Mathematics Thread

[KongShou]

Yeah well no one got higher so I probably am entered for it. I had about 10 mins left actually, but I kept going "yeah that looks right" while checking.

dont you have to qualify for it? Anyway gj for the high mark. Im struggling with the BMO questions. Can you do any?

 

[5BLD]

dont you have to qualify for it? Anyway gj for the high mark. Im struggling with the BMO questions. Can you do any?

Probably.
My main problem is accuracy because I tend to work too fast and have a short attention span. I've done well in the previous olympiads though due to so few questions forces me to pay attention.

 

[KongShou]

Probably.
My main problem is accuracy because I tend to work too fast and have a short attention span. I've done well in the previous olympiads though due to so few questions forces me to pay attention.

Have you done the BMO before tho? If you have then what did u get?

 

[TDM]

I got 97 in thy senior, i made lots of errors as usual, where i go "yay this is so exciting i found a 3 line method" and forgot to divide by 2 or something

Yea, I do that a lot. I got a part of a mentoring scheme question wrong because I didn't see the word camera had the letter 'a' in it twice :fp

ooh i got 100 in the senior, so close. I just qualified for BMO1. Did you get in too? I kinda ran out of time in the SMC. LOL

100 was the minimum needed for BMO1 this year.

 

[brandbest1]

So about that research paper I have to write---

My first draft of it is due next Friday. My (tentative) topic is Diophantine Equations, like the methods to solve them and some basic theory behind them. (Sorry cheesecakecuber ) Does anyone have any good sources about them that preferably cost little to no money?

Also what special equations should I cover in my paper?

 

[CheesecakeCuber]

So about that research paper I have to write---

My first draft of it is due next Friday. My (tentative) topic is Diophantine Equations, like the methods to solve them and some basic theory behind them. (Sorry cheesecakecuber ) Does anyone have any good sources about them that preferably cost little to no money?

Also what special equations should I cover in my paper?

Haha np Brandbest, almost all of maths is fun to research. Anyway, for Diophantine equations I would mention perhaps Fermat's Last Theorem, but I say this tentatively because how Andrew Wiles made his proof is very abstract to me and seems really difficult to understand. Perhaps others here can help explain if you ask? I would consult wikipedia and I believe Numberphile on youtube has a vid.

Look what I found: http://www.math.ubc.ca/~cbruni/pdfs/Techniques%20of%20Diophantine%20Equations.pdf

 

[TDM]

rofl the Kangaroo was so much easier than the Challenge. Except one question about semicircles, where I don't think they gave enough information. Could just be me missing something completely obvious, though. And that parallelogram one. I had no idea how to do it. I'm never good with geometry though. The only other one I guessed was the quadratic. I know I definitely got one easy one wrong because I missed something completely obvious (forgot to divide by something from earlier in the question). Other than that, I think I did quite well. Did anyone else here do the senior kangaroo?

 

[ChickenWrap]

Calc 1 was super easy, but Calc 2 is a bit more difficult. Out of curiosity, does anyone know how those compare to A/B calc in typical high schools? I heard it is much harder than the HS versions (I am in a weird situation where I have to take all my HS classes at a college).

 

[ChickenWrap]

I wouldn't be concerned about how difficult it is...you're taking A/B calc to pass the AP exam, right? You should be more concerned about if they are preparing you for this test.

No, I am actually taking all of my high school classes at a college so I get HS credit and college credit...graduating next semester with 2 years of college already done. I have never heard of an AP exam, what is that?

 

[brandbest1]

Haha np Brandbest, almost all of maths is fun to research. Anyway, for Diophantine equations I would mention perhaps Fermat's Last Theorem, but I say this tentatively because how Andrew Wiles made his proof is very abstract to me and seems really difficult to understand. Perhaps others here can help explain if you ask? I would consult wikipedia and I believe Numberphile on youtube has a vid.

Look what I found: http://www.math.ubc.ca/~cbruni/pdfs/Techniques%20of%20Diophantine%20Equations.pdf

I was thinking of Fermat's Last Theorem, but I don't want to delve into any collegiate mathematics here, just high school math regarding Diophantine equations.
Some ones I have in mind:
\(
ax + by = c, x^2 + y^2 = z^2, x^4 + y^4 = z^2, \text{Pell's equation}
\)

 

[vcuber13]

Have you ever heard of taxicab numbers?

 

[TheNextFeliks]

Lol. For math we were supposed to find a parabola irl and take a picture of it. Then use quad regression to find the graph/equation. Then we have to make a four slide PowerPoint. One page for title, one for picture with graph one about the contents of the picture.

I have a picture of a parabola. In front of a Barnes and Noble. So one of my slides is about Barnes and Noble. Lol.

 

[CheesecakeCuber]

I was thinking of Fermat's Last Theorem, but I don't want to delve into any collegiate mathematics here, just high school math regarding Diophantine equations.
Some ones I have in mind:
\(
ax + by = c, x^2 + y^2 = z^2, x^4 + y^4 = z^2, \text{Pell's equation}
\)

Haha, I see. Perhaps your teacher would give you extra credit? Anyway, your choices look pretty good!

Lol. For math we were supposed to find a parabola irl and take a picture of it. Then use quad regression to find the graph/equation. Then we have to make a four slide PowerPoint. One page for title, one for picture with graph one about the contents of the picture.

I have a picture of a parabola. In front of a Barnes and Noble. So one of my slides is about Barnes and Noble. Lol.

Lol, seems legit for math class. What grade are you in and what math are you taking?

 

[Ickathu]

I need help finding the solution to this:

sum k=1 -> infinity: (k^2)/(2^k)

How do I solve this (without typing it into Wolfram Alpha, because I've already done that)? I should be able to solve it without the use of Calculus, and preferably without just plugging in values for the first several terms of k and looking at what it's converging towards.

 

[CheesecakeCuber]

I need help finding the solution to this:

sum k=1 -> infinity: (k^2)/(2^k)

How do I solve this (without typing it into Wolfram Alpha, because I've already done that)? I should be able to solve it without the use of Calculus, and preferably without just plugging in values for the first several terms of k and looking at what it's converging towards.

Perhaps I'm stupid, but is the sequence starting at k=1 to infinity, of (k^2)/(2^k)? I've been beating myself up trying to solve this (even disregarding your requirements) and I want to confirm that the first few terms are: 1/2, 1, 9/8, 1, 25/32? So this is special since no common ratio, r, is present?

 

[Ninja Storm]

I need help finding the solution to this:

sum k=1 -> infinity: (k^2)/(2^k)

How do I solve this (without typing it into Wolfram Alpha, because I've already done that)? I should be able to solve it without the use of Calculus, and preferably without just plugging in values for the first several terms of k and looking at what it's converging towards.

Why would you want to solve it without calculus?

ratio testttttttttttttttttt

EDIT: Or were you looking for the sum?

 

[CheesecakeCuber]

Why would you want to solve it without calculus?

ratio testttttttttttttttttt

EDIT: Or were you looking for the sum?

I assumed he was looking for the sum. I just can't solve it now...

 

[Ickathu]

Perhaps I'm stupid, but is the sequence starting at k=1 to infinity, of (k^2)/(2^k)? I've been beating myself up trying to solve this (even disregarding your requirements) and I want to confirm that the first few terms are: 1/2, 1, 9/8, 1, 25/32? So this is special since no common ratio, r, is present?

that is correct. Start at k=1 and sum to k=infinity. Those are the first terms that I got as well.

Why would you want to solve it without calculus?

ratio testttttttttttttttttt

EDIT: Or were you looking for the sum?

Because I haven't done calc yet (just started 2 weeks ago) and it was off of a test that only uses problems that don't require calculus.

And yes, I'm looking for the sum.

 

[CheesecakeCuber]

that is correct. Start at k=1 and sum to k=infinity. Those are the first terms that I got as well.



Because I haven't done calc yet (just started 2 weeks ago) and it was off of a test that only uses problems that don't require calculus.

And yes, I'm looking for the sum.

Well, can we agree that there doesn't seem to be a common ratio because of the pattern where 1 alternates with some other number? This is where I'm stumped. I was just going to take partial sums to make another infinite series then find the limit of that series, but you said no Calc...

Edit: After dinner I will try and solve it like this, although I have a feeling that something annoying will happen.

Edit2: Ok, in desperation I consulted Wolfram and it says the sum is

Spoiler

6

but I just can't fathom how that can be. The partial sums increase and decrease and don't seem to approach any number.

 

[Ickathu]

Well, can we agree that there doesn't seem to be a common ratio because of the pattern where 1 alternates with some other number? This is where I'm stumped. I was just going to take partial sums to make another infinite series then find the limit of that series, but you said no Calc...

Edit: After dinner I will try and solve it like this, although I have a feeling that something annoying will happen.

Edit2: Ok, in desperation I consulted Wolfram and it says the sum is

Spoiler

6

but I just can't fathom how that can be. The partial sums increase and decrease and don't seem to approach any number.

It doesn't alternate between 1 and another number. There are only 2 cases where (k^2)/(2^k)=1 --> k^2=2^k --> k=2, 4. (http://www.youtube.com/watch?v=mLQNvuZH3GU). So it goes 1/2, 1, 9/8, 1, 25/32, 36/64, 49/128, ....
After the first 2 terms (1/2, 1) the terms decrease, but with no common ratio (decimal approximations: 0.5, 1, 1.125, 1, .75, .54, .36, ....)