Name
Abstract | ||
|---|---|---|
In this paper, we prove a geometrical inequality which states that for any four points on a hemisphere with the unit radius, the largest sum of distances between the points is 4+4*sqrt(2). In our method, we have constructed a rectangular neighborhood of the local maximum point in the feasible set, which size is explicitly determined, and proved that (1): the objective function is bounded by a quadratic polynomial which takes the local maximum point as the unique critical point in the neighborhood, and (2): the rest part of the feasible set can be partitioned into a finite union of a large number of very small cubes so that on each small cube the conjecture can be verified by estimating the objective function with exact numerical computation. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.4204/EPTCS.352.4 | Automated Deduction in Geometry (ADG) |
DocType | ISSN | Citations |
Conference | EPTCS 352, 2021, pp. 27-40 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zhenbing Zeng | 1 | 0 | 2.37 |
| Jian Lu | 2 | 122 | 20.39 |
| Yaochen Xu | 3 | 0 | 1.01 |
| Yuzheng Wang | 4 | 0 | 0.68 |