Jordan: Euclidean Geometry

My name is Jordan and a sub-topic of mathematics that I enjoy would be Euclidean Geometry. I like this topic because ¬†with just 5 axioms and 5 common notions, many theorems can be proved. When looking through Euclid’s first book of elements there are many postulates with proofs from these axioms and notions. While the first 4 axioms seem to be very simple and almost common sense, the 5th axiom is more complicated and has had many people try to disprove it.

For more information on Euclidean Geometry, here is a link. http://en.wikipedia.org/wiki/Euclidean_geometry

After Euclid’s time a man of the name Rene Descartes used another way of expressing the Pythagorean Theorem using algebra. Using the distance between two points he wrote the equation: $|PQ| = \sqrt{ (p-r)^2 +(q-s)^2}$ Which we commonly see written as $A^2 +B^2 = C^2$. This discovery has changed the way people all over the world find lengths of triangle sides.

 

6 thoughts on “Jordan: Euclidean Geometry

  1. kencoiteux

    Hi. Euclidean geometry is interesting but it gets so much more exciting when Euclid’s 5th Postulate is tossed out the window. Have you gotten to study this yet?

  2. Jordan Post author

    I have gotten to touch on that in a Modern Geometry class that I had taken and I agree that it can get pretty interesting.

  3. Sarah Devore

    Having taken a course here at BSU where we talked in great detail about Euclidean geometry, there is a special place in my heart for the five axioms. Have you looked a lot into the postulates that come out of the axioms? My favorite postulate involves how to construct an equilateral triangle using a compass and a straight edge. That blew my mind when I took my geometry class. A lot of his proofs are proof by construction, and I found that it helped in my initial understanding. Though, then we started breaking his rules, but having the foundation really helped.

  4. grantrosandick

    I don’t believe I’ve learned about Euclidean Geometry. Has any person actually disproved his fifth axiom? I do however know the Pythagorean Theorem very well as I’m sure most people do. Everyone knows how important this theorem is, as long as you need to find the length of a side of a triangle.

  5. Samuel Coskey

    The “parallel postulate” is the axiom that is famously known to be not provable from the others (which justifies its inclusion as an axiom rather than a theorem).

  6. Marc Garland

    I really want to look more into this now! You have sparked my interest! Maybe I should take math 211… Unless this was in 187 but I feel like I would not let this fly over my head. Cool!

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