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Suitable topic for Maths IA?

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Is the topic of Euclidean/non-euclidean geometry and the Riemann Sphere too hard of a topic for a Maths SL IA? I was thinking of exploring that in relation to map-making, specifically, finding out how much accuracy/info is lost when map-making (i.e. turning something 3D into 2D). I also want to know if the topic is viable and capable of getting good marks. I was thinking that I could gather satellite data and compare them with various maps (some claim to be 'perfect' or 'near perfect') where I can physically measure the distances.

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Wow, that seems very interesting. It seems like a good topic and I'd say it could be an idea. I'd still suggest having a chat with your maths teacher to see what he thinks. 

I don't believe that it's too hard for SL, but it's always good if you can show something coming from the curriculum.

I also did my investigation on a subject barely part of the curriculum but added some basic second/third equation making, linking it back to the class material. I ended up getting a 7 on it.

The advantage of your subject is that it's very different (in the sense that I haven't heard of another one like it before). I personally think that standing out like that is a plus. On the other hand, the complexity shouldn't handicap you. Your work should be between 6 and 12 pages and those go by fast when you have a good topic.

In short, I'd say go for it but confirm with your teacher first.

Good luck

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12 hours ago, Martijn.S said:

Wow, that seems very interesting. It seems like a good topic and I'd say it could be an idea. I'd still suggest having a chat with your maths teacher to see what he thinks. 

I don't believe that it's too hard for SL, but it's always good if you can show something coming from the curriculum.

I also did my investigation on a subject barely part of the curriculum but added some basic second/third equation making, linking it back to the class material. I ended up getting a 7 on it.

The advantage of your subject is that it's very different (in the sense that I haven't heard of another one like it before). I personally think that standing out like that is a plus. On the other hand, the complexity shouldn't handicap you. Your work should be between 6 and 12 pages and those go by fast when you have a good topic.

In short, I'd say go for it but confirm with your teacher first.

Good luck

Thank you very much for the reply but I just received some pretty devastating news (considering I spent so much time researching this topic). Basically I emailed my teacher with a 'planning form' where I discussed my aims/the maths I will use etc... (essentially what I wrote in my first post). I also mentioned that I'd consider the fact that there are many different map projections each which use different methods and each for different purposes (e.g. the mercator projection and american polyconic...) . He replied to my email saying " My first instinct is that this seems like a pretty complicated plan. It is superficially easy to explain that a sphere can't be mapped onto a 2D surface but it is mathematically very tricky. You would need maths far above the level of the SL course for which you get no credit at all and you just run the risk of being penalised if you get any of it wrong or explain it insufficiently." Then he suggested that I should rethink my topic but if I truly wanted to stay with something related to 'travel' that I should do something that involves something like using "Dijkstra's algorithm to plan a route along major roads compared with flying directly (using Euclidean geometry first then using non-Euclidean if I were to take into account Earth's curvature". Hmph, definitely wasn't something I was pleased to hear. What is your opinion on the underlined sections of his email? (sorry for being so long-winded, I'm just quite stressed and disappointed)

edit:  Also, although it may be too much to have to explain the whole "a sphere can't be mapped onto a 2D surface", is it still a possibility to use Euclidean/non-euclidean geometry in terms of map-making? Or is that also too difficult and above the level of the SL course?

Edited by red_hypergiant

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Concerning the underlined parts, I'm sure he has a point. On the other hand, I'm not an expert in Euclidian geometry and I don't know much about the mathematical aspect of mapping a 3D object into 2D, nor the level of maths necessary.

About the "you get no credit", that's not completely true; you do get credit (if you read a sample report, you can find e.g. "exceeds curriculum" sometimes).

I asked my ex-maths teacher about the Dijkstra's algorithm, and he told me that you can apply it in SL, but proving it is complex. There is actually a chapter dedicated to that in an option of the maths HL curriculum (at least, that's what he told me). So as long as you just use it without proving it (which the IB likes), it should be okay for SL.

I'm sure you could use (non-)Euclidean geometry in some form or sense in relation to the topic of travel. In that case, it might also be worth checking out things like "the great circle" and the "rhumb line" (orthodrome/loxodrome) if you haven't yet. 

1 hour ago, red_hypergiant said:

edit:  Also, although it may be too much to have to explain the whole "a sphere can't be mapped onto a 2D surface", is it still a possibility to use Euclidean/non-euclidean geometry in terms of map-making? Or is that also too difficult and above the level of the SL course?

Honestly, the best way to know if it'll work is by trying. Try doing a draft calculation to see which equations you have to use, and if 90% are in SL, then you should be alright. It might be slightly time-consuming, but it's probably the most effective way of knowing if it works.

Good luck.

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2 hours ago, Martijn.S said:

Concerning the underlined parts, I'm sure he has a point. On the other hand, I'm not an expert in Euclidian geometry and I don't know much about the mathematical aspect of mapping a 3D object into 2D, nor the level of maths necessary.

About the "you get no credit", that's not completely true; you do get credit (if you read a sample report, you can find e.g. "exceeds curriculum" sometimes).

I asked my ex-maths teacher about the Dijkstra's algorithm, and he told me that you can apply it in SL, but proving it is complex. There is actually a chapter dedicated to that in an option of the maths HL curriculum (at least, that's what he told me). So as long as you just use it without proving it (which the IB likes), it should be okay for SL.

I'm sure you could use (non-)Euclidean geometry in some form or sense in relation to the topic of travel. In that case, it might also be worth checking out things like "the great circle" and the "rhumb line" (orthodrome/loxodrome) if you haven't yet. 

Honestly, the best way to know if it'll work is by trying. Try doing a draft calculation to see which equations you have to use, and if 90% are in SL, then you should be alright. It might be slightly time-consuming, but it's probably the most effective way of knowing if it works.

Good luck.

Sorry, I didn't completely understand the 3rd paragraph, but did you mean that the IB likes us to use it without proving or that the IB likes you to prove it (sorry if that was obvious). The only reason I'm slightly reluctant to take the idea using Dijkstra's algorithm is because I'm sure it is overused and it just doesn't seem as authentic. So I rethought my initial idea and sort of altered it.

Considering he seems okay with the use of Euclidean and non-euclidean geometry, I assume I can also apply that to map-making just the same (because I want to keep it on that topic). So what I've come up with is this:

Basically, I'm going to change my aim/idea so that it'd be something like "determining whether using a geographic coordinate system (i.e. lat long data) is more accurate than using map projections (i.e. measuring distance on google maps)". I did more research and found a website that demonstrated the formula used when finding the distance using lat/long data and there are also various websites that measure the distance on google maps (it uses the web mercator projection) so that's where I'll get my data from. But then I just realized...how is it 'maths' if I'm just stating distances found on the internet (at least the google maps one, whats the math)?? The conclusion will obviously be that the lat/long data is more accurate because it actually takes into account the curvature of Earth... However, is it a problem that I've come up with an obvious conclusion? So is there a need to mathematically prove that lat long data is more accurate than map projections? In other words, do Math IAs expect us to use math to prove our answer to the RQ or just to aid in answering the RQ (if that makes sense)?

So what are your thoughts on this alternative idea? Btw, thanks for all the advice you've given, much appreciated! 

Oh yeah, and here's the formula I mentioned...take a look if you want: http://www.movable-type.co.uk/scripts/latlong.html and here https://www.math.ksu.edu/~dbski/writings/haversine.pdf -> its the 'haversine' formula... I assume that is what you meant by 'the great circle'. Do you think that that's too much for the SL course? Gosh, right now, the only math that is somewhat included in the SL course is measuring distances! (Sorry again for this long post that has way too many questions)

Edited by red_hypergiant

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17 hours ago, red_hypergiant said:

Sorry, I didn't completely understand the 3rd paragraph, but did you mean that the IB likes us to use it without proving or that the IB likes you to prove it (sorry if that was obvious).

Sorry about the ambiguity. Yes, the IB likes it if you can prove an equation. They see it like you're thinking by yourself and are challenging the system. In short, they see it as critical thinking, which is part of the learner profile.

I don't know how overused the Dijkstra's algorithm is since I haven't heard anybody use it yet. I'm sure people do use it as a topic, but nobody in my year, nor the year before me, used that algorithm (and my teacher wasn't able to name anybody that had in the past ten years, either). Maybe it's a regional thing, but I've personally never heard/read of anybody considering using it (in SL, in any case). Then again, if you see that plenty of other people are using it in your class, it might indeed be better to avoid it.

Your online lat/long calculator is good and useful. But if you want to impress the IB, you should try demonstrating it (show how it was created). 

Furthermore, it would probably be better to use an actual map and measure from that (that's my personal opinion). It shows more personal investment and the errors are likely to be more visible (I don't know if Google has a correction system).

Next: yes it might be "simple" to just state data from the web. It's not mandatory to use maths in every part of your IA but the more, the better (you should have at least 80% of actual math). You normally need a minimum of six pages total, and you probably won't get those by just calculating distances and copying them from the internet. What might be an idea is that you try proving the math part of the Haversine formula, measuring the distances on a map, and realising the lat/long calculated distances are more accurate. If you would then be able to find some kind of simple solution to this inaccuracy (don't make it too complex, because I'm sure it can be), I'm sure that would be well-seen. 

Moreover, different map projections are used depending on the latitude region, because of their respective advantages (conformity, equidistance, equivalence) in those regions (at least that's what I learned in aviation class). Maybe you could somehow include that? (just brainstorming).

To answer your final question, yes I think it can be a good idea, but with the catches mentioned above. I personally think it would be good if you could do something with your conclusion, or somehow prove the inaccuracy of maps mathematically.

Hope it helps.

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Hmmm... To provide my own thoughts:

Honestly I'd say that your original idea of projecting from 3-D onto 2-D is potentially beyond HL (and maybe even Further HL) maths, and pretty certainly beyond SL maths. Obviously if you can understand it, it's really great, but from my own personal experience, stereographic projection (projection of a sphere onto a plane, which is what you've proposed) involves some quite convoluted algebra and concepts. The Haversine function doesn't seem too bad, but I'm not too sure if it's commensurate with the SL syllabus (I think it's probably OK, as it bears some similarity to Further HL geometry, which is almost definitely beyond SL by definition). I agree with @Martijn.S that you should attempt to provide some personal input, and just copying data makes it difficult to show personal engagement. 

Dijkstra's algorithm, on the other hand, may be far too simple if you just apply it without proof. While taught as part of one of the Maths HL options (Discrete Mathematics), it covers only about 3-4 pages in the textbook, which took just under half an hour to do IIRC. The proof would be worthwhile to look into though. While I personally think that popularity of a topic isn't really much of a concern (there's bound to be overlap, as you aren't expected to create something original), I'm fairly certain that Dijkstra's algorithm is a rare topic in IAs anyways, as it's a pretty specific topic rarely discussed in most online websites that give IA topics. 

For your question about answering the RQ, I think you should aim to use maths as much as possible to provide an answer, as the IA isn't really so much about mathematical history or concepts as it is about applying maths. 

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