IA (HL) Portfolio Type I -- How Many Pieces

[nlitement]

EDIT: Nevermind. Dang, I just found a way of calculating the number of pieces for a D-dimensional object taking n number of cuts using just one elegant formula. It involves combinatorics.

But still not sure how to go about proving it. I just made an observation in terms of how S, X, and Y can be presented and found regularities. What next? I'm still not really sure what they want for proof...

Edited March 27, 2011 by Austin Glau

[pieee]

Does anyone knows 3D geometry software for drawing 3D cube in IB HL IA how many pieces ?

hey guys i need a little help with the general form for an 'n' dimensional object.. If someone could help it would be greatly appreciated..

Moreover, i am also having difficulty on using the spreadsheet part..can we use a GDC? if no, how do we use a GDC?? please guys help...

Thank You...

just use excel for the spreadsheet (unless the problem is that you can't open excel??) Basically, make a table with k dimensions across and n cuts down. Fill out the table with the maximum parts for each cut in each dimension. There should be a pretty obvious pattern that only requires adding - at least that's how i did it.

[procrastinator]

hey guys, I'm having trouble with the 3D object...

I have the recursive formula as P(n-1)+[0.5(n-1)^2 - 0.5(n-1)+n]

but how do i do the proof by induction?

I know that Pn is *something*= conjecture (my cubic function), but i can't figure out what that *something* is...

all help is appreciated

EDIT:

I'm finished with everything except the conclusion...any ideas on what i could say in this?

and can somebody tell me how to model the cubes for n=4, 5 using google sketchup?

Edited March 28, 2011 by procrastinator

[nlitement]

hey guys, I'm having trouble with the 3D object...

I have the recursive formula as P(n-1)+[0.5(n-1)^2 - 0.5(n-1)+n]

but how do i do the proof by induction?

I know that Pn is *something*= conjecture (my cubic function), but i can't figure out what that *something* is...

all help is appreciated

EDIT:

I'm finished with everything except the conclusion...any ideas on what i could say in this?

and can somebody tell me how to model the cubes for n=4, 5 using google sketchup?

The instruction paper states quite explicitly how you should obtain the conjecture.

EDIT: Oh, okay, so you've got the conjecture. The inductive proof should be very straightforward.

Also, there is a reason why they keep asking you to restate the equations in a certain form. You could review them in the conclusion. Hope this helps ;P

Edited March 28, 2011 by nlitement

[Chandman]

The one thing that is bothering me is that I'm not really proving anything in 4 dimensions. I'm coming up with a hypothetical recursive formula and proving that it generates the same values a fourth degree polynomial. But since i can't say for sure that it matches actual data, as i have none, am I really proving anything at all?

Edited March 29, 2011 by Chandman

[nlitement]

The one thing that is bothering me is that I'm not really proving anything in 4 dimensions. I'm coming up with a hypothetical recursive formula and proving that it generates the same values a fourth degree polynomial. But since i can't say for sure that it matches actual data, as i have none, am I really proving anything at all?

I don't think there's any way for somebody of high school level to give a rigorous proof for the whole thing. What I did was just state the patterns, try to provide some sort of an explanation, found the general formulas then proved that the general formulas fit the pattern formulas. You won't be able to view anything in 4D, hence why the paper asks "what would you expect it to be".

[afros]

So i've completed the first three tasks and i have succesfully proved all of the conjectures. How do i use a spreadsheet for obtaining a 4d projecture? I'm really not clear on that part..

[afros]

So i've completed the first three tasks and i have succesfully proved all of the conjectures. How do i use a spreadsheet for obtaining a 4d projecture? I'm really not clear on that part..

anybody...? I've put all of the values given for n=1,2,3,4,5,6... and so on in an excel spreadsheet based on the formula i recieved that i know are right, but now i'm not seeing any similarities that would allow a prediction/conjecture for 4d... Hints anyone?!

[pieee]

So i've completed the first three tasks and i have succesfully proved all of the conjectures. How do i use a spreadsheet for obtaining a 4d projecture? I'm really not clear on that part..

anybody...? I've put all of the values given for n=1,2,3,4,5,6... and so on in an excel spreadsheet based on the formula i recieved that i know are right, but now i'm not seeing any similarities that would allow a prediction/conjecture for 4d... Hints anyone?!

I put the dimensions (Sn, Rn, Pn) across and the cuts (n=1,2,3,4,5) down and then just, literally, observed. It only asks for conjectures so I followed the instructions for the previous steps by looking for a recursive rule. The recursive rule was pretty simple - requires only addition and could be found by observing the chart only. I guess there are multiple ways of finding this so you could look beyond the chart, although I don't think that's necessary. Some people used combinatorics but I haven't learned that yet... Or maybe I have, I just don't know it's called combinatorics. Anyway, after finding the recursive, go from there to solve for the explicit. I was kinda unsure of my answer at first - thought it was a little too simple, but it works. so.. good luck!

[luire]

Hey guys I'm new here...and i need help with this IA

I've basically finished everything which is great, but i'm having trouble with one small (but important) part.

I've gotten the general formula involving combinatorics, but i don't know how to explain how i came up with the idea of using combinatorics. I just came up with it for no particular reason, and tested it and it worked, so i don't know how to explain why randomly i've decided to use combinatorics...

can anyone help me with this please? any help would be much appreciated, thank you in advance!

[Guest]

Hey everyone,

is this the other portfolio for May 2011, since I just did the patterns within systems of linear equations and my teacher recommended us to do the other type 1 portfolio for may 2011 since it would help us with our mathematical thinking however he did not give us the sheet as he is not allowed to.

Would it be possible if any one of you could send a copy of the IA for me if this is the other type 1 maths portfolio for may 2011 exams.

Thanks so much in advance!

I can help you guys with other any subjects

there's a subject called math hl portfolios 2010-2012 or something like that, all the subjects are on there

[Guest]

Hi, guys, I've got a quick question, if anyone is willing to answer me...

So, I've found rules for 1D, 2D, and 3D using the differentiation method. However, I really don't see the difference between finding a rule and finding a conjecture... I mean, what is it they're asking for exactly?

[aangel42]

For the proofs, is it necessary to use combinatorics? We haven't learned them yet, so I would have to self-learn them and then do the proofs - and I'd still probably be wrong, not to mention waste loads of time. Is it necessary - like if you don't have them mentioned anywhere, is your portfolio/proof incomplete?

[ZiggyM]

For the proofs, is it necessary to use combinatorics? We haven't learned them yet, so I would have to self-learn them and then do the proofs - and I'd still probably be wrong, not to mention waste loads of time. Is it necessary - like if you don't have them mentioned anywhere, is your portfolio/proof incomplete?

I did this portfolio at the end of last year, I think I did alright at it (our school doesn't give us our marks) and I have never in my life heard of combinatorics. So unless I used them without realising, I'd say it isn't necessary. I just proved my confecture by induction, proving that my recursive rule was equal to my algebraic rule. I don't think anyone in my class used combinatorics, my way was pretty standard, atleast I hope so!!

And for the post above (I'm still figuring out how the site works) I'd say that the rule is your conjecture, but a way to think about it I suppose is that the expression you find is like your hypothesis - in this case called a conjecture. You don't call your hypothesis a rule until you have proved it, do you? I don't anyway So your conjecture and rule are the same thing, but they just mean different things? It's kind of like a guess I suppose. If that's what you're asking?

You did it using differentiation? That sounds completely different to what I did

[aangel42]

How do you get 15 parts from a cube using just 4 cuts? How do you depict it using software? I'm able to show 8 parts using 3 cuts, but don't know how to show the 15 parts using one more cut.

PLEASE HELP, I've been pulling the hair out of my head doing this for the last 2 hours - thanks in advance!

[ZiggyM]

How do you get 15 parts from a cube using just 4 cuts? How do you depict it using software? I'm able to show 8 parts using 3 cuts, but don't know how to show the 15 parts using one more cut.

PLEASE HELP, I've been pulling the hair out of my head doing this for the last 2 hours - thanks in advance!

Bear in mind I did this a while ago now.

What you have to do to get the 15cuts is to not have any at right angles to any of the others. So all of your cuts need to be on angles - so not straight through? If that makes sense. I did it using google sketchup and I made the 'cuts' by just drawing lines on the sides and making sure they all match up as when the four lines are connected they make a plane. Bear in mind that you won't be able to see all of the 15 parts, some will be on the inside of the cube.

Oh don't worry, I did that for a very long time too Spent a lot of time with silly software trying to draw pictures!

[Guest]

For the proofs, is it necessary to use combinatorics? We haven't learned them yet, so I would have to self-learn them and then do the proofs - and I'd still probably be wrong, not to mention waste loads of time. Is it necessary - like if you don't have them mentioned anywhere, is your portfolio/proof incomplete?

I did this portfolio at the end of last year, I think I did alright at it (our school doesn't give us our marks) and I have never in my life heard of combinatorics. So unless I used them without realising, I'd say it isn't necessary. I just proved my confecture by induction, proving that my recursive rule was equal to my algebraic rule. I don't think anyone in my class used combinatorics, my way was pretty standard, atleast I hope so!!

And for the post above (I'm still figuring out how the site works) I'd say that the rule is your conjecture, but a way to think about it I suppose is that the expression you find is like your hypothesis - in this case called a conjecture. You don't call your hypothesis a rule until you have proved it, do you? I don't anyway So your conjecture and rule are the same thing, but they just mean different things? It's kind of like a guess I suppose. If that's what you're asking?

You did it using differentiation? That sounds completely different to what I did

Thank you very much! I got it a while ago, because I realized I had an algebraic expression that I found using the DIFFERENCE method (my bad, I said differentiation but meant difference... It's basically the method of finite differentiation), and once I had used that I noticed a recursive rule that works for other dimensions as well, and I guess that's the conjecture, which I will now have to prove. Gah. :/

Just one question though: I was able to get the 15 parts with 4 cuts, but now I'm having trouble finding the 26 parts with 5.

And for the person who was looking for the 15 parts with 4 cuts, I had a hard time finding it but it's actually quite easy: you have to cut through all of the parts except 1. That means that you cut it in diagonal through the cube, and it makes a little piece within the cube that you won't necessarily be able to see, while one of the big parts won't be cut at all.

And someone in the other pages recommended a program (which I am recommending as well, because it works quite well) called Doorzien. It's Dutch, but you don't have to understand the language to understand the program, since it's pretty straightforward. Hope I helped!

[medic8209]

For the proofs, is it necessary to use combinatorics? We haven't learned them yet, so I would have to self-learn them and then do the proofs - and I'd still probably be wrong, not to mention waste loads of time. Is it necessary - like if you don't have them mentioned anywhere, is your portfolio/proof incomplete?

I did this portfolio at the end of last year, I think I did alright at it (our school doesn't give us our marks) and I have never in my life heard of combinatorics. So unless I used them without realising, I'd say it isn't necessary. I just proved my confecture by induction, proving that my recursive rule was equal to my algebraic rule. I don't think anyone in my class used combinatorics, my way was pretty standard, atleast I hope so!!

And for the post above (I'm still figuring out how the site works) I'd say that the rule is your conjecture, but a way to think about it I suppose is that the expression you find is like your hypothesis - in this case called a conjecture. You don't call your hypothesis a rule until you have proved it, do you? I don't anyway So your conjecture and rule are the same thing, but they just mean different things? It's kind of like a guess I suppose. If that's what you're asking?

You did it using differentiation? That sounds completely different to what I did

Thank you very much! I got it a while ago, because I realized I had an algebraic expression that I found using the DIFFERENCE method (my bad, I said differentiation but meant difference... It's basically the method of finite differentiation), and once I had used that I noticed a recursive rule that works for other dimensions as well, and I guess that's the conjecture, which I will now have to prove. Gah. :/

Just one question though: I was able to get the 15 parts with 4 cuts, but now I'm having trouble finding the 26 parts with 5.

And for the person who was looking for the 15 parts with 4 cuts, I had a hard time finding it but it's actually quite easy: you have to cut through all of the parts except 1. That means that you cut it in diagonal through the cube, and it makes a little piece within the cube that you won't necessarily be able to see, while one of the big parts won't be cut at all.

And someone in the other pages recommended a program (which I am recommending as well, because it works quite well) called Doorzien. It's Dutch, but you don't have to understand the language to understand the program, since it's pretty straightforward. Hope I helped!

Please could you help with the link to doorzien for mac as the one Im accessing is not the full version ... most buttons are duds...many thanks

[Guest]

For the proofs, is it necessary to use combinatorics? We haven't learned them yet, so I would have to self-learn them and then do the proofs - and I'd still probably be wrong, not to mention waste loads of time. Is it necessary - like if you don't have them mentioned anywhere, is your portfolio/proof incomplete?

I did this portfolio at the end of last year, I think I did alright at it (our school doesn't give us our marks) and I have never in my life heard of combinatorics. So unless I used them without realising, I'd say it isn't necessary. I just proved my confecture by induction, proving that my recursive rule was equal to my algebraic rule. I don't think anyone in my class used combinatorics, my way was pretty standard, atleast I hope so!!

And for the post above (I'm still figuring out how the site works) I'd say that the rule is your conjecture, but a way to think about it I suppose is that the expression you find is like your hypothesis - in this case called a conjecture. You don't call your hypothesis a rule until you have proved it, do you? I don't anyway So your conjecture and rule are the same thing, but they just mean different things? It's kind of like a guess I suppose. If that's what you're asking?

You did it using differentiation? That sounds completely different to what I did

Thank you very much! I got it a while ago, because I realized I had an algebraic expression that I found using the DIFFERENCE method (my bad, I said differentiation but meant difference... It's basically the method of finite differentiation), and once I had used that I noticed a recursive rule that works for other dimensions as well, and I guess that's the conjecture, which I will now have to prove. Gah. :/

Just one question though: I was able to get the 15 parts with 4 cuts, but now I'm having trouble finding the 26 parts with 5.

And for the person who was looking for the 15 parts with 4 cuts, I had a hard time finding it but it's actually quite easy: you have to cut through all of the parts except 1. That means that you cut it in diagonal through the cube, and it makes a little piece within the cube that you won't necessarily be able to see, while one of the big parts won't be cut at all.

And someone in the other pages recommended a program (which I am recommending as well, because it works quite well) called Doorzien. It's Dutch, but you don't have to understand the language to understand the program, since it's pretty straightforward. Hope I helped!

Please could you help with the link to doorzien for mac as the one Im accessing is not the full version ... most buttons are duds...many thanks

This is the link: http://www.fi.uu.nl/toepassingen/00349/toepassing_wisweb.html

Just click on Start Doorzien 4, it will open a java window linked to your browser, so if you want to quit your browser, it will also quit Doorzien. For some reason, I can't seem to make the download version work, but it's ok because the applet is pretty good anyways.

[BlancheBunny103]

Hi guys, pls help me out with this IA. Thanxx

For last part of 2D circle where they ask for the formula in the form of R = X + S

I don't really get it What is S? And is R = 0.5n^2 +0.5n + 1

Thanxx a bunch, much appreciated