Part 1:
Regular hexagon ABCDEF is surrounded by two parabolas. One contains A,B,C,D and the other contains D,E,F,A. What is the ratio between the area of the intersection of the parabola's interiors to the area of the hexagon?
Part 2:
Regular hexagon ABCDEF is surrounded by two parabolas. One contains A,B,C,D and the other contains C,D,E,F. What is the ratio between the area of the intersection of the parabola's interiors to the area of the hexagon?
Part 3:
Regular hexagon ABCDEF is surrounded by two parabolas. One contains A,B,C,D and the other contains B,C,D,E. What is the ratio between the area of the intersection of the parabola's interiors to the area of the hexagon?
See: Summary of results
simulation vs. analytic
case samples overlap area ratio to hexagon
--------------------------------------------------
1 50000000 3.0796536 1.1853592
1 100000000 3.0790308 1.1851195
1 500000000 3.0792820 1.1852162
1 1000000000 3.0792030 1.1851858
1 2000000000 3.0791954 1.1851829
Analytic (32/27) = 1.185185185...
2 50000000 3.3678683 1.2962931
2 100000000 3.3677205 1.2962362
2 500000000 3.3679970 1.2963427
2 1000000000 3.3678796 1.2962975
2 2000000000 3.3678441 1.2962838
Analytic (35/27) = 1.296296296...
3 50000000 5.6759160 2.1846611
3 100000000 5.6774601 2.1852554
3 500000000 5.6772449 2.1851726
3 1000000000 5.6772286 2.1851663
3 2000000000 5.6773593 2.1852166
Analytic (59/27) = 2.185185185...
Edited on July 28, 2023, 9:48 pm
soln
