IA Type I - Lacsap's Fractions

[psylocke]

first of all please remove all your equations. if you want you can PM them to me and I'll inform you tomorrow if your equations are correct (everything). sorry I can't make it now because I'm so tired and sleepy. in the meantime check this thread http://www.ibsurviva...caps-fractions/ or just read that and if you still can't get the right general statement, PM me all those equations and I'll tell you if they're correct or not.

some sense of certainty does reassure.

hi there. i've read this entire thread and even created an account and everything just for the purpose of getting this IA done but i still can't PM you. is there some other way i can contact you besides using this thread? i really, reeeaaaally need your help omg pleaseibegyou

[dessskris]

@ Desy Glau: should I include the method using technology as a means of checking my results? Or will this be "too much"?

Also, I read your comment on the scope and limitations. Is it enough to write about negative numbers, rational, irrational, real, zero, etc? I read something about how the scope and limitations are a way for students to prove their skills or something!

include it. it's not too much as long as it's related to maths in fact you're required to validate or in a way prove your general statement and if you could do it with technology it would be really awesome

oh, there's one more limitation which I think someone has mentioned. think about the relationship between n and r. if n=5, could r be 13? etc

actually not really, the limitation is not a crazily important part of this task. all parts of the IA should be used equally efficiently by students to show their abilities.

Edited November 8, 2011 by Desy Glau

[dessskris]

Hi, sorry. I am really having trouble with the second half of the assignment. The E_n® part. I don't understand when they ask for a general statement. Do they want a formula? If so, can anyone help guide me towards how to find that formula? I know how to get the numerator but the way i get the denominator is kind of tricky. HELP!!!

yes general statement is basically a formula.

tips for finding denominator have been written all over this thread, please read the first few pages or even the whole thread.

only if you still don't get it or if you have other questions, just ask. but please post specific questions, I'm unlikely to answer questions like "how to find the denominator?" because I have answered it before.

[dessskris]

I really need help, i have no idea how to get the denominator GS. I already plotted and i got

y = 2.5x - 2.5

R² = 0.947

and

y = 2x - 1.6

R² = 0.970

but i have no idea of what to do im freaking out i have like 3 more hours to finish this project im screw pls help me!

it's supposed to be a quadratic function, not linear.

[dessskris]

Guys, I'm really clueless on how to make a general statement for the relationship between the row number and the numerator. I tried plotting and all but I don't know what to do with it.. Tips please. Thank u.

numerator? look at the pattern, what's the difference? is there any pattern in the difference? if so, what is the difference? is this a common difference? if so, what does it mean?

hint: in a linear equation, the first difference is a common difference. in a quadratic equation, the second difference is a common difference. in a cubic equation, the third difference is a common difference. in an nth polynomial, the nth difference is a common difference.

if you want to go for an easier method, just find the best regression for the graph you have plotted (use your GDC or graphing software)

[dessskris]

Does anybody know a good way to conclude your work? I don't really know how to put it...

restate all the general statements you've found, summarise any pattern, include the limitations.

[nash7]

Hey! I'm new to the site and I've been reading over the posts and I've found them to be helpful but I still cannot figure out the formula for the denominators. I figured out the whole pyramid all the way up to the 11th row by using the patterns, however. I also heard that there is a way to find it using a quadratic equation. Can I get some help please...it'd be greatly appreciated! :/

[Daniel Inchan Jung]

Is it just coincidence that "Lacsap" is "Pascal" spelt backwards, or does this have something to do with solving it?

Don't fret over it.

It's IB's way of saying that the task is similar to that of Pascal's Triangle.

For instance take:

y=x^-1

That is essentially y=1/x

which is the "reverse" of y=x^-1

Therefore Pascal^-1

is equal to 1/Pascal which is equal to Lacsap^.

And to add on to Desy's reason as to using n and r instead of x, is so that you do not add any more unnecessary confusion to the task. For instance, why do you need x when one has n, which has already been described as the row number and functions as x.

Hope that makes sense o_o

Hey! I'm new to the site and I've been reading over the posts and I've found them to be helpful but I still cannot figure out the formula for the denominators. I figured out the whole pyramid all the way up to the 11th row by using the patterns, however. I also heard that there is a way to find it using a quadratic equation. Can I get some help please...it'd be greatly appreciated! :/

If my assumption is correct, the process is similar to that of what you did for the numerator. However I'd suggest that you go to page 2, post #23 in the link provided.

Edited November 9, 2011 by Daniel Inchan Jung

[dessskris]

Hey! I'm new to the site and I've been reading over the posts and I've found them to be helpful but I still cannot figure out the formula for the denominators. I figured out the whole pyramid all the way up to the 11th row by using the patterns, however. I also heard that there is a way to find it using a quadratic equation. Can I get some help please...it'd be greatly appreciated! :/

be specific, which part do you not get? if you're that desperate, use graphical method.

[dessskris]

I've tried to look into the relationship between the Lacsap's triangle and the Pascal's triangle. however, I could not see the relationship other than the pattern in each row.

in Pascal's, the numbers in the middle are greater than numbers on the edge, whereas in Lacsap's, the numbers on the edge are greater than the numbers in the middle.

perhaps that's the best thing I could say. if anyone had noticed any significant similarities or differences between the two, please enlighten me. thank you!

[Daniel Inchan Jung]

Get a table of a and r. Then you find the GS for a in terms of r.

Get a table of b and r. Then you find the GS for b in terms of r.

Get a table of c and r. Then you find the GS for c in terms of r.

So you've got a, b and c. Put them in the general statement involving n. You will get the GS for the denominator in terms of n and r.

Desy, I'm curious as to what you meant by the quote above.

Do you mean to literally find a GS for a/b/c in terms of r and find the zero, or am I missing something here?

Edited November 10, 2011 by Daniel Inchan Jung

[dessskris]

Get a table of a and r. Then you find the GS for a in terms of r.

Get a table of b and r. Then you find the GS for b in terms of r.

Get a table of c and r. Then you find the GS for c in terms of r.

So you've got a, b and c. Put them in the general statement involving n. You will get the GS for the denominator in terms of n and r.

Desy, I'm curious as to what you meant by the quote above.

Do you mean to literally find a GS for a/b/c in terms of r and find the zero, or am I missing something here?

sorry if it wasn't clear. I mean:

tabulate the values of a and r. then, try to find an expression of a in terms of r. for example: (note that this is a totally random example)

same thing for b and c.

do you get it?

but you do need to show some working to get the formula.

once you are done, for example this is what you get: (again, note that this is a totally random example)

a=r²+1

b=1-r

c=5r

denominator=an²+bn+c

denominator=(r²+1)n² + (1-r)n + 5r

I hope that was clear enough. any question just ask.

Edited November 20, 2011 by Desy Glau

[Daniel Inchan Jung]

any question just ask.

My general statement seems to look... weird. Seems to be off quite a bit. It may be because I did something wrong with the denominators.

The GS of the denominators are quadratic right? If so there may be rounding errors involved.

Edited November 10, 2011 by Daniel Inchan Jung

[dessskris]

My general statement seems to look... weird. Seems to be off quite a bit. It may be because I did something wrong with the denominators.

The GS of the denominators are quadratic right? If so there may be rounding errors involved.

hmmm I think mine is weird too because it's quite long. why do you think yours is weird?

yes it's quadratic. the coefficients are supposed to be exact.

[Daniel Inchan Jung]

My general statement seems to look... weird. Seems to be off quite a bit. It may be because I did something wrong with the denominators.

The GS of the denominators are quadratic right? If so there may be rounding errors involved.

hmmm I think mine is weird too because it's quite long. why do you think yours is weird?

yes it's quadratic. the coefficients are supposed to be exact.

SOLVED

Edited November 10, 2011 by Daniel Inchan Jung

[mattie matic]

I followed Desy's instructions EXACTLY AS DESCRIBED from the April 11th post, and I got it !! Took about an hour of tortuous arithmetic, those fractions can be painful... but I got the general formula ! And it works! I generated the denominators for the 9th and 10th rows in just a couple seconds with just my formula. Desy, you are my hero.

I knew it would be a 2 degree polynomial, but I originally tried a relationship row by row, rather than considering all the r = 1 values, then all the r=2 positions... so I was really getting nowhere fast. But now I can see why it works the way it does. Now all I have to do is write up the stuff.

By the way, I love how there is also a relationship between the formula for the numerator and the denominator, which is way cool.

Thanks again !! I will sleep deeply tonight !

[dessskris]

I followed Desy's instructions EXACTLY AS DESCRIBED from the April 11th post, and I got it !! Took about an hour of tortuous arithmetic, those fractions can be painful... but I got the general formula ! And it works! I generated the denominators for the 9th and 10th rows in just a couple seconds with just my formula. Desy, you are my hero.

I knew it would be a 2 degree polynomial, but I originally tried a relationship row by row, rather than considering all the r = 1 values, then all the r=2 positions... so I was really getting nowhere fast. But now I can see why it works the way it does. Now all I have to do is write up the stuff.

By the way, I love how there is also a relationship between the formula for the numerator and the denominator, which is way cool.

Thanks again !! I will sleep deeply tonight !

I'm always very happy to hear that people know their way through the IA :') (and always very upset when people don't get my explanations... )

good luck with the write up!! any question regarding the structure/presentation you can also ask here

[jademan10]

I have a general question: Will i be penalised if i dont use technology too much? I ask this mainly because i can find the formulas arithmetically but most of my class is using technology. There are 3 points in the criteria awarded for use of technology, so if i only used it to plot the graphs , yet i show how i found the formulas through mathematical induction, can i still get a good mark?

Thanks!

Edited November 12, 2011 by jademan10

[dessskris]

I have a general question: Will i be penalised if i dont use technology too much? I ask this mainly because i can find the formulas arithmetically but most of my class is using technology. There are 3 points in the criteria awarded for use of technology, so if i only used it to plot the graphs , yet i show how i found the formulas through mathematical induction, can i still get a good mark?

Thanks!

maths induction? I don't think you could use maths induction for this.

no you won't get the technology marks unless you actually used it.

my suggestion would be: keep your calculation and everything, after that just plot its graph and find the best fit regression using your calculator and show it to prove/validate that your formula is correct. this way, you won't only get the technology mark, but also the quality of work mark which not everybody could get.

[barneystinsonforlife]

Get a table of a and r. Then you find the GS for a in terms of r.

Get a table of b and r. Then you find the GS for b in terms of r.

Get a table of c and r. Then you find the GS for c in terms of r.

So you've got a, b and c. Put them in the general statement involving n. You will get the GS for the denominator in terms of n and r.

Desy, I'm curious as to what you meant by the quote above.

Do you mean to literally find a GS for a/b/c in terms of r and find the zero, or am I missing something here?

sorry if it wasn't clear. I mean:

tabulate the values of a and r. then, try to find an expression of a in terms of r. for example: (note that this is a totally random example)

same thing for b and c.

do you get it?

once you are done, for example this is what you get: (again, note that this is a totally random example)

I hope that was clear enough. any question just ask.

Thank you so much for all of your help! You've really helped me get through this IA. I just have one question about the GS. I understand that it is supposed to be a quadratic, but I don't quite understand the above method. Which values do you plug into a chart for a,b,and c?