Further to my original post (#649, p44):
Attached, please find an Excel spreadsheet containing the calculations for my analysis. The exact numbers are given with no coarse round-off. (Please check my math.)
Here are a few additional notes:
- If the "Volume/Area" assumption is correct, then any geometric solid that can be represented by two independent parameters (e.g., cylinders, prisms, pyramids, cones) may be forced to fit. So there are myriad possibilities.
- The exceptions are single parameter shapes like spheres and cubes. You can choose the parameter to match volume or area but not both. However, once you do so, if you do get a match for the other quantity, then it's a good bet that the shape is a sphere or cube.
- The "Volume/Area" is akin to aspect ratio (in this case, it's a characteristic length), in that it says something about the general properties of the shape. For example, "8234/57" is a large ratio, but the "volume" number is small, which suggests a tall, thin object (whatever it ends up being). For my "guess", I chose a tall, slender pole (in keeping with past FIRST games). Conversely, "62326/15806" is more "massive" than the first shape, but the ratio is much smaller, suggesting a large but very shallow object (like a flat platform or a pyramid with gently sloping sides or a very squat cone).
- As people have rightly pointed out, the drawing I posted is pure speculation. There is not enough information to specify the exact shapes. However, if you ask yourself, "What Would FIRST Do?", then certain shapes (balls, platform, poles) seem to be more likely than others (e.g., 9' tall cones with a narrow base).
- The most "tantalizing" match concerns the number "1963". If we assume it is a circular area, then the corresponding diameter is "49.99" units --- extremely close to "50". To me, this appears to be more than a coincidence. It strongly suggests something round or spherical with a diameter of 50 cm or perhaps 50 inches (rejecting something measured in mm as too small for FRC).
- The most "irritating" object is Shape 2 ("61126/1963"). It is almost an exact match for a 50-unit sphere --- almost! In fact, it is off by 4%. You can get an exact match if you assume a prolate spheriod (i.e., a squashed sphere) with major and minor diameters of 50 and 48.3, respectively. (Could this be a slightly saggy "yoga ball"???) You can also get an exact match if you assume a perfect 50-unit sphere with a small bite, flat or hole taken out of it (for hooking onto a pole, perhaps???).
Anyway, I hope this helps.
Attached is a drawing of a torus that matches Shape 1 (major diameter = 45.98 units, with an outside diameter almost exactly equal to a sphere that matches Shape 2).