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Type I - Lacsap's Fractions


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Hey everyone, truly appreciate the help.

My question isn't relating to the derivation of the actual formula - that's easy enough. I'm curious as to what content we should include in our introduction, conclusion (immediately after the general statement is given), and scope/ limitations.

Thanks in advance for any input!

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Please. someone, help because after working continuously for 18 hrs on my portfolio I am brain dead. It's about denominator.

I have read in other post that people have found that value b is b-1. I have a problem with it. I have found 5 formula for 5 terms of denominators and I can see, that a-is constant, c is r squared but b seems to have a pattern which struggle to formulate.

Regarging b I have it -0.5 ; -1.5; -2.5; -3.5; -4.5 ( somehow in all formula it's with minus)

I can see that it's b-1 but what actually is b ??? And why in my case I have it with minus while the general formula is an²+bn+c

For example, if I want to find the denominator for row 15 term 2, a is constant, c will be 15² and what about b ? It will be something minus 1 but what ???

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Please. someone, help because after working continuously for 18 hrs on my portfolio I am brain dead. It's about denominator.

I have read in other post that people have found that value b is b-1. I have a problem with it. I have found 5 formula for 5 terms of denominators and I can see, that a-is constant, c is r squared but b seems to have a pattern which struggle to formulate.

Regarging b I have it -0.5 ; -1.5; -2.5; -3.5; -4.5 ( somehow in all formula it's with minus)

I can see that it's b-1 but what actually is b ??? And why in my case I have it with minus while the general formula is an²+bn+c

For example, if I want to find the denominator for row 15 term 2, a is constant, c will be 15² and what about b ? It will be something minus 1 but what ???

That's up to you to find out! You're almost there though, just keep trying

i am still not seeing the pattern at all.

Go back and read all the posts. If that doesn't work, write the numbers down and stare at them! You'll eventually see it... hopefully. Feel free to ask again if you have an actual question

Good luck

Edited by brofessional
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Hey everyone, truly appreciate the help.

My question isn't relating to the derivation of the actual formula - that's easy enough. I'm curious as to what content we should include in our introduction, conclusion (immediately after the general statement is given), and scope/ limitations.

Thanks in advance for any input!

Introduction: Basically you want to present all the elements of your project you are about to cover. So you present your objective which is basically unreavelling the Lacsap triangle and how you will do it. What steps wil you take in your presentation to find the general statement. How you decipeher the triangle, by finding reguarities? What will you do with this information? *hint hint --> general statements etc. You can also mention what devices you used in order to accomplish this project. Ex: type of caculator.

Conclusion: Sum up all the things you have done and all your discoveries etc. Explain why the equation you found is valid, along with the restrictions you found. You could also explain how you accomplished your work succesfully thanks to your calculator and other software.

I hope that helps a bit. :)

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Hi! First of all, thank you for all the help! Only thanks to you guys was I able to find the GS before the math class on friday and appear smarter in my teachers eyes :D

But I just have a small question. Is it enough to say that the general statement for the numerator is a quadratic function because when the quadratic function that is found through the graph is rearranged slightly, it resembles the triangular number? And that the GS for the denominator is a quadratic function because the trend in the denominators and numerators are the same. By the trend, I mean the pattern in sequence of numerators: 1, 3, 6, 10, 15 and denominators in eg. En(1): 1, 2, 4, 7, 11.

I hope that made sense :D Thank you!!

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If I understand correctly, you woud explain that the general statement for the numerator and denominator is a quadratic function because of the reguarities you found? (aka tringular numbers and the trend)

Tbh, you could explain that for the pattern you observed for both numerator and denominator but that is not enough to justify why the equations are a quadratic functions.

Hint: Dig deeepperrr, what makes a quadratic function a quadratic function? The degrees? Think about the process you took to find them, graphic calculations or through algebra....

Good luck! :lol:

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To be honest, I found it on the calculator. The quadratic function has a r^2 value of 1. But someone on the forum said that this wasn't a good enough reason, so I am kind of unsure on how to explain it.

But thank you! Im gonna try to dig deeeepperrr lol ^^ right now I'm too tired to think properly at all. Only slept like 4 hours last night...

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To be honest, I found it on the calculator. The quadratic function has a r^2 value of 1. But someone on the forum said that this wasn't a good enough reason, so I am kind of unsure on how to explain it.

But thank you! Im gonna try to dig deeeepperrr lol ^^ right now I'm too tired to think properly at all. Only slept like 4 hours last night...

As long as you...

1. Explain your process of finding the GS for both. (so yes the graph method but also your observations on the triangle) Leading to ur ultimate GS

2. Justify your equation is correct (HINT: continue the triangle...somehow... :P)

3. Cite the restrictions

But to really know if you did EVERYTHING, go over the IB evaluation sheet for this assignement. (Your teacher should've given you that upon recieving the portfolio). And make sur you did the requirements for like everything :P

I think you should be fine! (Speaking from personal experience) Hope that might help you a bit more!

yes you should definetly SLEEP. Good luck again!

Edited by funny10sport
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To be honest, I found it on the calculator. The quadratic function has a r^2 value of 1. But someone on the forum said that this wasn't a good enough reason, so I am kind of unsure on how to explain it.

But thank you! Im gonna try to dig deeeepperrr lol ^^ right now I'm too tired to think properly at all. Only slept like 4 hours last night...

As long as you...

1. Explain your process of finding the GS for both. (so yes the graph method but also your observations on the triangle) Leading to ur ultimate GS

2. Justify your equation is correct (HINT: continue the triangle...somehow... :P)

3. Cite the restrictions

But to really know if you did EVERYTHING, go over the IB evaluation sheet for this assignement. (Your teacher should've given you that upon recieving the portfolio). And make sur you did the requirements for like everything :P

I think you should be fine! (Speaking from personal experience) Hope that might help you a bit more!

yes you should definetly SLEEP. Good luck again!

Oh, thank you! That helped a lot!!

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What does Criterion A mean on the Internal assessment criteria?

It says "This criterion addresses appropriate use of mathematical symbols (for example, use of '≈' instead of '=' and proper vector notation."

Hold that thought right there: is IB saying that I must use the squiggly equals sign? I thought that sign was only used when you have an approximate value! What's the deal? Or is IB saying that you should use the squiggly equals sign instead of the regular equals sign in the appropriate contexts - e.g. 3.14 ≈ pi versus 3.14 = pi?

Edited by Prince Hamlet
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What does Criterion A mean on the Internal assessment criteria?

It says "This criterion addresses appropriate use of mathematical symbols (for example, use of '≈' instead of '=' and proper vector notation."

Hold that thought right there: is IB saying that I must use the squiggly equals sign? I thought that sign was only used when you have an approximate value! What's the deal? Or is IB saying that you should use the squiggly equals sign instead of the regular equals sign in the appropriate contexts - e.g. 3.14 ≈ pi versus 3.14 = pi?

all that means is if ur rounding use the squiggly and if you know it is exact use the normal. but there is a lot more to criterion A than using the correct equals sign. i think of it as being able to write out math in a correct understandable fashion.

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How long is everyone's IA? Mine is coming to be about 6-7 pages ... but some classmates have IAs that are 25 pages long :o?!?!

To be honest, it doesnt matter how long or short it is. What matters is the content in your portfolio. HOWEVER, considering the fact its like ONLY 6-7 pages, I say you didnt elaborate enough... Mine was 18-19 pages, which is average I think. Anyway, that was the average my teacher was expecting out of us.

Thanks. My IA is due tomorrow. Are there any things I should watch out for - any easy mistakes I can fix right now? I think I have all the math down.

COMMUNICATION, that's all I can tell you. If you got the math down, be sure to eplain everything in an approprate and profound manner. If you want to really ace this, the best suggestion I can give you is look over the IB evaluation sheet to see if you accomplished all the necessary requirements (as I stated earlier) for each criteria

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Guest revathivm555

i got the general statement for the numerator but how would u find the gs for the denominator if it is not contant....eg. the denominators in row 5 are 11 9 9 11...smbdy pls help!

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everyone is using quadratic regression but how is it known that the general statement is a quadratic? it could be working for a quadratic regression because it is just a part of a cubic or quartic or greater type of function.

Because the values increase and decrease in a parabolic fashion. Basically, it's only increasing and decreasing once no matter what row you compute it for (even based on things like noticing the patterns of how everything adds up). If it did something like decrease, then increase, then decrease again it would be cubic, etc etc.

i got the general statement for the numerator but how would u find the gs for the denominator if it is not contant....eg. the denominators in row 5 are 11 9 9 11...smbdy pls help!

Try using systems of equations. Me and a lot of my friends used it for this IA and quite a few of us got 7's haha.

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