Maths IA on latte art!?!?

Hi, it's me again. I may not have been super helpful last time so I'll try to give you some ideas on this latte art idea.

First of all, I think you should go for it. The IAs are so much more enjoyable to do if you're interested in the idea that you're using. I did mine about baseball (which is something I am quite interested in) and it was actually one of my favorite IAs to write.

In terms of collecting data; this might be a tad difficult with the timeframe that you have to work with. I'm no expert in latte art (I've never made a latte myself) but I think that the latte art is when you pour the frothy milk into the cup with the espresso in it already (right?) and the movements and stuff make it pretty (like I said - no expert). If that is true, I guess you could try to play around with one or two of these variables that could influence the art (i.e. time spent frothing the milk, height from which the milk is poured, etc).

The collection of data/measuring might be the most difficult part. I'm not sure if you could use surface area because that would be really difficult to measure (although if you had an app or smth like that it could definitely work). Alternatively, you could go for a slightly less scientifically rigorous method (it is math, after all) and take a picture of, say, 10 latte arts that you made (with each one having the variable changed by a set amount - e.g. if you changed milk frothing time, each cup could have been frothed for 10 additional seconds) and have 2 or 3 of the people on your barista course grade each one out of 10 (without telling them the frothing time). Take the mean (math!) and then you have a large set of data where you have the independent variable (whatever you choose to change) and the dependent variable (the average grade out of 10 [or 5]). With this data, you could do Pearson's correlation coefficient and some statistical tests to determine if changing the independent variable impacts the quality of the latte art (there are lots of stat tests you can do). Just check that whatever math you do fits with the level of the course (I'm not sure if you're doing AA or AI).

I hope this helps a bit more. This is really just a simple idea because after all, it is a math IA and not science, so how you collect the data is not as important as what you do with it. Also, I just showed how you could integrate statistics with this, but if you wanted to do surface area or smth you could maybe try to fit it in with trig and geometry (not sure how, but I'm sure you could make it work). For me (as a bit more scientifically-minded) I found statistics easier because it's kind of what you do in science where you collect and analyze data. But make it your own project based on your interests. Read the criteria thoroughly to make sure that you're ticking all the boxes and you should do just fine.

Good luck