Sums of distances between points of a sphere
Given N points on a unit sphere in k+1 dimensional Euclidean space, we obtain an upper bound for the sum of all the distances they determine which improves upon earlier work by K. B. Stolarsky when k is even. We use his method, but derive a variant of W. M. Schmidt's results for the discrepancy...
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| Format: | Article |
| Language: | English |
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Wiley
1982-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171282000647 |
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| _version_ | 1832550700215697408 |
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| author | Glyn Harman |
| author_facet | Glyn Harman |
| author_sort | Glyn Harman |
| collection | DOAJ |
| description | Given N points on a unit sphere in k+1 dimensional Euclidean space, we obtain an upper bound for the sum of all the distances they determine which improves upon earlier work by K. B. Stolarsky when k is even. We use his method, but derive a variant of W. M. Schmidt's results for the discrepancy of spherical caps which is more suited to the present application. |
| format | Article |
| id | doaj-art-671f6ba49a5c4955b9c19fd65bbeac72 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1982-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-671f6ba49a5c4955b9c19fd65bbeac722025-02-03T06:06:00ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251982-01-015470771410.1155/S0161171282000647Sums of distances between points of a sphereGlyn Harman0Department of Mathematics, Royal Holloway College, Surrey, Egham TW20 OEX, UKGiven N points on a unit sphere in k+1 dimensional Euclidean space, we obtain an upper bound for the sum of all the distances they determine which improves upon earlier work by K. B. Stolarsky when k is even. We use his method, but derive a variant of W. M. Schmidt's results for the discrepancy of spherical caps which is more suited to the present application.http://dx.doi.org/10.1155/S0161171282000647geometrical inequalitiesextremum problemsirregularities of distribution. |
| spellingShingle | Glyn Harman Sums of distances between points of a sphere International Journal of Mathematics and Mathematical Sciences geometrical inequalities extremum problems irregularities of distribution. |
| title | Sums of distances between points of a sphere |
| title_full | Sums of distances between points of a sphere |
| title_fullStr | Sums of distances between points of a sphere |
| title_full_unstemmed | Sums of distances between points of a sphere |
| title_short | Sums of distances between points of a sphere |
| title_sort | sums of distances between points of a sphere |
| topic | geometrical inequalities extremum problems irregularities of distribution. |
| url | http://dx.doi.org/10.1155/S0161171282000647 |
| work_keys_str_mv | AT glynharman sumsofdistancesbetweenpointsofasphere |