Comments on my IA idea?

Student42098

Hey are people allowed to comment on my HL maths IA idea? If so:
I'm planning to do it on finding the maximum possible surface area of a minimal surface: a catenoid.
https://www.youtube.com/watch?v=mziis4pbBOw
Notice how in the video (link above) the soap bubble catenoid stretches until it eventually collapses into two disks. My aim would be to find the largest possible surface area for the catenoid (or at least a value than can be increased and decreased by multiples of 10 but otherwise stay the same) before it collapses.

Reply 1

ian.slater

12

Original post by Student42098

Hey are people allowed to comment on my HL maths IA idea? If so:
I'm planning to do it on finding the maximum possible surface area of a minimal surface: a catenoid.

I'm not sure I get what you're planning to do. Could you have a go at explaining your idea a bit more fully?

Reply 2

Student42098

OP

The plan is to try to find the maximum surface area a catenoidal soap bubble can reach (this value will stay constant for any unit of area as long as the separation between the rings of the catenoid and its radius are of the corresponding unit) before it collapses. To do this I have to find the separation-diameter ratio, integrate to find the surface of revolution of any catenoid and then plug in values found using the separation diameter ratio.

Reply 3

ian.slater

12

Original post by Student42098

The plan is to try to find the maximum surface area a catenoidal soap bubble can reach (this value will stay constant for any unit of area as long as the separation between the rings of the catenoid and its radius are of the corresponding unit) before it collapses. To do this I have to find the separation-diameter ratio, integrate to find the surface of revolution of any catenoid and then plug in values found using the separation diameter ratio.

I'm struggling to get my head round this. That doesn't mean it's a bad idea .. it does mean that explaining what your project is will take some work.

I thought a bubble is created with some surface area. Surface tension evens out which forms the characteristic shape. Gradually the area reduces and eventually the surface breaks when some critical value/shape is reached. I can't immediately see what sets a maximum area. Is it just a cylinder?

As a separate concern, you may get an integral you can't handle. It may be a function that does integrate, but using techniques beyond IB, or it may not integrate at all. I think you should plan for these possibilities in advance.

Reply 4

Student42098

OP

Original post by ian.slater

I'm struggling to get my head round this. That doesn't mean it's a bad idea .. it does mean that explaining what your project is will take some work.

I thought a bubble is created with some surface area. Surface tension evens out which forms the characteristic shape. Gradually the area reduces and eventually the surface breaks when some critical value/shape is reached. I can't immediately see what sets a maximum area. Is it just a cylinder?

As a separate concern, you may get an integral you can't handle. It may be a function that does integrate, but using techniques beyond IB, or it may not integrate at all. I think you should plan for these possibilities in advance.

Firstly, I used the wrong word by saying "bubble". I meant film. The shape which im trying to find the maximum surface area of is a soap bubble film between two rings. As for the second concern, I've already made sure it will work so thats no problem. As for the first one, if say the separation-radius ratio (we use separation-radius to do this, not separation-diameter as we are taking the midpoint of the catenoid as the origin and integrating between 0,0 and x0,y0. We then just multiply that integral by two. This way we don't get a negative value which wouldn't work as surface area is a scalar value) were 1/2, then would the maximum possible surface area not be when the rings were at maximum separation and of maximum radius?

Reply 5

ian.slater

12

Original post by Student42098

Firstly, I used the wrong word by saying "bubble". I meant film. The shape which im trying to find the maximum surface area of is a soap bubble film between two rings. As for the second concern, I've already made sure it will work so thats no problem. As for the first one, if say the separation-radius ratio (we use separation-radius to do this, not separation-diameter as we are taking the midpoint of the catenoid as the origin and integrating between 0,0 and x0,y0. We then just multiply that integral by two. This way we don't get a negative value which wouldn't work as surface area is a scalar value) were 1/2, then would the maximum possible surface area not be when the rings were at maximum separation and of maximum radius?

Sorry to be slow, but I'm still trying to grasp your idea.

At first I thought you were talking about the area just before the film breaks, which I saw as being a minimum. Now you mention varying the ring size and separations. Obviously you can make a film as big as you like with big enough rings. So there must be some constraint. I'm not sure either that you get just one size of film for given ring configuration? Given that you are setting up some kind of constrained optimisation, making the constraints clear is important.

Reply 6

Student42098

OP

If im setting my ring size at a radius of two, then if separation radius ratio at which the ring breaks were 1/2 (for example) wouldntthe maximum area be where the separation is 1?

Reply 7

Rubgish

13

If I am understanding you correctly, what you want to try and do is take two identical hoops with a film between them, and by varying the distance between the hoops, find at which distance the surface area of the film is greatest.

How much initial work have you done on this? I know you've said that you've checked out the integral and that you know it will work. It'd be interesting to see what you've done with regards to this, as I think it's probably going to be significantly more complicated than you would initially think.

Comments on my IA idea?

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