On Tue, May 28, 2013 at 4:54 PM, kirby urner <email@example.com> wrote:
> Taking a more algebraic approach, using the tools I'd > expect in a STEM class for the age of the student in the > video, I find that the best strategy for maximizing > volume is to maximize the radius and minimize the height. > > http://4dsolutions.net/ocn/python/cylinder.py
There's a large literature on just this problem on the web, so we can't saddle Dy/Dan with having made it up from scratch. The more usual constraint is to hold perimeter constant and optimize for volume. My approach below, of holding area constant, has this other solution, which has a punch line: a mile wide, inch deep, is way more substantive than a mile deep, inch wide: the lesson of the cylinder. Over-specialists, take notice.
The above link includes both constraints as options. There's no use of calculus demonstrated but there is a sense of a maximum we might compute exactly, in the perimeter case, so that might be a next stop along the way.
<< using derivative to locate a maximum >>
where << >> signifies a "hyperlink" or "segue" to a neighboring topic. Allowing for more non-linear, not-lock-step explorations of the terrain is encouraged in STEM. You'll keep coming back to the same topics from different angles and that's as it should be.
> PS: if you're a high school student reading this and your > STEM classes do not give you access to free software such > as Python, then consider writing to the governor of your > state and expressing displeasure at the backwardness of > your curriculum and the unwanted negative impact on your > future this deficiency may have. Demand to have an > interactive full featured programming language in your > curriculum, not just calculators. Don't take no for an > answer. The hardware is dirt cheap and the software is > gratis. Schools that can't supply such minimal equipment > are poorly funded and administered. You deserve better. > Have more self esteem. >