Algebra Extra Credit Blog #3

^In dividing this cake, A marks the cut where
you think the two pieces have equal value.

B shows the division where your friend thinks

the two pieces are equal. By a new method, you'd
get the leftmost piece and your friend would get
the rightmost piece, and the two of you would
share the middle section.
-- E. Roell

Have you ever wondered what mathematicians really study? And where they develop theories? Well, you have probably never heard of this one......

An article states: "Sharing can be hard. Every kid knows that, and mathematicians do, too. So mathematicians have spent a lot of time thinking about how to make sharing easier." Now we know how they spend most of their time :) (Just kidding!) This particular article tells us how we should cut a cake in equal parts so that each one of us is happy with our piece. An old solution was known as "I cut, you choose", which implies that you decide on how to cut the cake, and the other person chooses which piece they prefer. Steven Brams of New York University does not agree with this theory and says, "...a division should be considered fair only if two people think they both got pieces of the same value." So Steven recommends that you and your friend ask someone else (an elder) to cut the cake where you want to, and then both of them would be happy!

SOURCE: http://www.sciencenewsforkids.org/articles/20061220/Note3.asp (Article)

http://www.sciencenewsforkids.org/articles/20061220/a1327_239.jpg (Image)