Re: [math-fun] Unconditionally stable nesting coffee cups?
If I didn't care about handles, I could do the following: Take the letter M & take the surface of revolution through the vertical center axis. If the outer legs of the M are splayed out, then the M's can nest. The liquid is held in the inner "v" of the M. For a lower center of gravity, consider an M with a "U" shaped central portion. For suitable U shapes, they can nest. The result looks like many dog bowls, some of which can nest. Now weld a "logical not"-shaped handle to this dog dish. In order to nest with another of the same form, we need to rotate one so it doesn't hit the handle of the lower dish. We also need to cut a slot into the outer rim of the upper dish when the lower handle will fit. If we iterate this construct, we get dishes with handles & offset slots. Depending upon the depth of the nesting, we may need to introduce additional slots, although these additional slots don't have to be so deep, because they hit handles 1,2,3,... cups down in the stack. Depending upon the design, we can have >2 handles which double as "outriggers", or one handle + additional slots. The most symmetrical version would have 3 handles at 120-degree positions, and N cups would nest, where N depends upon the angular width of the handles. At 02:05 PM 11/3/2014, Mike Stay wrote:
You could use the usual truncated cone (bottom smaller than top) with three legs coming off the rim to give it the stability you're looking for.
On Mon, Nov 3, 2014 at 1:55 PM, Dave Dyer <ddyer@real-me.net> wrote:
How about a conventionally shaped cup with a slight outward bevel, but with 3 handles that are long enough to touch the desk, and serve as outriggers.
Or easier still, take nesting dog-dishes (see below), and weld a "C" to the _bottom_ outer rim of the dog dish. These open "C" handles wouldn't interfere with the nesting of the dog dishes at all, so long as we rotate the dishes while nesting. These handles look more like the handles on some old single-candle candleholders. At 02:22 PM 11/3/2014, Henry Baker wrote:
If I didn't care about handles, I could do the following:
Take the letter M & take the surface of revolution through the vertical center axis.
If the outer legs of the M are splayed out, then the M's can nest.
The liquid is held in the inner "v" of the M.
For a lower center of gravity, consider an M with a "U" shaped central portion.
For suitable U shapes, they can nest.
The result looks like many dog bowls, some of which can nest.
Now weld a "logical not"-shaped handle to this dog dish.
In order to nest with another of the same form, we need to rotate one so it doesn't hit the handle of the lower dish. We also need to cut a slot into the outer rim of the upper dish when the lower handle will fit.
If we iterate this construct, we get dishes with handles & offset slots. Depending upon the depth of the nesting, we may need to introduce additional slots, although these additional slots don't have to be so deep, because they hit handles 1,2,3,... cups down in the stack.
Depending upon the design, we can have >2 handles which double as "outriggers", or one handle + additional slots.
The most symmetrical version would have 3 handles at 120-degree positions, and N cups would nest, where N depends upon the angular width of the handles.
At 02:05 PM 11/3/2014, Mike Stay wrote:
You could use the usual truncated cone (bottom smaller than top) with three legs coming off the rim to give it the stability you're looking for.
On Mon, Nov 3, 2014 at 1:55 PM, Dave Dyer <ddyer@real-me.net> wrote:
How about a conventionally shaped cup with a slight outward bevel, but with 3 handles that are long enough to touch the desk, and serve as outriggers.
participants (1)
-
Henry Baker