rhombic | Parser and helpers around SQL | SQL Database library
kandi X-RAY | rhombic Summary
kandi X-RAY | rhombic Summary
Rhombic can parse SQL with 2 different parsers with different sets of operations applicable in each case:.
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QUESTION
I've reached a wall in publishing my paper due to the issue of two platonic solids I'm coding for their SA:V: The cube and octahedron.
Normally, when one derivates the SA:V ratio for a cube and octahedron, it will come out to 6/a and (3*sqrt(6))/a, respectively.
When you take those ratios as a ratio, you get a constant non 1:1 ratio for all size regimes so, how is my output a 1:1 relationship?
Output (click link):
Relevant code for both shapes in all instances for user request, tabulation, and graphing (ignore icosahedron code): First Instance:
...ANSWER
Answered 2021-Apr-22 at 03:12You are calculating "Surface Area to Volume Ratio of Platonic Polyhedra Against Referential Sphere for Given Diameter" [boldface added]
So before you compare the cube to the octahedron, you compare the cube to the sphere of the cube's diameter, and the octahedron to the sphere of the octahedron's diameter.
(I presume this means circumscribed spheres; I'm not going to check inscribed spheres.)
The SA/V ratio of a sphere is 6/d, where d is the diameter.
The maximum diameter of a cube of edge-length a is sqrt(3)a, so the cube/sphere ratio is (6/a)/(6/(sqrt(3)a)) = sqrt(3)
The maximum diameter of an octahedron of edge-length a is sqrt(2)a, so the octahedron/sphere ratio is (3sqrt(6)/a)/(6/(sqrt(2)a)) = sqrt(3)
So the ratio comes out to 1:1, due to the comparison to spheres.
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