Investigative Maths
My husband is mocking me for writing about maths. He says I've crossed the border into geekdom.
So one of my papers this semester (my last one before I'll be out there teaching.. yay) is entitled "Developing an Investigative Approach in Mathematics Education". It involves a lot of practical examples, which of course we then have to find the answer to.
One such example is as follows:
20 people are at a party.
There is a cake covered with icing on the top and all the sides. It measures 20cm by 20cm on the top.
You need to cut it so that everyone gets exactly the same amount of icing.
How do you cut it?
Well I thought about this for a long time and drew lots of little diagrams and used up all my brain power.
My answer? Put it in a blender.
posted by Liz, Scott and Harry @ 9:48 pm
5 Comments:
You're not a geek!! However blogging about maths isn't going to get your blog very popular. Try changing your blog to Maths in the Nude!!! Then you'll get some hits!!
From memory, all you need to do is pretend it's a circular cake, and cut it like that. So, find the middle, and make slices of 360 divided by the number of people.
Something similar - although it is stipulated that it is a square cake (oops I don't think I wrote that), so you've got the problem of the corners.
What you do is cut the cake into quarters, corner to corner. This eliminates the issue of the corner people getting more icing, as they only get one side of the corner.
Then you cut each quarter as you would a pie, into 5 equal pieces (like how you would if it was circular - what you said before) and vwa la.
So really it's the same as your solution isn't it? Except you'd need to make sure that you start the cutting at the right place (on the corner) and that each corner is cut in half.
I didn't get it til someone pointed out how to solve the corner bit.. duh..
It sounds SO obvious now! Yet I was going round in circles and was totally on the wrong track. It's funny how often it is that way ae...
Thanks for stopping by.
Or, cut it into 16 and there's bound to be some people who are gluten intolerant and can't eat any anyway...
Yeah, I got my things mixed up. For non-circular cakes, instead of dividing the 360 degrees into equal pieces, what you do is you make sure you cut the pieces so they have an equal share of the perimeter.
Cutting the corner like a pie means the pieces closer to the edges will get slightly less.
The reason using the perimeter works is because the area of a triangle is the base times the vertical height. The vertical height is always the same, so we've just gotta keep the base of the triangles all the same, which you do by dividing the cake up on the basis of perimeter.
Apparantly it's supposed to work for pentagons & hexagons & other regular shapes as well.
Ok, now I'm gonna stop being geeky.
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