11-17-2006, 11:34 PM | #1 |
Entmoot Secretary of the Treasury
Join Date: Feb 2003
Location: Campsite-by-Giraffe
Posts: 5,408
|
Math
Okay, I feel that we (or at any rate, I) am in dire need of a Math thread. I seem to remember there being one, but the closest I could find was a Math Problem thread, which far from encompasses the rather broad scope that discussion of math requires.
I think to start, I would like it if someone could attempt to teach me how to do a formal proof, as I have learned little in that regard from Geometry.
__________________
KI6PFA Amateur Radio Operator
|
11-18-2006, 05:19 PM | #2 |
Dread Mothy Lord and Halfwitted Apprentice Loremaster
Join Date: Dec 2002
Location: Thomas Aquinas College, Santa Paula, CA
Posts: 10,820
|
Do you mean, like in Euclid?
__________________
Crux fidelis, inter omnes arbor una nobilis. Nulla talem silva profert, fronde, flore, germine. Dulce lignum, dulce clavo, dulce pondus sustinens. 'With a melon?' - Eric Idle |
11-18-2006, 07:21 PM | #3 |
Entmoot Secretary of the Treasury
Join Date: Feb 2003
Location: Campsite-by-Giraffe
Posts: 5,408
|
Yes. Euclidean geometry. But it's proofs I need help with. The logic is there, but how does that tell you what steps to make (remember, logic is a double-edged sword: Dr. Pangloss told Candide to let someone drown because they bay they were in must have logically been created for the man to drown in).
__________________
KI6PFA Amateur Radio Operator
|
11-18-2006, 07:23 PM | #4 |
Fenway Ranger, Lord of Red Sox Nation
Join Date: Aug 2005
Location: College!
Posts: 1,976
|
Easy. In the left column, do the equations, etc. In the right column, give your reasons for doing it. I'll try to do it here, although vBulletin doesn't have columns...
1. a=x ----------------1. Given 2. a=a-----------------2. Reflexive Property 3. 2a=a+x--------------3. Addition 4. 2a-2x=a-x-----------4. Subtraction 5. 2(a-x)=(a-x)---------5. Associative Property 6. 2=1------------------6. Division I don't think I got all the names right, but you get the idea. And I challenge you to find out what's wrong with this proof! Can you give me an example problem?
__________________
Adventure...betrayal...heroism... Atharon: where heroes are born. My wife once said to me—when I'd been writing for ten or fifteen years—that I could always go back to being a nuclear engineer. And I said to her, 'Harriet, would you let someone who quit his job to go write fantasy anywhere near your nuclear reactor? I wouldn't!' (Robert Jordan) |
11-18-2006, 07:26 PM | #5 |
Entmoot Secretary of the Treasury
Join Date: Feb 2003
Location: Campsite-by-Giraffe
Posts: 5,408
|
Well, I can't, because I can't post triangles or things like that.
I will maybe later. I have to go to the star party soon.
__________________
KI6PFA Amateur Radio Operator
|
11-18-2006, 09:24 PM | #6 |
Halfelven Daughter of the Dunedain, President of Entmoot
Join Date: Jul 2005
Location: In trouble. As usual.
Posts: 4,674
|
I never was good at math. After basic Algebra, it went over my head. It just looked like numbers and letters with signs and intergers.
__________________
"Acaly und Hektor fur Presidants fur EntMut fur life!"~ inked Don't meddle in the affairs of Dragons, for you are crunchy and taste good with ketchup. "Don't be such a sour wolf" Stiles ~ Heart Monitor http://www.wattpad.com/user/IceQueenofMitera |
11-18-2006, 09:52 PM | #7 | |
Word Santa Claus
Join Date: Feb 2004
Location: Chicago, IL
Posts: 2,922
|
Quote:
That said, I never learned how to do formal proofs (alas).
__________________
Sufficient to have stood, yet free to fall. |
|
11-19-2006, 10:05 PM | #8 | ||
Entmoot Secretary of the Treasury
Join Date: Feb 2003
Location: Campsite-by-Giraffe
Posts: 5,408
|
Quote:
Quote:
__________________
KI6PFA Amateur Radio Operator
|
||
11-20-2006, 03:05 PM | #9 | |
Dread Mothy Lord and Halfwitted Apprentice Loremaster
Join Date: Dec 2002
Location: Thomas Aquinas College, Santa Paula, CA
Posts: 10,820
|
Quote:
__________________
Crux fidelis, inter omnes arbor una nobilis. Nulla talem silva profert, fronde, flore, germine. Dulce lignum, dulce clavo, dulce pondus sustinens. 'With a melon?' - Eric Idle |
|
11-22-2006, 01:47 PM | #10 | |
Fëanorophobic
Join Date: May 2004
Location: Between the pages of a book
Posts: 1,417
|
Quote:
Proof by Induction: You start with a hypothesis, say, for instance: 2n + 1 is an odd number for all integers n. To prove this: First check that it holds true for n = 1 ==> 2(1) + 1 = 3 (Odd) Then, assuming it holds true for n = n, try proving it for n = n + 1 2 (n + 1) +1 = 2n + 2 +1, but from our assumption 2n + 1 is odd so (2n +1 ) + 2 must also be add ==> proof done. So basically: 1-check your hypothesis for n=1 2- assume it holds true for n = n and then prove it for n = n + 1 Note that this method only proves the hypothesis to be true for all positive integral values of n Btw, kudos on starting a math thread It's nice to find someone else with a passion for math! |
|
11-22-2006, 09:36 PM | #11 |
Entmoot Secretary of the Treasury
Join Date: Feb 2003
Location: Campsite-by-Giraffe
Posts: 5,408
|
Thanks. It's not quite a two column proof, but it sounds good.
I love math. I want to know it, but things like proofs are hard to memorize (especially when they are not taught to you).
__________________
KI6PFA Amateur Radio Operator
|
11-26-2006, 12:31 PM | #12 | |
Fëanorophobic
Join Date: May 2004
Location: Between the pages of a book
Posts: 1,417
|
Quote:
Personally, I like number theory (that started when I tried solving the 3n+1 hypothesis posted by someone on the problems thread) and I also like Calculus and Trig. |
|
11-28-2006, 01:46 AM | #13 |
Entmoot Secretary of the Treasury
Join Date: Feb 2003
Location: Campsite-by-Giraffe
Posts: 5,408
|
Obsessed? Hardly. I need help! I can't understand proofs. They're so...illogical. I mean, why would anyone need to follow a chain of logic just to come to what is a logical conclusion anyway! It's a self-perpetuating maelstrom of logical fallacy.
__________________
KI6PFA Amateur Radio Operator
|
11-29-2006, 09:09 PM | #14 |
Entmooter
Join Date: Jan 2000
Posts: 793
|
See this as a game, starting out at the bottom using only pre-defined objects and rules that govern how these object interact and play, building up other objects and rules about them, and like this on and on as if climbing a ladder towards a more complicated 'world'.
Proofs are the process of climbing these steps from what we know to what new property we want to dig up. Even if the conclusion you want to get at seems easy to understand as if it didn't need to be proven, you nevertheless need to be sure it can be obtained from simpler statements, ie that there is indeed a ladder that goes from the basic premises up to the conclusion. You can learn to understand and create proofs by studying them closely, remembering that each step must be accounted for by earlier results. Think about Sherlock Holmes observing details and building up a case against an enemy, making sure that each step is right. If one step is wrong, then all that follows is nonsense (eg like the 'proof' above that '2=1'!) A good example to study is a proof of the Pythagorean theorem. In fact there are many of them, some easier than others, some more interesting than others; some turn quickly into algebraic manipulations, others are almost purely geometric all the way. [And I've seen at least one that uses calculus (more than two millenia after pytha's proof!), to the point of asking oneself if that proof contains a vicious circle!] Anyway, I'm not gonna teach you. Take your time, think about the necessity of each step for the particular ladder the proof is making you climb. Memorizing is not as important as understanding for this. It's not necessarily easy though, and the steps to take don't always come out of the sky: thought and sweat must be applied. But when you have to give a proof of some math statement, you can always begin by: "Ok, what do I know right now?", and from what you know proceed to what you want to prove. When you've done that, you must then make sure that "what you know" is right, and especially -- and this can be quite important -- doesn't depend on what you wanted to prove in the first place (you don't want to place yourself in a vicious circle). So, how would you begin to prove Pythagoras's theorem? Or the statement that there is an infinity of prime numbers? Or that there are no rational numbers for which the square is 2? What simpler statements can you make that could lead to these? Can you say "If I could only prove this little detail, then the rest would follow"? Little by little, pieces of the puzzle fall into place. Or not. As in writing abilities can be aided by reading around what others have written, reading proofs and understanding the motivations behind the steps can also help you, little by little, to acquire some ease at doing your own stuff. Or not. Just remember to have fun.
__________________
-= Ok, Start Dreaming Again! =- |
11-29-2006, 09:24 PM | #15 |
Fenway Ranger, Lord of Red Sox Nation
Join Date: Aug 2005
Location: College!
Posts: 1,976
|
That's a really cool way to explain it!
__________________
Adventure...betrayal...heroism... Atharon: where heroes are born. My wife once said to me—when I'd been writing for ten or fifteen years—that I could always go back to being a nuclear engineer. And I said to her, 'Harriet, would you let someone who quit his job to go write fantasy anywhere near your nuclear reactor? I wouldn't!' (Robert Jordan) |
12-03-2006, 11:14 AM | #16 |
Fëanorophobic
Join Date: May 2004
Location: Between the pages of a book
Posts: 1,417
|
I'm interested in Chaos Theory. I've done some background reading on it, but mainly in "popular science" books so I have yet to see a single equation or formula relating to it. If anyone knows about it or can direct me to a website about it I'd be grateful.
|
12-04-2006, 12:03 AM | #17 |
Entmoot Secretary of the Treasury
Join Date: Feb 2003
Location: Campsite-by-Giraffe
Posts: 5,408
|
Doesn't that have something to do with fractals?
__________________
KI6PFA Amateur Radio Operator
|
12-06-2006, 03:12 PM | #18 | |
Cyber Elf Lord
Join Date: Sep 2001
Location: Left of Rock, Right of Hard Place
Posts: 986
|
Quote:
There are many sites on Math. http://www.google.com/search?client=...=Google+Search I like personally like The Drexel Math Forum.
__________________
Sincerely, Anthony 'Many are my names in many countries,' he said. 'Mithrandir among the Elves, Tharkûn to the Drarves; Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not.' Faramir What nobler employment, or more valuable to the state, than that of the man who instructs the rising generation? Cicero (106BC-43BC) |
|
12-06-2006, 05:14 PM | #19 | |
Entmoot Attorney-General,
Equilibrating the Scales of Justice, Administrator ♎ Join Date: Jan 2003
Location: Stockholm, Sweden
Posts: 3,891
|
Chaos theory is certainly a fascinating branch of mathematics. Chaos is when you can't predict the behaviour of e.g. a mathematical function. A chaotic function is very sensitive to its initial input in that small changes in the input will result in dramatic and unpredictable differences in the output - the famous butterfly effect.
Quote:
In ecology, there's a (simplified) equation to predict the size of a biological population: next year's population = R * this year's population * (1 - this year's population) where R is the growth rate and the population is a number between 0 and 1. The equation is repeated over and over (next year's population becomes this year's population). For low values of R, the population will eventually even out at a certain number, it will reach a steady state. No matter how many times you repeat the equation, you'll get the same answer all the time. For high values of R, the equation doesn't reach a steady state. You will get different numbers for every time you repeat the equation and it won't be possible to predict the behaviour of the equation. Here's a website for you Beren. That's where I got the equation above. http://www.imho.com/grae/chaos/chaos.html
__________________
An unwritten post is a delightful universe of infinite possibilities. Set down one word, however, and it immediately becomes earthbound. Set down one sentence and it’s halfway to being just like every other bloody entry that’s ever been written. ☻ |
|
12-06-2006, 07:46 PM | #20 |
Entmoot Secretary of the Treasury
Join Date: Feb 2003
Location: Campsite-by-Giraffe
Posts: 5,408
|
Thanks. I will have to look into this one myself.
__________________
KI6PFA Amateur Radio Operator
|
|
|
Similar Threads | ||||
Thread | Thread Starter | Forum | Replies | Last Post |
"Temporary" Venting Thread II | Earniel | General Messages | 1010 | 08-04-2007 10:03 AM |
Anti-Homeschool Germany | Meriadoc Brandybuck | General Messages | 77 | 03-18-2007 10:07 AM |
"Temporary" Venting Thread | Rían | General Messages | 1008 | 03-31-2006 05:57 AM |
All-nighters and Other Academic War Stories | Nurvingiel | General Messages | 26 | 09-07-2005 12:23 AM |