Mathematical Present Wrapping

I love wrapping Christmas presents, especially when it gives me an excuse to be a little bit mathematical about it So the standard method of wrapping a present is like this, you wrap the paper round, put a bit of tape on it, fold in the ends

But for certain shapes of presents this method gets a bit more interesting and slightly cool things happen So that’s a standard cuboid shape, but if your present happens to have a completely square cross section at the end like this, what you can do is, first of all make sure your paper comes halfway up the face, like this and then if you do the standard method of wrapping it round, putting a bit of tape on it, and then folding in the ends you’ll find that where the ends fold in, all the corners meet exactly in the middle and you get this fantastic cross shape on the end which for certain patterns of wrapping paper looks really really nice Another nice one is if your shape is an equilateral triangular prism – like this Toblerone (TM) (other equilateral triangular prism shaped chocolate bars are available) What you can do in this case is make sure that your paper comes up to exactly the same height as the chocolate bar You’ll then find that if you do the standard method that the end of the paper will line up exactly and cover the entire triangular end Look at that! It’s beautiful! It lines up and covers it exactly

And in fact if you don’t want to put a bit of tape on the outside you could even use some double sided tape or glue to hold that end down so it looks completely neat and perfect If your shape is cylindrical like this one you can also use a bit of maths to work out how much paper you need so instead of doing anything tedious like rolling it around I can use my understanding of the mathematical constant pi Because the circumference is pi times the diameter so I know that I need to cut here in order to have the right amount of paper to wrap this cylindrical present and let’s see

Oh yeah! Perfect! Another nice one is if the thing that you’re wrapping is slightly squidgy, like this bag of marshmallows What you can do now if your pattern on your paper is small enough is line up the pattern exactly so that you can’t even tell that that’s where the edge of the paper is [mysterious tape hand] all you need to do then is put a bit of tape on and fold in the ends This also works with soft toys, cushions and other squidgy things But the best one of all is if your present is a square shape that’s relatively flat like this And in this case there is an alternative method you can use that I think is really nice So the standard way of doing this would be to take a piece of paper with a bit of a gap here and that measures long enough to wrap round the whole present And then wrap it like that But what you can do instead is take a square piece of paper the size of this square (the length of the edge) is measured using this object so you take the diagonal (which we’ll call d) and you’ll also need to measure the height of the box (which we’ll call h) The length of this piece of paper is now calculated by This method of calculating the edge of the square was worked out by Dr Sara Santos who appeared on the One Show in 2012 to explain her method You can watch that video here There’s also another nice video outlining this method available here

Anyway, to wrap to your present you take your square bit of paper, you can fold it in half twice to get these nice guidelines And then place your present on the paper at 45 degrees You then fold in the two corners opposite, like this, and you can put a bit of tape here if you want You can then fold in the other two corners You may need to do a little bit of

kindof tucking in at the edges to make sure that’s completely neat But all four corners will meet exactly in the middle And it looks beautiful! It’s simple, it’s neat and it just makes sense And in fact if you’re feeling really super hardcore you can just secure the entire thing using one bit of tape, here There you have it: the Diagonal Wrapping method Merry Christmas everyone! [cool electronic Christmassy music]