Monday, June 30, 2014

That's All Folks

For the past 8 weeks, I have spent two days a week traveling through the history of mathematics.

Sounds...boring right? Honestly, it was anything but. I've never been one for history or facts, but learning about my area of concentration deeper, was the furthest thing from boring.

The course started with our definition of math. We needed to get an understanding of what we already knew before we could develop our thoughts.

Next, we moved onto the Greek where we learned about Thales, Pythagoras, and Euclid. We learned not only about the contributions of these mathematicians but facts about the people themselves. We researched weird facts about Pythagoras which, I never would've thought to do on my own. He was apparently suuuuper weird. Some of Thales' foundational results include:

  • A circle is bisected by any of its diameters 
  • The angles at the base of an isosceles triangle are equal
  • When two straight lines cut each other, the vertically opposite angles are equal
  • Two triangles are equal in all respects if they have two angles and one side receptively equal

After, we learned about Archimedes. His claim to fame was seeing if the King got jipped on his gold crown. Archimedes did this by simply using water displacement. He simply found the crown's volume by immersing the crown and exact measurement of pure gold in a tub filled with water to the brim. He measured the spillage and compared the volumes of spillage. If the crown was made of pure gold, the volumes would be the same...but they weren't. Thank you, Archimedes. Archimedes also has a puzzle, that was a pain to complete but a sense of accomplish came shortly after finally figuring it out. Try it here.

Then we had tessellations! Everyone's favorite. I think I'll always be excited about tessellations. Along with tessellations we learned about Al Khwarizmi, who was an Islamic mathematician who wrote on Hindu-Arabic numerals and was among the first to use zero as a place holder.

Skipping ahead, we arrive at Galileo where we learned about his though experiments and conducted one of our own. Which would be awesome to somehow use in my classroom one day. On this day we collected data using what we had, the predict what we would need, very similar to what Galileo would do.

Day 12 brought us the topic of women in mathematics. Weird, I know, but women can do math too. Here we learned about Sophie Germain and her proof. Astounding the work that this female did, even making connections with Gauss, which was another mathematician we learned about. Sophie proved that women can do math just as well as men.

We then met Georg Cantor, the Infinity Man. This man brought to light set theory. Cantor revolutionized the foundation of mathematics with set theory. Set theory is now considered so fundamental that it seems to border on the obvious but at its introduction it was controversial and revolutionary. The controversial element centered around the problem of whether infinity was a potentiality or could be achieved. You go, Georg Cantor.

Our mathematical journey ended with John Conway, who created life, one of the earliest studied and most well known examples of cellular automaton.

In 8 weeks we covered the highlights and sequence that math was explored in. This class has brought light to several topics that I may have not been able to explore in my career. It was fascinating to see to development of mathematics through contributions and discoveries. Quite interesting. It's interesting to look back to that first day, not knowing what to expect and being asked if math was discovered or invented. I won't tell my opinion, because I don't want yours to be altered but I will say that after this course, I have a better understanding as to what math actually is.

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