Senior Project

My idea for our senior project is a little bit odd, but I think it could be interesting. In many of the homework assignments this year, there has almost always been a puzzle of some sort on the back which relates to math, such as sudoku, chess etc. My idea is that everyone in the class, (in groups or on their own) comes up with a puzzle game based on mathematics.

I think this project could be really interesting because there could be anything from beginners mathematics all the way up until calculus, and it could teach these concepts and theories in a fun and hands-on way. I think that these puzzles could also be made out of several different materials. Some puzzles might be done on paper like sudoku, whereas others could involve entire boards and pieces such as Go.

This project might not be complex enough on its own to be considered a senior project, but I'm sure that with some work and class participation it could be turned into something really interesting. Thank you for considering my idea, I look forward to hearing feedback soon.

QQC Eleven

Quote:

"That oneness has led to intolerance and centuries of bitter, bloody battles."

Question:

Has the number one had at least some affiliation with all wars?

Comment:

When I think about it, the number one really has had some affiliation with most known wars. The belief that there is only one god or one chosen religion, that there is only one proper form of government or that there is only one way we can go: slaves or no slaves. So what I was wondering was, if the number one has created all of these problems, what would happen if we started believing that there was two or three of everything. Two main religions, two forms of government etc. Would some of our problems go away, or would more arise. While two religions might not ever get into a battle with each other because they are both "the chosen ones" then wouldn't they start attacking all of the other religions, doubling religious battles? So which is worse, the number one, or a higher number?

QQC Ten

Quote:

"Their method of defining numbers with fractions is surprisingly similar to the way in which numbers with fractions are represented using binary in computers today."

Question:

If binary is reminiscent to an abacus, could binary be taught through an abacus?

Comment:

My question is odd, (as always) but I have a reason for asking it. If binary is not only reminiscent to an abacus, but possibly derived from it, then binary could be taught not only to younger children, but older people as well. By bringing something a bit more familiar to someone that didn't grow up in the technological age, a lot of older people would be able to not only use, but understand how a computer works. Also, a lot of kids could learn how a computer functions early on. I know that this knowledge isn't critical, but I know that people have been trying to teach me binary for a long time, but I still don't understand it. If it could be simplified and explained in an older, more familiar way, then everyone could get just a little bit more educated.

QQC Nine

Quote:

“In prehistoric times, people would use their flint axes and cut grooves, so they could keep records of numbers.”

Question:

If we didn’t have actual written numbers, how were we able to count tally marks?

Comment:

I thought it was really interesting to see that a method of counting that we still used today originated in prehistoric times. What I was curious about though, was that (even though we could follow along with our fingers and toes) how were we able to count and keep track of all of the tick marks if there weren’t real numbers yet, (such as 1, 2, 3 etc.)? Did we carry slabs around with the tally marks carved into it, because that seems rather impractical, (granted, it might not have been at the time)? What I am also curious about now is how long will we use tally marks? We have been using this method of counting since early man, so will we continue using it for the rest of time, or will there be a point where we discover a more convenient way of keeping track of things? These are odd questions, but they are questions that I am genuinely curios about.

QQC Eight

Quote:

“At the university, Gauss was attracted by philology but repelled by the mathematics courses, and for a time the direction of his future was uncertain.”

Question:

Why is it that so many mathematicians don’t seem to actually like mathematics?

Comment:

I know that this is an odd question, (especially since the wording of this quote makes me wonder if “repelled by” is a good thing or a bad thing) but it made me think. In several of the readings we have done this year, there seems to be a common trend where some of the most famous mathematicians actually don’t like mathematics. This made me wonder, did the only pursue mathematics because they had natural gifts in the subject, were they forced into it, what is the common trend? I think this question could also potentially answer many questions about insanity in “geniuses”. If all of these famous mathematicians don’t actually like what they are doing, then why wouldn’t they have problems mentally? I think this is something that should be researched further because it could possibly answer many of the questions about insanity and genius.

QQC Seven

Quote:

"He averaged about 800 printed pages a year throughout his long life, and yet he almost always had something worthwhile to say and never seemed long-winded."

Question:

Was everything that he published his original work, or was some of his research a variation of someones' work?

Comment:

I found this line to be of particular interest because it reminded me of something I hear quite often. Lately, I have been hearing the line, "So many things have been created, that it is impossible to have an original thought anymore". When I read this quote, the first thing that popped into my head was that line. This got me to wondering, were all 800 or so pages a year original thoughts, or were they thoughts created by something someone else said? It is an odd question, but I believe it is an important one, because while math is about facts, in many ways it is also about creativity. Math is all about problem solving and deep thinking, and if you aren't looking at a problem from all angles, you might not find the answer you are looking for. So what I am saying, is that if we really aren't capable of having original thoughts, then eventually creativity might disappear all together. In my personal opinion, it is very difficult to be a critical thinker without creativity, because then you're outlook might become just a bit too one-sided.

QQC Six

Quote:

"This beautiful formula reveals a striking relation between the mysterious number pi and the familiar sequence of all the odd numbers."

Question:

Was phi discovered thanks to this formula?

Comment:

When I read this quote, I couldn't help but wonder if the formula discovered was the same one that helped us discover phi. I know that pi is used for unit circles and discovering the circumference of circles and spheres, but I couldn't help but wonder if Leibniz's research contributed to phi. Phi and pi follow similar properties since they are both numbers that can help us recognize patterns and "unique" shapes, so that is why I was curious about it.