Linear Algebra - Plane Geometry

Linear Algebra - Plane Geometry - 2nd Research project MTH...

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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 two-dimensional 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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Linear Algebra - Plane Geometry - 2nd Research project MTH...

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