2
nd
Research project
MTH 222T/331T
Linear Algebra: Plane geometry
Plane geometry is a topic that will be familiar to most people. It is the same as
what the average high school geometry class teaches. The purpose is to expose you to an
axiomatic system and also to how to write proofs. Plane geometry is really just basic
Euclidean geometry, it is only concerned with twodimensional shapes. The proofs that
we write typically follow two forms, they can be written out in the form of a paragraph,
something that I would do if I were not feeling confident in the math of a given problem.
The other way is to write lines by line in steps, stating something about the problem and
then next to it stating why it holds true. The goal of them is to logically/cleverly work
you way around a problem to prove something that while it may seem obvious, it is not
necessarily so easy to prove.
Euclid lived about 2300 years ago, constructing his proofs from what we would
probably call not very pretty vector algebra. As you are keeping all the vector algebra
straight, it often leads to much more elegant proofs along the way. We are saying that
once we prove something we can state it as a theorem. This is nice because when you
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 Fall '07
 Davis
 Linear Algebra, Algebra, Geometry, Pythagorean Theorem, Euclidean geometry, vector algebra

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