FYI -- I guess that this high school science project is no longer politically correct... http://en.wikipedia.org/wiki/Potassium_nitrate Into the 19th century, niter-beds were prepared by mixing manure with either mortar or wood ashes, common earth and organic materials such as straw to give porosity to a compost pile typically 1.5×2×5 meters in size.[9] The heap was usually under a cover from the rain, kept moist with urine, turned often to accelerate the decomposition, then finally leached with water after approximately one year, to remove the soluble calcium nitrate. Dung-heaps were a particularly common source: they contain ammonia from the decomposition of urea and other nitrogenous materials. It then undergoes bacterial oxidation (first by means of the Nitrosomonas bacteria) to produce (calcium) nitrite, and then (by means of the Spirobacter bacteria) to produce (calcium) nitrate. It is then converted to potassium nitrate by filtering through the potash of wood ashes. At 11:22 AM 5/9/2012, Charles Greathouse wrote:

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It is possible to unify these two subjects, as some fertilizers are also solid rocket fuel...

I suspect the crossover appeal is limited!

Charles Greathouse Analyst/Programmer Case Western Reserve University

On Wed, May 9, 2012 at 12:12 PM, Henry Baker <hbaker1@pipeline.com> wrote:

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It is possible to unify these two subjects, as some fertilizers are also solid rocket fuel...

At 08:08 AM 5/9/2012, Cordwell, William R wrote:

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In solid rocket motors, it can be desirable to have a roughly constant burning (surface) area. One solution is to start out with a star shaped hole down the middle; the star erodes as it burns, but the hole also gets larger. Of course, the outside surface is not burning in this case, so it doesn't directly apply to the fertilizer question, but it seems as though you could have a cylinder with an inside hole that gets larger at a similar rate as the outside surface gets smaller.

-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Warren Smith Sent: Wednesday, May 09, 2012 8:58 AM To: math-fun; David Langer; Monty McGovern; Holt, Robert Subject: [EXTERNAL] [math-fun] shapes with constant surface area

The surface of "slow release fertilizer" beads gradually erode, say at 1 centimeter per year. With a spherical bead, the resulting curve of "fertilization rate" would decline with time e.g. it would be proportional to (1-t)^2 for 0<t<1 for a 1cm-radius bead. It might be better to have beads with constant fertilization rate 1.

QUESTION: is there a shape (or set of shapes) whose surface area stays constant as they erode?

The answer in 1 and in 2 dimensions is "yes." In 3D the answer is less obvious, but I have a (presently rather messy) argument the answer also is yes.

More advanced question: you might want the rate to increase with time (as your plants grow bigger they need more)... or be some other curve... WHICH curves F(t) are achievable fertilization-rate curves?

-- Warren D. Smith