Toilet Roll Pyramid Equation

Hello 2014!!

OK, so for one reason or another a pyramid of toilet rolls has begun to form next to the toilet in our house.

One reason may be this: Here’s one I made earlier

Another may just be that the recycling bin was a bit full and the kids thought it would be fun.

Anyway, last night I started to wonder if there was a mathematical equation which would, given the height or width of the widest row of rolls, give you the total rolls in the pyramid.

There is and it’s pretty simple…

Given that x = height in rolls or widest row in rolls the equation is (x²+x)/2

One could be forgiven for thinking “well it should be half of x²“, as x² should be the total in the square, that the pyramid (or if stacked aligned left) triangle, is half of. In actual fact though half of x² would only include half of the longest line in the pyramid as this crossed the divide between the two halves.

OOOO                    OOOO 
OOOO  <--- pyramid      OOOO
OOOO         half ----> OOOO
OOOO                    OOOO

(4²+4)/2 = (16+4)/2 = 20/2 = 10

Now it’s a very long time since I did any maths like this really. Day to day stuff doesn’t often cover equations to calculate the total number of toilet rolls in a toilet roll pyramid (lord knows why). So I was fairly pleased with myself for realising this simple formula.

My kids on the other hand were pretty apathetic about the whole thing 😦

Oh well, the geek in me was pleased either way 🙂


P.S. once the Pyramid reaches 10 high I’ll add a picture 🙂


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