm. of strings of lights
and on the top with a 3 meter (300 cm) star (or angel)
For the whole period of the holidays, the tree will illuminate the entire square, thanks to 100,000 LED lights (the maximum foreseen by the public announcement which I do not think corresponds to the approximately 94 meters provided by the formula) of warm white color, respecting the tradition of Christmas tree and its elegance, with an intermittent effect to make the plant even more scenic both day and night.
The more than 700 Christmas balls are also white in color (and here we are approaching the expected 618), partly glossy and partly opaque, which reflect the light of the LEDs, further amplifying it without creating a disturbing element.
The Christmas tree decorations and decorations have been provided in full compliance with current regulations and in full harmony with the attention to environmental issues.
Therefore a responsible use of the plastic with which the Christmas balls are made (in line with the campaign of the group "Sky Ocean Rescue - A sea to save") and with the reuse of the LED strings that will be returned to suppliers after use in the Christmas time.
When, at the end of the Christmas holidays, the tree will be turned off and abandoned, Sky undertakes to coordinate the activities for the reuse of the tree itself, with a project for the construction of urban furniture of public utility, thanks to the precious collaboration of which I was saying, between Sky Academy and the Politecnico di Milano - School and Department of Design.
A special jury, composed of Sky Academy and Politecnico di Milano representatives, will select the best idea, which will be implemented in the next phase of the project, which in fact provides a practical workshop for the physical transformation of the wood of the Christmas tree in urban furnishings to be placed in the Milan area.
In conclusion, is there the possibility of creating an "ideal" and truly perfect tree?
Surely the perfect tree is a matter of personal preference, and in this sense it cannot be defined by a set of mathematical rules.
Mine, which has been made since 1956 (my father bought it among the first "fake" ones), will certainly be imperfect, indeed perhaps decidedly miserable as foliage, but too redundant in decorations, many still of the time, therefore certainly very kitsch.
But it is adorned with all the balls, decorations and lights accumulated in 60 years, at least with the ones that have not been lost or broken, and surely for me it is always a wonderful memory that would have no equal in perfection ..... not even with "math" !!!!
The "imperfect" but "sixty-year" Christmas tree set up,
as per tradition, in Sant'Ambrogio on 7 December 2017
Post a Comment