Calculus Project - Requesting Advice

[Alessandro Angeletti]

Good afternoon,

I'm looking to complete a Mathematics Calculus Exploration for my course, before starting to write up my project I was hoping to find someone that could offer some advice or comments to make my project more successful.

First of all my project seems very simple at first glance however more complex once reflected upon.
My research question is: "Finding the most accurate volume of a Jelly Bean".
To complete this project I will use three different methods, the first one being braking down the shape of a Jelly Bean into straight lines and completing volumes of revolution of those lines and then sum their volume.
The second method will be forming several piece wise function of the Jelly Beans shape through polynomial regression and then completing volumes of revolution of these [however only rotating π].
The third method will be finding a single polar equation of the Jelly Beans shape and then finding its volume once more.
However this will only work under the assumption that a Jelly Bean has a smooth shape [no bumps or lumps along its surface].

Before starting to work on the project I had three questions that hopefully you guys would be able to answer.

1) What piece of graphing software is there available online to construct graphs of polar equations? [If possible free]
2) Is there a more efficient/concise way of finding the volume of a Jelly bean through the use of piece wise functions or polar equations?
3) Are there any more assumptions that I should make for this project?

Please leave any more suggestions of advice that you think would be useful.
Thank you all very in advance for your help.

 

[Lucas SV]

I think the assumption of smoothness of the jelly bean is good enough. Even lumps in the jelly beam seem to be smooth (i.e. no sharp lumps), probably because of the way they are prepared. It is probably reasonable to assume a symmetry under reflection (exchanging the two ends of the bean). It is more tricky to find the shape of a jelly bean but you can model it as a deformed ellipsoid. An ellipsoid is classified by 3 numbers, so maybe a jelly bean is classified by 4 numbers, the additional number being the deformation.

 

[jedishrfu]

You could also use the archimedean water immersion of the jelly bean to determine its volume by water displaced.

With respect to free software, you could check out freemat. Its a MATLAB clone with simple plotting capability. There are other software tools available if you search for them via google.