Course reflection

Dear reader, 

I think that over the course of 442 I learned a lot about different cultures and arts. I still think about the knuckle counting idea of the Babylonians regularly, and talk about it with people who aren't interested. 

I also remember working on the market vendor problem, which I solved a bit like a game and less mathematically. 

Maybe because it's more recent, I remember learning about the Mayans, and how they gave personality and character to numbers. I remember being very surprised and inspired by the depictions and art which came with Mayan numbers. I hope that when I go on teaching that I continue to remember those.

I enjoyed working on the most recent art projects, both my projection drawing and the Islamic tiling. I found it quite enjoyable to do art since I often don't have the time to do it.

Of course the thing I will cherish the most is the amazing group in this course with me. We had so much fun together, and learned from Susan and Melihe about more than just math or history. I think that I will look back at the time that I spent in class with everyone very fondly.

Sun Tzu math problem

 my original approach was seeing that 1/4 + 1/3 + 1/2 = 13/12 . I decided that this approach would make sense because each person is having so much of a dish and they end up having 13/12 dishes each. Then we can solve by multiplying by 5 to get 65 dishes to 60 people. 

However I considered this problem with Shannon who first looked at the least common multiple which was 12 and that for every 12 people we would need 13 dishes. This led to the same answer, however I think that his way may have been more like the way that people had done it in the past.

I think that sometimes the story can matter as it can draw the reader into the context of the problem, but there are times when those stories can distract from the problem. The context of that story would matter in order to make a reader invested. Some readers may find some comfort in culturally important stories, but I’m unsure if it has mattered that there is a western story in a boring math problem. Like a driving problem in the US isn’t made more relatable or interesting simply by it being a trip between Washington DC and Virginia. That could be my bias though.

Major reading

 I stopped and thought about when they brought up the idea of personifying numbers with characters. What an interesting idea! How do you connect number with these characters? What does that mean?

I stopped at 5 being a funny by accident woman, what a weird way to personify a number. Who is deciding these? When?

Euclid reply

 

• Why is Euclid and Euclidean geometry still studied to this day? Why do you think this book has been so important (and incredibly popular) over centuries?
• Is there beauty in the Euclidean postulates, common notions and principles for proofs? How can we define beauty if these are considered beautiful?

I think Euclidean geometry is still studied because as we continue to learn mathematics we want to discuss the basics in a logical way. I think the idea is that people can access math from a basic way which is accessible to people with only a few basic rules.

I think that the beauty in Euclid’s postulates is the simplicity and accessibility of them. There are definitely better written ways of accessing the material, but they are the “earliest” version and allow people to enter into a world outside of their own math world. Maybe a beautiful ideal of mathematics and vision of Ancient Greece.

Assignment 1 personal reflection

  

It was a long journey of many wrong turns and cooperation. We started by looking at the different ways we could split up the circle with a triangle, but then turned to the method they were using to solve for the area using surcomscribed and inscribed squares. This allowed us to see how the different ways we could orient the triangles we wanted to use for Pythagoras. We spoke to Shannon who helped out by looking at the triangle of just one side instead of the square. From there it was obvious to me that the equations followed. 

I think that the presentation is a different story, we came into it without too much talk. Perhaps we should have discussed the roles more so that we could speak more confidently about the equations. I think I could have written on the board more clearly and maybe focused on projecting my voice. I want to focus on the performance for my next presentation as opposed to the material because I am already pretty good at math and I don’t need students to see that I am but I need to be able to convey that knowledge convincingly.

1/2(d-(sqrt d^2-c^2)) * typo

Scales problem

 I started by making the equation: a+b+c+d=40 because that would provide me with the largest value that we can make with the 4 weights. Then I decided that a<b<c<d. Then I walked down the list from the first equation.

Ex. 

a+b+c+d=40

b+c+d=39

a=1

b+c+d=38+a

a+c+d=37

b=3

Ect.

After following this for a bit I found that a=1, b=3, c = 9, and d=27.

Mathematics in Egypt (the old days)

 the image looks like people surveying land for farming or a farmers land.

Post reading the article, yes they were surveying. I am curious what they thought of sqrt(2) and other irrational number in ancient Egypt and how many they were aware of besides sqrt(2). I was surprised that they had a unit which measured sqrt(2). Very surprising. 

EDIT:

It was surprising because having an irrational number as a unit seems a bit of an odd choice, because how could you be able to understand the number you are measuring. It makes me wonder what they understood about the irrational numbers, and how much they knew about geometry. If Pythagoras drowned his student for irrational numbers like sqrt(2), but if Egyptians knew about it before Pythagoras then why did he drown his student?