The Ham
and
Sandwich
Theorem
This delicious theorem stems from the branch of mathematics
known as measure theory. The definition of this theorem can be
loosely simplified as follows. Given slices of ham, bread and cheese
placed any way you like, there exists one flat slice of a knife (a plane)
that will bisect each of the ham, bread and cheese. In other words,
you can share it with a friend so that both of you get exactly the same
amounts of all three slices. (4)
Interestingly enough,
the two-dimensional counterpart of
the above theorem is named ‘The Pancake
Theorem’.
It was also later proven in n-dimensions
by a guy named Turkey..!
Each layer in the sandwich represents
a plane
The Ugly
Duckling Theorem
The Ugly Duckling Theorem
is an argument showing that
the classification of objects
(flowers, numbers, male/female)
is not really possible
without some sort of prior
knowledge of those objects.
The name of the theorem
is from the story written
by Hans Christian Anderson
because it shows that a
duckling is just as similar to
a swan as two ducklings are
to each other. We can differentiate
them apart only if we
have some previous knowledge
(bias) about ducks and
swans(5) .
The Ugly Duckling Theorem
saw a re-emergence
recently with the extensive
study on Artificial Neural
Networks.
No Free Lunch
Theorem
The name of this theorem
originates from a phrase used
in America in the 19th century.
At that time, the American
bars lured in dinking customers
promising them a ‘freelunch’
only if they purchased a
drink from the bar.
Long story short, the
theorem has to deal with the
fact that a person cannot
get ‘something for nothing’.
There is always a cost even if it
seemed free. Again, this theorem
is widely used in optimization
particularly in the field
of Machine Learning (6).
Banana Split
Theorem
The Banana Split Theorem
belongs to the branch of mathematics
known as category theory.
This theorem can be represented
as a function in the
programming language Haskell.
The strange name derives
from the fact that this function
is written using brackets
(| |) that resemble two bananas
facing each other and another
supporting function for this
function is called the ‘split’.
Hence, their combination can
be termed a banana split! (8)
GAUGE Magazine
University of Peradeniya
Page
9