Piggy bank maths

It feels strange watching Alex learn the basics of mathematics. So many solutions that come so naturally to me are a struggle for him, not through lack of intelligence on his part, but from their unfamiliarity as he tries to understand the basic concepts.

This morning it was money. When you think about it there's a lot of basic arithmetic stored in a piggy bank.

Alex wanted a milky pop from the canteen. That's 10 cents. Now he wants 5. For most of us that's easy, 5 x 10c = 50c. But he's barely touched on multiplication yet, so it's back to addition.

Fortunately, they've done counting on tens (a prelude to multiplication), otherwise the addition is very painful.

Okay, so we've got the first answer, now the problem is how to make it with coins. If you don't have a 50c coin then you need to make 50 from smaller denominations, say 2 x 20c and 1 x 10c. Again, we've got multiplications going on, or counting on twenties.

Then he wants to buy one for his friend. So now we have 5 + 1 = 6 milky pops. And we need to add 10c to the total cash required.

My spelling all that out was torturous, wasn't it? But that's the least level of detail required when you are starting out. For me now, I don't even have to consciously think about such sums. This level of mathematics is more of an emotional response than intellectual. Relationships between numbers have become intuitive feelings. Coins have shapes, you don't even have to think about the numbers on them, you just know how they fit together to make new numbers.

But I can see that developing in Alex. Sometimes he'll immediately pick the right answer to a mathematical question and it's only when he starts thinking about it too hard that he might struggle and get it wrong. It's fascinating to watch.

Time and Relative Dimensions in Cake: Baking a TARDIS (and a Dalek)

"People assume that time is a strict progression of cause to effect, but *actually* from a non-linear, non-subjective viewpoint - it's more like a big ball of wibbly wobbly... time-y wimey... stuff." The Doctor, Blink

There was an incident fifty years ago this month. Another that happened a tenth of that time ago at almost the same time of year. The two events are not connected by cause and effect, except they were today and by a big ball of squeezy wheezy blue stuff.

On November 23 this year we celebrate fifty years of Doctor Who. I'm not that old (though my Mum shares a name of one of his original companions), but I grew up watching the British series. I've been fortunate enough too my son Alex has similarly developed an enjoyment of the program and asked for a Doctor Who cake to celebrate his birthday this year.

What better way to celebrate five and fifty years with a cake of the Doctor's time machine, a blue policebox called the TARDIS? After all, it's rectangular, which hopefully meant it would be relatively easy to bake and decorate. We may have been "forced" to outsource the party to a play centre this year, but at least can put some effort into a decent cake.

Cake decorating seems to have expanded into more general society, judging by the number of cake decorating shops and shows on the topic on Pay TV. I have a couple of colleagues at work who are obsessed by the subject. Neither my wife B nor I are professional, semi-professional or even vaguely professional cake decorators. However, articles on the Internet and various YouTube videos make it seem a lot easier than it actually is.

Armed with a YouTube video and a few blog posts we set about making the TARDIS. Whilst the TV version may be bigger on the inside than the outside ours was just cake on the inside covered with icing.

Baking the actual cakes was the easy bit. B did the orange cake and I the chocolate mud cake (sans coffee). Both recipes are delicious. That night we also made the chocolate modelling paste to construct the outer shell of the TARDIS cake. We used melted white chocolate, corn derived glucose syrup and blue gel dye. This formed a thick blue dough which we rolled up and left overnight and into the next day.

I printed out a picture of the TARDIS as a template, but it was too large. How large should the template be? This is where relative dimensions come in, along with a bit of math. Yes, mathematics is useful!

Volume (V) = height (H) x width (W) x depth (D)

First find the maximum volume of cake available for use (Vc) by using the above equation (Vc = Hc x Wc x Dc) and the dimensions of the cake. Also we need to calculate the relative scale of the TARDIS (t) by using the dimensions of the template (m) where the dimensions can be written as a ratio with one side = 1. Despite the template being only two dimensional we know the depth = width as the base of the TARDIS is square. We need

Vt = Ht x Wt x Dt = (Hm x Wm x Dm)/Dm . Because of the square base this simplifies to Vt = Hm/Dm (neglecting units here).

For your information, Hm/Dm comes out to be about 1.6. So the TARDIS dimensions are of the ration 1:1:1.6.

If we let H, W, D be the dimensions that we'll use for our cake and taking advantage of the fact that the base is square then we get:

D = (Vc * Dm / Hm) ^ 1/3
W = D
H = Hm/Dm * D

And those are the dimensions that you need to make the cake. This meant carving the cake into blocks and pasting together with butter cream. The whole lot was covered with butter cream. We then cut out the four vertical sides of the TARDIS from the blue chocolate modelling paste with white icing for the windows and black writing icing for details. I printed the signs on ordinary paper and cut them out - they stuck easily enough to the chocolate.

And there you have it!

Alex gets a second birthday party at childcare, where he has a Doctor Who obsessed teacher. So we made a simpler Dalek cake using leftover red fondant from the previous year's birthday cake (briefly microwaved to soften), liquorice strips and chocolate coated marshmallows.

Now I've educated you about some mathematics, maybe you would like to read Andy Connelly's article in the Guardian about the Science of Cake.

Celebrity mathematicians

I knew that the head of Qantas, Alan Joyce, studied mathematics at university, as did (uggh) right wing columnist Miranda Devine. I didn't know that it might be the only thing she shares in common with South Park co-creator Matt Stone, who has a joint major in film and mathematics from the University of Colorado.

Other (more) famous people with mathematics degrees include past and present presidents of Singapore, Peru and the Philippines, along with Teri Hatcher and Art Garfunkel.

A high flying mathematician

Alan Joyce has been named as the next CEO of Qantas. Apparently, the current head of Jetstar has a Masters in Mathematics and Physics. Maybe I should put running an airline down as one of my goals!