ima doin mah math

ok /sci/ heres one I'd like to see you solve. I know for a fact I need to level my calculus more for this one, but right now I'm busy C grinding.

a hollow cone [dunces hat]:
    /\
   /  \     \slant height = 30cm
  /    \
 /      \
(________* <- A fly on the very rim
|____| <- radius = 10cm

Diametrically opposite the fly (opposite rim) is a patch of honey, the fly can only walk along the wall of the cone, what is the shortest possible route it can take to get to the honey?

Cone's are actually one of those nice manifolds that you can map to a region on euclidean 2-space without distorting surface area.  Think of it as the ability to fold/bend a section of paper into a desired shape.  This is useful because it means that we can just draw a straight line between our two points on the mapping and then convert that  line into the respective curve in 3-space.   The proof of this DOES require calculus, but if your willing to just accept it, the rest of the problem requires only geometry and trig.  The region you get should have the form 0<=r<=L, 0<=THETA<=A, where r,THETA are polar coordinates, L is the distance from the top of your cone to an edge, and A depends upon the pointyness of your cone (0<A<2*pi).  If you're decent at math you should be able to work out a solution from here, but it's long and messy so I'm not going to do it.

is the answer thirty?
I did some maths, but too lazy to type...

>>3 got it.  Using L=30, A=2*pi/3.  You get the start point as (0,30) and end at (pi/3,30) (polar coordinates in a 2-d mapping)  You can see this is just a side of a regular hexagon with side length 30 centered at the origin.

>>3 here
I just drew the net of the cone, did a straight line and played with simple geometry trig stuff till I got it.