Be a Supporter!

Mathematics Club

  • 27,072 Views
  • 506 Replies
New Topic Respond to this Topic
A-Carrot-By-Dr-Riot
A-Carrot-By-Dr-Riot
  • Member since: Dec. 11, 2002
  • Offline.
Forum Stats
Member
Level 12
Blank Slate
Response to Mathematics Club Apr. 4th, 2004 @ 09:29 AM Reply

At 4/1/04 05:00 PM, hyphon wrote: I've got this GCSE (that's the basic secondary education qualification, for Americans) math problem which I'm having a little trouble understanding. I never have problems with numbers, it's just the question I don't get and would appreciate help:
I've already done part A) but don't get B). As it is a "hence or otherwise" question, I'll still post part A).
By expanding both sides, or otherwise,
A) show that:
(m^2 + 1)(n^2 + 1) = (m + n)^2 + (mn - 1)^2
Simply enough (through expanding), I did this:
(mn)^2 + m^2 + n^2 + 1 = 2mn + n^2 + ((mn)^2 - mn - mn + 1)
Therefore:
(mn)^2 + m^2 + n^2 + 1 = (mn)^2 + m^2 + n^2 + 1
However:
Using this result, or otherwise,
B) write 500050 as the sum of 2 square numbers
I just don't understand how to link the two parts of the question.
Sorry if i've missed something really obvious.

I figured this out while sitting in my room lamenting about a failed relationship with my ex girlfriend, it seems all my breakthroughs come when I'm feeling like shit.

Anyways, the answer should be pretty obvious once you do a prime factorization of 500050
You get 2*5*5*10001
(2*5*5)*10001
(50)*(10001)
(49+1)*(10000+1)
(7^2+1)*(100^2+1)

Use 7 and 100 as values for m and n in the original equation
(7+100)^2 + (7*100-1)^2
107^2+699^2

There's your answer. Sorry it took a while.

A-Carrot-By-Dr-Riot
A-Carrot-By-Dr-Riot
  • Member since: Dec. 11, 2002
  • Offline.
Forum Stats
Member
Level 12
Blank Slate
Response to Mathematics Club Apr. 4th, 2004 @ 09:50 AM Reply

At 4/1/04 05:20 PM, charleswhitesaber wrote: could someone help me with factoring trinomials

If you're still looking for help on this problem, please give me some more specific information on the kind of help you need.

A-Carrot-By-Dr-Riot
A-Carrot-By-Dr-Riot
  • Member since: Dec. 11, 2002
  • Offline.
Forum Stats
Member
Level 12
Blank Slate
Response to Mathematics Club Apr. 6th, 2004 @ 07:04 AM Reply

Okay, here's a puzzle:
Farmer bob has 8 identical gold coins, and a uranium coin. The uranium coin is obviously waay heavier, but Farmer bob is suffering from radiation poisoning and really can't tell which one it is, by weight or any other indication. Farmer bob has a scale, and if two weights are placed on the scale, he can determine which side is heavier.

How many weighings does it take, and what process should he use to guarantee that he finds the uranium coin.

Grim
Grim
  • Member since: Feb. 19, 2003
  • Offline.
Forum Stats
Member
Level 07
Blank Slate
Response to Mathematics Club Apr. 6th, 2004 @ 08:15 AM Reply

At 4/6/04 07:04 AM, Dr_Arbitrary wrote: Okay, here's a puzzle:

Assume Bob knows that u238 is heavier than Au

Table A is on right of scale
Table B is on left of scale
Tray C is off to the side somewhere

A = 2 coins + B = 2 coins + C = 3 coins

If A = lower, then u238 coin is in A
take coins from A, clear B and place 1 coin from A into A and one into B
Lower tray = u238 coin
(2 measurements)

If B = lower; repeat above process with coins from B
Lower tray = u238 coin
(2 measurements)

If A=B in levelness, C must contain u238, so
Clear A and B trays
Put one coin from C into A, out one coin into B and keep one in C
If A<>B then lower tray = u238
If A=B then C = u238
(3 measurements)

Grim
Grim
  • Member since: Feb. 19, 2003
  • Offline.
Forum Stats
Member
Level 07
Blank Slate
Response to Mathematics Club Apr. 6th, 2004 @ 08:25 AM Reply

At 4/6/04 08:15 AM, River_Warden wrote: half-assed response

Sorry, last case is 4 remain in C
So must repeat final separate of contents of C up to 2 more times
(thus 3 measurements, but different description)

A1+A2 = B1+B2 (hold C1+C2+C3+C4)
C1+C2 <> C3+C4 (assume C1+C2 < C3+C4 for this demo)
C1 <> C2 (assume C1 < C2 for this demo)

Sorry for the premature release

A-Carrot-By-Dr-Riot
A-Carrot-By-Dr-Riot
  • Member since: Dec. 11, 2002
  • Offline.
Forum Stats
Member
Level 12
Blank Slate
Response to Mathematics Club Apr. 6th, 2004 @ 08:49 AM Reply

I don't want to sound like a jerk, but from the looks of it, your answer is incorrect. I think you were confused by the wording of my question, sorry about that.

Just to clarify, there are 9 coins total, 8 of them are actually gold.

BWS
BWS
  • Member since: Jun. 5, 2003
  • Offline.
Forum Stats
Member
Level 24
Blank Slate
Response to Mathematics Club Apr. 6th, 2004 @ 01:23 PM Reply

Im brilliant. I taught myself how to transform something from a region to another, with Jacobian, and I found a better way than my Professor. Im pimp dizzle.

A-Carrot-By-Dr-Riot
A-Carrot-By-Dr-Riot
  • Member since: Dec. 11, 2002
  • Offline.
Forum Stats
Member
Level 12
Blank Slate
Response to Mathematics Club Apr. 6th, 2004 @ 04:40 PM Reply

Hey everybody, I'm pretty sure I've got mathematica working for good, so if anyone has anything extremely difficult they need worked out, just let me know. Mathematica -> Power

Grim
Grim
  • Member since: Feb. 19, 2003
  • Offline.
Forum Stats
Member
Level 07
Blank Slate
Response to Mathematics Club Apr. 6th, 2004 @ 11:44 PM Reply

At 4/6/04 08:49 AM, Dr_Arbitrary wrote: something far too polite

You sir, are too kind. The fur of the ass shall be worn proudly upon my shoulders both for reading comprehension and quick trigger finger. (head hanging a little lower).

If I may try again, (same assumption that the farmer recognizes that the u238 coin will weigh more than the gold coin)

Tray on Left of Balance = A
Tray on Right of Balance = B
Tray on table beside Balance = C

First Weighing
A1+A2+A3 vs B1+B2+B3 (C1+C2+C3 set aside)

Condition 1
A = B; therefore u238 is contained within set C
Clear A and B and distribute 1 coin from C into each tray

Condition 1.1
A=B thus C is the u238 coin
Condition 1.2
A>B thus A is the u238 coin
Condition 1.3
A<B thus B is the u238 coin

Total # of Measurements for Condition 1 = 2

Condition 2
A>B
Clear tray B and C (pocket the gold) and distribute 1 coin from set A into each tray (A, B and C)

Condition 2.1
A=B thus C is the u239 coin
Condition 2.2
A>B thus A is the u238 coin
Condition 2.3
A<B thus B is the u238 coin

Total # of Measurements for Condition 2 = 2

Condition 3
A<B
Clear tray A and C (pocket the gold) and distribute 1 coin from set B into each tray (A, B and C)

Condition 3.1
A=B thus C is the u239 coin
Condition 2.2
A>B thus A is the u238 coin
Condition 2.3
A<B thus B is the u238 coin

Total # of Measurements for Condition 3 = 2

All Condition Scenarios require no less than 2 comparisons to determine the u238 coin

A-Carrot-By-Dr-Riot
A-Carrot-By-Dr-Riot
  • Member since: Dec. 11, 2002
  • Offline.
Forum Stats
Member
Level 12
Blank Slate
Response to Mathematics Club Apr. 7th, 2004 @ 12:49 AM Reply

The winner, it's you, River_Warden.

I'm a am drunk right now, so I'll leave you with another puzzle if you're up for it,
part 1, what is a general equation for the sum of consecutive integers from 1 to x.
basically, what equation will fulfill the equation, 1,3,6,10,15...

Part 2, Instead of looking up an answer, figure it out yourself and describe the techinique you used.

Part 3, try it with consecutive square numbers, or cubes

Grim
Grim
  • Member since: Feb. 19, 2003
  • Offline.
Forum Stats
Member
Level 07
Blank Slate
Response to Mathematics Club Apr. 7th, 2004 @ 01:57 AM Reply

At 4/7/04 12:49 AM, Dr_Arbitrary wrote: part 1, what is a general equation for the sum of consecutive integers from 1 to x.
basically, what equation will fulfill the equation, 1,3,6,10,15...

Part 2, Instead of looking up an answer, figure it out yourself and describe the techinique you used.

Part 3, try it with consecutive square numbers, or cubes

Part 1 - have long since forgotten the equation 8-(
Ok, lets see....

Don't know how to so sigma so I'll just write SIG

X is the maximum variable on top of SIG
I is equal to 1 (as a start, because my first thought is -Integers and +Integers are going to behave diffently unless you use ABS())

Start with 1 and add X, times the maximum number X then divide the pair (2) (the logic is breaking down here but I'll try to explain what I am thinking - may not be right)

Start with 1
If I count 1 of something (like fingers) and assign the ordinal value to each finger, then mirror to the other hand and inverse it

1 on bottom, 1 on top, the sum the pair is 2 = (x + 1)
2 x 1 =2
Divide 2 by 2 = 1

Next x is 2
If I count 2 fingers, then mirror to the other hand and inverse it

1 2 on bottom, 2 1 on top, the sum of any pair is 3 (x + 1)
3 x 2 =6
Divide 6 by 2 = 3

Say x is 3
If I count 3 fingers, then mirror to the other hand and inverse it

1 2 3 on bottom, 3 2 1 on top, the sum of any pair is 4 (x + 1)
4 x 3 =12
Divide 12 by 2 = 6

And so on so the progression is 1, 3, 6, 10, 15 etc...

I know, solve for x with fingers.....pretty lame

Anyway, back to the thought process...

If I write the Integers down in a column and match the running sum beside it like so, I see the following relationship:

Int Sum Delta

1 1
2 3 X^2 - 1(X-1)
3 6 X^2 - 1X
4 10 X^2 - 2(X-1)
5 15 X^2 - 2X
6 21 X^2 - 3(X-1)
7 28 X^2 - 3X
8 36 X^2 - 4(X-1)
9 45 X^2 - 4X
10 55 X^2 - 5(X-1)

Part 2/3 - Oooow my head hurts.

At this point, I have to take a break and actually do some work related work.

Please critique the method (madness) so far and let me know where I need to catch the train to get back on track

A-Carrot-By-Dr-Riot
A-Carrot-By-Dr-Riot
  • Member since: Dec. 11, 2002
  • Offline.
Forum Stats
Member
Level 12
Blank Slate
Response to Mathematics Club Apr. 7th, 2004 @ 03:45 AM Reply

Somehow, I'm still drunk, but I'll give you a hint, the generalized formula for the sum of x for x=1 to n =
1/2 * n * (n+1)... I think

Grim
Grim
  • Member since: Feb. 19, 2003
  • Offline.
Forum Stats
Member
Level 07
Blank Slate
Response to Mathematics Club Apr. 7th, 2004 @ 05:01 AM Reply

At 4/7/04 03:45 AM, Dr_Arbitrary wrote: Somehow, I'm still drunk, but I'll give you a hint, the generalized formula for the sum of x for x=1 to n =
1/2 * n * (n+1)... I think

Answer to part 1 - yes

Now the extrapolation back onto the finger scenario for the single instance (calculate the next number)

n = set of evens
n+1 = set of odds
1/2 is the normalization of the delta

I'll try to draw it out:

87654321
++++++++
12345678
---------------
99999999

9 * 8 = 72
(n+1) * n = 72

72 / 2 = 36
1/2 * n * (n+1)

2x Check against series => 1,3,6,10,15,21,28,...36

So the first series is on track, on to the Squares and Cubes

A-Carrot-By-Dr-Riot
A-Carrot-By-Dr-Riot
  • Member since: Dec. 11, 2002
  • Offline.
Forum Stats
Member
Level 12
Blank Slate
Response to Mathematics Club Apr. 7th, 2004 @ 11:15 AM Reply

I'm not going to comment on your math so far, mostly because I'm really tired and am in no position to critique anything.

There's really no 'correct' answer for the problem I posed, I just remember how I did it, and wondered if anyone else had a creative way of figuring it out. So far, your answer looks VERY creative.

Grim
Grim
  • Member since: Feb. 19, 2003
  • Offline.
Forum Stats
Member
Level 07
Blank Slate
Response to Mathematics Club Apr. 7th, 2004 @ 01:10 PM Reply

At 4/7/04 11:15 AM, Dr_Arbitrary wrote: I'm not going to comment on your math so far, mostly because I'm really tired and am in no position to critique anything.

There's really no 'correct' answer for the problem I posed, I just remember how I did it, and wondered if anyone else had a creative way of figuring it out. So far, your answer looks VERY creative.

You definitely have a future in politics, if you so desire. Numbers and I have never officially been friends. I score better with symbols and occasionally recognize patterns in development.
As for the rote memorization 8-P. Too tired at this point to review further but will approach fresh in the next 18-20 hours after some sleep. The second post is way out. Need to rethink it. Currently looking at a series of structured arrays of macaroni 1x2, 2x3, 3x4, 4x5 (helps with the visualization)

- side point - can't remember where I picked up the finger method but seem to recall an application where the consecutive integers didn't need to start at 1 .

I'll let ya know if I come up with something useful. General question, outside of the direct solution to the formula, is there a practical application for running series

i.e. Parabolic curves (quadratic functions) describe interaction of moving bodies under the influence of gravity

Linear equations describe an ideal vector without influence of outside forces

Derivatives describe the area under a curve - hence volume of a non-linear geometric shape

Closest thing I could come up with would be propagation of something (objects = physical volume, or something abstract such as $ = a bank balance) with uniform growth

Sorry if the posts are a little abstract. I am not currently engaged with a specific course and am approaching this as a refresher to firm up the grey matter

Ravens-Grin
Ravens-Grin
  • Member since: Jun. 3, 2003
  • Offline.
Forum Stats
Member
Level 05
Blank Slate
Response to Mathematics Club Apr. 8th, 2004 @ 10:09 PM Reply

Hey I'm pretty good at math. I'm kinda accelerated about 3 years beyond my peers, so that's not bad. I can basically answer any question up to some parts of Calculus.

AIM id: butterballlz

BWS
BWS
  • Member since: Jun. 5, 2003
  • Offline.
Forum Stats
Member
Level 24
Blank Slate
Response to Mathematics Club Apr. 11th, 2004 @ 07:19 PM Reply

At 4/8/04 10:09 PM, Ravens_Grin wrote: Hey I'm pretty good at math. I'm kinda accelerated about 3 years beyond my peers, so that's not bad. I can basically answer any question up to some parts of Calculus.

Sure, go ahead and post. If you have any questions feel free to ask because there are a few of us that can do high level math.

Which reminds me, Dr. A, do you know how to use Mathematica for Vector Fields? If so, I may ask for a few VF screen shots.

TheGrayFox
TheGrayFox
  • Member since: Apr. 19, 2003
  • Offline.
Forum Stats
Member
Level 23
Blank Slate
Response to Mathematics Club Apr. 11th, 2004 @ 07:43 PM Reply

I'm having uber trouble with my math homework... 2... +...2....=??? Oh dear God it's too hard I'm going to kill myself!! The frustration!!

BWS
BWS
  • Member since: Jun. 5, 2003
  • Offline.
Forum Stats
Member
Level 24
Blank Slate
Response to Mathematics Club Apr. 11th, 2004 @ 08:07 PM Reply

At 4/11/04 07:43 PM, TheGrayFox wrote: I'm having uber trouble with my math homework... 2... +...2....=??? Oh dear God it's too hard I'm going to kill myself!! The frustration!!

I know that youre being sarcastic, and therefore you intended to be funny, but that wasnt funny at all. Try again.

JoS
JoS
  • Member since: Aug. 11, 2003
  • Offline.
Forum Stats
Moderator
Level 04
Blank Slate
Response to Mathematics Club Apr. 11th, 2004 @ 08:42 PM Reply

Fuck I would never be able to do any of this shit. I will just stick to my social sciences. Oh God I am dreading takign economics already.


Bellum omnium contra omnes

BBS Signature
BWS
BWS
  • Member since: Jun. 5, 2003
  • Offline.
Forum Stats
Member
Level 24
Blank Slate
Response to Mathematics Club Apr. 11th, 2004 @ 08:47 PM Reply

At 4/11/04 08:42 PM, RugbyMacDaddy wrote: Fuck I would never be able to do any of this shit. I will just stick to my social sciences. Oh God I am dreading takign economics already.

Economics only uses very basic algebra for Macro and Micro 1. Once you get to higher level Econ classes youll use Calculus, but the Calculus youll use is very basic as well. Unless youre taking Econometrics, you dont need to worry about the mathematical portion of the class.

A-Carrot-By-Dr-Riot
A-Carrot-By-Dr-Riot
  • Member since: Dec. 11, 2002
  • Offline.
Forum Stats
Member
Level 12
Blank Slate
Response to Mathematics Club Apr. 11th, 2004 @ 09:47 PM Reply

At 4/11/04 07:19 PM, BWS wrote: Which reminds me, Dr. A, do you know how to use Mathematica for Vector Fields? If so, I may ask for a few VF screen shots.

I know what you're asking, although it's been a while since I had to do any vector fields. I have no clue how to get mathematica to do what you want. I really only use it as a calculator.

TheGrayFox
TheGrayFox
  • Member since: Apr. 19, 2003
  • Offline.
Forum Stats
Member
Level 23
Blank Slate
Response to Mathematics Club Apr. 11th, 2004 @ 10:04 PM Reply

At 4/11/04 08:07 PM, BWS wrote:
I know that youre being sarcastic, and therefore you intended to be funny, but that wasnt funny at all. Try again.

You didn't find that funny because you're a gay ass math nerd. You're a "Cmon let's do calculus" on a Saturday party night kind of guy, sad.

MrTrivia
MrTrivia
  • Member since: Jan. 28, 2003
  • Offline.
Forum Stats
Member
Level 55
Gamer
Response to Mathematics Club Apr. 11th, 2004 @ 10:46 PM Reply

Here's a "new math" problem:
Jimmy has 6 crayons. 4 of them are broken.
Suzie has 8 crayons. 6 of them are broken.
Who should be sadder?


Jack of all trades, Master of none
Head Scientist of NG Mafia
& proud member of Anime Club

BBS Signature
TheGrayFox
TheGrayFox
  • Member since: Apr. 19, 2003
  • Offline.
Forum Stats
Member
Level 23
Blank Slate
Response to Mathematics Club Apr. 11th, 2004 @ 10:58 PM Reply

At 4/11/04 10:46 PM, mr_trivia wrote: Here's a "new math" problem:
Jimmy has 6 crayons. 4 of them are broken.
Suzie has 8 crayons. 6 of them are broken.
Who should be sadder?

The crayons because they're broken :( Poor crayons....

I think the correct answer is... Neither because they share the same value of crayons... Or... Synagogue..

MrTrivia
MrTrivia
  • Member since: Jan. 28, 2003
  • Offline.
Forum Stats
Member
Level 55
Gamer
Response to Mathematics Club Apr. 11th, 2004 @ 11:10 PM Reply

At 4/11/04 10:58 PM, TheGrayFox wrote:
At 4/11/04 10:46 PM, mr_trivia wrote: Here's a "new math" problem:
Jimmy has 6 crayons. 4 of them are broken.
Suzie has 8 crayons. 6 of them are broken.
Who should be sadder?
The crayons because they're broken :( Poor crayons....

I think the correct answer is... Neither because they share the same value of crayons... Or... Synagogue..

That's the thing about new math: there's no wrong answer. It's supposed to build children's self-esteem and disguise the fact that they're dumbasses.


Jack of all trades, Master of none
Head Scientist of NG Mafia
& proud member of Anime Club

BBS Signature
TheGrayFox
TheGrayFox
  • Member since: Apr. 19, 2003
  • Offline.
Forum Stats
Member
Level 23
Blank Slate
Response to Mathematics Club Apr. 11th, 2004 @ 11:40 PM Reply

At 4/11/04 11:10 PM, mr_trivia wrote:
That's the thing about new math: there's no wrong answer. It's supposed to build children's self-esteem and disguise the fact that they're dumbasses.

Hahaha, exactly... When my father was studying at a European University, if you were caught using a calculator you would honestly get beat and kicked out of class for a week. Crazy :) He's amazing at math, chemistry and physics sigh would I kill to be as smart as him. He laughs at all the “New Math” he thinks it’s for morons “Color in ½ of a circle” Congratulations… You’re a moron. Nowadays… The best way to learn is in your room, by yourself.

A-Carrot-By-Dr-Riot
A-Carrot-By-Dr-Riot
  • Member since: Dec. 11, 2002
  • Offline.
Forum Stats
Member
Level 12
Blank Slate
Response to Mathematics Club Apr. 12th, 2004 @ 12:44 AM Reply

My personal recommendation is Schaums Outlines, they have tons of worked problems on most subjects. Right now I'm learning group theory.

I wonder how much money it would cost for the Department of Education to pay for an internet course that anyone could take, not for credit or anything, maybe a standardized test for that, but courses so that anyone who wants to learn algebra can learn it from the internet.

I know that the US Navy has a program that pretty much is independent of instructors to teach the fundamentals of electronics. They use a program called NIDA, it worked pretty well for me and most people really only need help with a few tricky parts.

TheGrayFox
TheGrayFox
  • Member since: Apr. 19, 2003
  • Offline.
Forum Stats
Member
Level 23
Blank Slate
Response to Mathematics Club Apr. 12th, 2004 @ 05:28 AM Reply

Another good way to teach Math.... Fear...

A-Carrot-By-Dr-Riot
A-Carrot-By-Dr-Riot
  • Member since: Dec. 11, 2002
  • Offline.
Forum Stats
Member
Level 12
Blank Slate
Response to Mathematics Club Apr. 12th, 2004 @ 06:43 AM Reply

If I ever become a high school teacher, I'll have a book with names of all the students, and a stopwatch. Every once in a while I'll point out a student and ask them a question, then turn on the stopwatch. Then, no matter how quickly they get the answer, I'll shake my head disaprovingly and jot something down in the book.