Wrapping Your Christmas Presents

NullRoot · 2007-12-05 03:14:16

I briefly thought of putting this in the Jokes section, because this must be the silliest thing I've seen dubbed as 'news' for a long time.

Formula created by University of Leicester researcher
...
Bluewater, the UKs leading shopping centre, discovered that Brits continually overestimate the amount of paper they need to wrap their Christmas presents. Following this new revelation, Bluewater today reveals the mathematical solution which will hopefully put an end to unnecessary paper wastage: A1 = 2(ab+ac+bc+c²)**
...
The formula has been created by Warwick Dumas from the Department of Mathematics, University of Leicester , who has been working with Bluewater to devise the perfect method of gift-wrapping that will help customers save time and money as well as reducing the amount of paper that will be wasted.
...
(**) A = area needed/ a, b, c = Dimensions of cuboid: a = longest, c = shortest

From: http://www2.le.ac.uk/ebulletin/news/press-releases/2000-2009/2007/12/nparticle.2007-12-04.6745557516

Right. Ok. The magic equation is Area=2ab+2ac+2bc+2cc. It took a university professor to tell us that the solution to how to wrap a cuboid is to use paper that has an area equal to the surface area of what we're trying to wrap (plus enough for some flaps on the end)?
I'm not sure why he threw in the 2cc? I know he put them in there for the little triangles on the end, but they won't be covering anything that wouldn't already covered, so this "solution" isn't really "[putting] an end to unnecessary paper wastage".

Now I suppose it's fair enough. Not all people are good at Math and not all people know how to work out the surface area of a cuboid, but even knowing this equation still isn't enough. We now need to find wrapping paper that is a+c (or 2b+2c) wide to actually use this equation or we end up either overwrapping or cutting off extra paper; in both cases there is wasted paper.

So... is this equation really fit for purpose? And how much do you reckon this professor got paid for telling Bluewater the equation for the surface area of a cuboid?

Last edited by NullRoot (2007-12-05 03:16:11)

Zach · 2007-12-05 03:18:48

Dude needs to get a life.

mathsyperson · 2007-12-05 03:26:44

Heh, I read that in the paper, but they'd put the formula as 2(ab+ac+bc+c), which doesn't make any sense because that c is a length so it couldn't contribute to working out an area.

Also, instead of longest to shortest, a to c meant length, width and height (meaning they were interchangable, and so they should be interchangable and so the formula not being symmetric doesn't make sense either).

At least your article makes mathematical sense, even if it's utterly pointless and not at all practically useful for the reasons you said.

NullRoot · 2007-12-05 03:35:56

That's amusing. They must have thought the "c2" was a typo and removed it .

I would have loved to eavesdrop on the conversation when they asked how he arrived at this magic formula and (to cover for himself) he started going into how he used advanced differential calculus to find the ideal solution for three variables.

"Gimme my commission now, kthxbai!"

MathsIsFun · 2007-12-05 08:18:25

Shouldn't they then provide a calculator in the gifts section? And possibly a tape measure?

Khushboo · 2007-12-05 17:15:08

I really dont understand why he came up with the extra c^2. It wasnt called for. Using the above equation you ought to have more wastage as one is going to either overuse the paper or perhaps remove the unwanted papers.....so there is wastage ....

regards

khushboo

NullRoot · 2007-12-05 21:27:14

I suspect that he's thinking a christmas present must be wrapped as the attached, which is the way I wrap presents. His assumption is that those four flaps (two on the visible side and two more on the opposite side) should have a height of C as well. Which would mean the area of those triangles is 4x0.5CC = 2CC.

Now that I think about it... that wouldn't work. We already know the ideal width for the paper is A+C, meaning that the height of those flaps should be HALF of C.

So his equation should ACTUALLY be:
Area=2ab+2ac+2bc+(4)(0.5)(0.5c)c
A = 2(ab+ac+bc)+c²

Last edited by NullRoot (2007-12-06 00:13:29)

Laterally Speaking · 2007-12-08 06:03:22

Also, finding out the area is not much use. You would be better off just finding out the hight and width of paper needed, instead of finding the area, then trying to backtrack to the dimensions.

Warwick Dumas · 2007-12-09 00:34:32

Hi all

Re the area etc, the report that I wrote is publicly available on request. It should be understandable to anyone familiar with calculus and basic trigonometry, so I do encourage you to read it. The point of finding out the area is purely to compare the areas given by using different methods.

The person who said that the widthways remainder on the paper is important, is absolutely correct, and obviously this fact is not contained in a formula for the area used. The answer is that you should be wrapping two or more things alongside each other so that the remainder does not have to be wasted. (If you were not going to do this, wrapping diagonally would be superior.)

Thank you for your comments.

Warwick Dumas

NullRoot · 2007-12-10 00:29:42

I will try and get a copy of your paper. If I do, I will read it.

You've obviously put some work into it and you've seen fit to come onto the forum and defend it, so the least I can do is give you the benefit of the doubt; I know how math savvy the media can be.

mathsyperson · 2008-12-24 01:22:24

BUMP

I was wrapping some presents earlier, and the problem of optimal wrapping is actually less trivial than it appears. I'd imagine that a fairly large proportion of presents are cuboidal, and that most people would place the present so that its sides are parallel to the edge of the paper, and then wrap around it.

Wrapping a cube like this means that you need this much paper:

-------------------------------
|         |         |         |
|    X    |         |    X    |  
|         |         |         |
|---------|---------|---------|
|         |         |         |
|         |         |         |
|         |         |         |
|---------|---------|---------|
|         |         |         |
|         |         |         |
|         |         |         |
|    X    |---------|    X    |
|         |         |         |
|         |         |         |
|         |         |         |
|---------|---------|---------|

The regions in the middle are the net of the cube, and the regions marked X are "wasted". Perhaps surprisingly, in this case the same area is wasted as the amount that is used!
People could perhaps cut out the net of the cube, and then use the corner pieces to wrap smaller presents, but I'd say it's rare that people do this.

I only realised this because I underestimated the length I would need to wrap a present, failed to cover it the "normal" way, and started considering alternatives.

As Warwick Dumas says, wrapping diagonally is indeed more efficient!

It makes for some interesting-looking presents though. For example, I have a (cuboidal) CD case wrapped in a present that is roughly a trapezoidal prism and the seams where the edges of the paper meet make an H shape instead of just a line.

Tigeree · 2008-12-25 19:23:35

Given the name of this thread I thought I might just say ..... I am sooooooo bad at wrapping presents and .............. Zach's right.

Last edited by Tigeree (2008-12-25 19:24:33)

Devantè · 2009-01-01 22:12:53

I don't think he got the chemistry kit he wanted this year.

Last edited by Devantè (2009-01-01 22:13:15)

Tigeree · 2009-01-03 19:29:17

me either.

Math Is Fun Forum

#1 2007-12-05 03:14:16

Wrapping Your Christmas Presents

#2 2007-12-05 03:18:48

Re: Wrapping Your Christmas Presents

#3 2007-12-05 03:26:44

Re: Wrapping Your Christmas Presents

#4 2007-12-05 03:35:56

Re: Wrapping Your Christmas Presents

#5 2007-12-05 08:18:25

Re: Wrapping Your Christmas Presents

#6 2007-12-05 17:15:08

Re: Wrapping Your Christmas Presents

#7 2007-12-05 21:27:14

Re: Wrapping Your Christmas Presents

#8 2007-12-08 06:03:22

Re: Wrapping Your Christmas Presents

#9 2007-12-09 00:34:32

Re: Wrapping Your Christmas Presents

#10 2007-12-10 00:29:42

Re: Wrapping Your Christmas Presents

#11 2008-12-24 01:22:24

Re: Wrapping Your Christmas Presents

#12 2008-12-25 19:23:35

Re: Wrapping Your Christmas Presents

#13 2009-01-01 22:12:53

Re: Wrapping Your Christmas Presents

#14 2009-01-03 19:29:17

Re: Wrapping Your Christmas Presents

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