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Which great idea of mathematics should I study/present?

T

Turin39789

Lifer
So I need to spit out a 16- 20 page paper on a great idea of mathematics. A list of suggested topics are in the poll.

Or maybe something else off the Top 100 theorems list here. Or something else I could make an argument for and do all this work for.

I need to be able to explain the mathematics I discuss, in a paper mostly understandable by regular folk and entirely understandable by the math inclined. I need to justify why I chose my topic and why it is a great idea of mathematics. I can include some bio info on the people involved in the theorem, and the state of math at the time the work was done. Why was the problem done, historical context etc.


At this point I am at a 0 starting point for any of the topics, so I thought I would ask here and see if anyone thought one was particularly interesting.

 
Originally posted by: nkgreen
No Pythagorean Theorem?

Out of that list, I'd choose the Calculating Machines though.
Click to expand...

We're going over a book


The book covers

Hippocrates' Quadrature of the Lune (ca
440 B.C.)
Euclid's Proof of the Pythagorean Theorem (ca
300 B.C.)
Euclid and the Infinitude of Primes (ca
300 B.C.)
Archimedes' Determination of Circular Area (ca
225 B.C.)
Heron's Formula for Triangular Area (ca
A.D
75)
Cardano and the Solution of the Cubic (1545)
A Gem from Isaac Newton (Late 1660s)
The Bernoullis and the Harmonic Series (1689)
The Extraordinary Sums of Leonhard Euler (1734)
A Sampler of Euler's Number Theory (1736)
The Non-Denumerability of the Continuum (1874)
Cantor and the Transfinite Realm (1891)

And we are going to write our papers similar to a chapter of the book, so can't use any of these.
 
Originally posted by: JohnCU
study the gibbs phenomenon of square waves (ringing)
Click to expand...

John my boy! Didn't you study engineering? Why are you so down with the math lingo?

*sends team to Clemson to do a degree check*
 
Originally posted by: NSFW
Please add "does 0.999999=1" to the poll.
Click to expand...

But does 1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=1?
 
Originally posted by: oiprocs
Originally posted by: JohnCU
study the gibbs phenomenon of square waves (ringing)
Click to expand...

John my boy! Didn't you study engineering? Why are you so down with the math lingo?

*sends team to Clemson to do a degree check*
Click to expand...

I think that was on the first page when we studied fourier transforms in EE.

 
Originally posted by: oiprocs
Originally posted by: JohnCU
study the gibbs phenomenon of square waves (ringing)
Click to expand...

John my boy! Didn't you study engineering? Why are you so down with the math lingo?

*sends team to Clemson to do a degree check*
Click to expand...

i had to take 7 math classes and for 3 of those i had the best calculus teacher on campus, i :heart: math

edit: and what tuxdave said
 
Originally posted by: JohnCU
Originally posted by: oiprocs
Originally posted by: JohnCU
study the gibbs phenomenon of square waves (ringing)
Click to expand...

John my boy! Didn't you study engineering? Why are you so down with the math lingo?

*sends team to Clemson to do a degree check*
Click to expand...

i had to take 7 math classes and for 3 of those i had the best calculus teacher on campus, i :heart: math
Click to expand...

Funny, I'm in the same field yet I hate math. I refer to it as my whore; I use it when I need it, but I won't get to know it.

And OP, do the golden number. It's an interesting as hell topic. I mean, you gotta believe that whoever came up with that was stoned as hell or tripping on acid. That alone is worth 5-7 pages.
 
whoa. legitimate responses!

Too bad you are all engineers. I was leaning towards an old algebra or geometry proof, but only because that is what we have been studying so far. I figure all the engineers in the class are going to stampeded to the fourier work. Prof would prefer we all do different topics, or at least only two of us per theorem.

How to count votes fairly, de Borda & Condorcet (mathematical economics) - sounds interesting though.

 
Originally posted by: oiprocs
Funny, I'm in the same field yet I hate math. I refer to it as my whore; I use it when I need it, but I won't get to know it.

And OP, do the golden number. It's an interesting as hell topic. I mean, you gotta believe that whoever came up with that was stoned as hell or tripping on acid. That alone is worth 5-7 pages.
Click to expand...

golden number would be cool. :thumbsup:
 
I thought Green's theorem is a neat one based on what you get out but to write 16-20 pages on it would be hard to do I would imagine.

Anything where you can show a geometric proof would be neat. The Quadratic Reciprocity Theorem and its subsequent proof by Eisenstein is kinda interesting
 
Originally posted by: PieIsAwesome
Originally posted by: NSFW
Please add "does 0.999999=1" to the poll.
Click to expand...

But does 1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=1?
Click to expand...

Of course not. 1.00...1 is a terminated decimal; .99999999 is a repeating decimal. You can't possibly have an infinite number of zeroes in 1.00...1 because the end one proves it finite.
 
Originally posted by: Atomic Playboy
Originally posted by: PieIsAwesome
Originally posted by: NSFW
Please add "does 0.999999=1" to the poll.
Click to expand...

But does 1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001=1?
Click to expand...

Of course not. 1.00...1 is a terminated decimal; .99999999 is a repeating decimal. You can't possibly have an infinite number of zeroes in 1.00...1 because the end one proves it finite.
Click to expand...

Heresy.
 
You should prove that the 4th dimension does exist. Now all you'll need to do is build your flux capacitor and find a Delorean to put it in.
 
Originally posted by: oiprocs
Originally posted by: JohnCU
Originally posted by: oiprocs
Originally posted by: JohnCU
study the gibbs phenomenon of square waves (ringing)
Click to expand...

John my boy! Didn't you study engineering? Why are you so down with the math lingo?

*sends team to Clemson to do a degree check*
Click to expand...

i had to take 7 math classes and for 3 of those i had the best calculus teacher on campus, i :heart: math
Click to expand...

Funny, I'm in the same field yet I hate math. I refer to it as my whore; I use it when I need it, but I won't get to know it.

And OP, do the golden number. It's an interesting as hell topic. I mean, you gotta believe that whoever came up with that was stoned as hell or tripping on acid. That alone is worth 5-7 pages.
Click to expand...

How difficult is the math supposed to be for the paper though? The Golden Ratio seems more like something you'd find for high school math with a good student than for college level, particularly when comparing it to most of the other topics you have. There are a lot of cool things you can do to get the golden number, like sqrt(1+sqrt(1+sqrt(1+..., or 1/(1+1/(1+1/(1+... One of my favorite books has an entire chapter devoted to it. (and an entire chapter devoted to Ramanujan - I find a lot of his stuff fascinating; as well as a chapter on prime numbers - another fascinating topic.)

I think about half of the topics on your list would lead to a rather dull paper.
 
Originally posted by: DrPizza
Originally posted by: oiprocs
Originally posted by: JohnCU
Originally posted by: oiprocs
Originally posted by: JohnCU
study the gibbs phenomenon of square waves (ringing)
Click to expand...

John my boy! Didn't you study engineering? Why are you so down with the math lingo?

*sends team to Clemson to do a degree check*
Click to expand...

i had to take 7 math classes and for 3 of those i had the best calculus teacher on campus, i :heart: math
Click to expand...

Funny, I'm in the same field yet I hate math. I refer to it as my whore; I use it when I need it, but I won't get to know it.

And OP, do the golden number. It's an interesting as hell topic. I mean, you gotta believe that whoever came up with that was stoned as hell or tripping on acid. That alone is worth 5-7 pages.
Click to expand...

How difficult is the math supposed to be for the paper though? The Golden Ratio seems more like something you'd find for high school math with a good student than for college level, particularly when comparing it to most of the other topics you have. There are a lot of cool things you can do to get the golden number, like sqrt(1+sqrt(1+sqrt(1+..., or 1/(1+1/(1+1/(1+... One of my favorite books has an entire chapter devoted to it. (and an entire chapter devoted to Ramanujan - I find a lot of his stuff fascinating; as well as a chapter on prime numbers - another fascinating topic.)

I think about half of the topics on your list would lead to a rather dull paper.
Click to expand...

"...explain the mathematics you are discussing:this might be achieved by giving proofs if they are short and/or understandable" include good examples ets.

"direct a significant portion of your project towards a general university audience and articulate clearly which sections are aimed toward experts. "

document at least 7 sources.


It sounds like a major PITA to me. I'm sure I'm going to learn something nifty in the process, but still a PITA.
 
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