History of Mathematics: Euclid

Euclid aka. Euclid of Alexandria I believe to be so important because he is considered the “Father of Geometry.” I find Euclid interesting because we know so much because of him, yet we know very little about him. In fact, even his birth and death are estimations based off writings found from his time period.  Euclid was believed to be a student of Plato, and is most famous for his work within geometry where he wrote 13 books known as, The Elements. These books are split up into the following topics:

Books one thru six discuss plane geometry

Books seven thru nine have to do with number theory

Book ten deals with Eudoxus’s theory of irrational numbers

Books eleven thru thirteen discusses solid geometry

Euclid was said to compile these Elements from a variety of men before him such as Hippocrates of Chios and Theudius.

I am most familiar with the 5 assumptions from Book I, that Euclid called postulates or axioms.

1. Given two points there is one straight line that joins them

2. A straight line segment can be prolonged indefinitely

3. A circle can be constructed when a point for its centre and a distance for its radius are given

4. All right angles are equal

If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if

5. produced indefinitely, meet on that side on which the angles are less than the two right angles.

These to me are some of the foundations for understanding geometry, specifically Euclidean geometry.


What is Math?

When I first read the prompt, “What is Math?” I honestly had to think about what exactly that meant. I struggled to start writing. I knew math involved numbers, symbols, one-step equations, pi, Fibonacci sequences, calculus, matrices, etc. but I felt that I needed to provide a deeper response than just the surface of mathematics. When I hear math, I see my future of being a math teacher in the education field teaching students deeper conceptual understanding versus a pure procedural approach. I see math as a creator. Math has been used to create many incredible things in modern day, especially in the field of technology. Math can be/is considered a necessity for life. With out being able to do basic math as in knowing how many loaves of bread you can purchase with a ten dollar bill or the adding of fractions to double a recipe, life becomes very difficult. Not everyone has room for a calculator in their pocket (unless they have one on their phone, which was created by use of mathematics).

These are just a few of the ideas that come to mind when I hear the question, “What is Math?” But, what about where math came from? The history? This is an idea that I don’t know much about, and I look forward to learning through out the MTH 495 Capstone course. I did read a graphic novel during the semester of Fall 2013 named, “Logicomix” which was about a mathematician/logician by the name of Bertrand Russell who struggled to make sense of logic. Throughout the story it discussed names such as Euclid.

Some of the top 5 discoveries/moments in the world of mathematics in my eyes include the following:

1. The Fundamental Theorem of Calculus

2. The Pythagorean Theorem

3. Fibonacci Sequence

4. Math Specific Technology (online applets, calculators, computer programs, educational tools)

5. Pi

The five discoveries above are not in a specific order, these are just the 5 that I feel are important to mathematics and how we teach the subject. I don’t know exactly where these were first discovered or by who, but hopefully these are some of the topics we discuss throughout the course.