Numerical experiments on the number of lattice points in a circle:
A lattice point is any point in the plane having integer Cartesian coordinates. If C is a circle in the plane, the lattice points of C are those lattice points on the boundary or in the interior of C. If C is a circle of radius (square root of r), and if C is centered at (0,0), A(r) denotes the numb...
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Stanford, California
1961
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| Series: | Applied Mathematics and Statistics Laboratory <Stanford, Calif.>: Technical report
17 |
| Subjects: | |
| Summary: | A lattice point is any point in the plane having integer Cartesian coordinates. If C is a circle in the plane, the lattice points of C are those lattice points on the boundary or in the interior of C. If C is a circle of radius (square root of r), and if C is centered at (0,0), A(r) denotes the number of lattice points of C and E(r) denotes the difference between A(r) and one-half the circumference of C. Numerical information is considered for the functions A(r), E(r), and E(r)/(the 4th root of r). A method is devised for computing A(r) on a digital computer for all values of r which are perfect squares in the closed interval (1,4 time 10 to the 10th power). The method is then utilized in a computer program, and A(r) is evaluated. Knowing A(r), approximate evaluations of E(r) and E(r)/(the 4th root of r) are readily obtained. The results of all computations are given in tabulated form. |
| Physical Description: | 64 S. |
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| 245 | 1 | 0 | |a Numerical experiments on the number of lattice points in a circle |c by Harry Lawrence Mitchell |
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| 490 | 1 | |a Applied Mathematics and Statistics Laboratory <Stanford, Calif.>: Technical report |v 17 | |
| 520 | 3 | |a A lattice point is any point in the plane having integer Cartesian coordinates. If C is a circle in the plane, the lattice points of C are those lattice points on the boundary or in the interior of C. If C is a circle of radius (square root of r), and if C is centered at (0,0), A(r) denotes the number of lattice points of C and E(r) denotes the difference between A(r) and one-half the circumference of C. Numerical information is considered for the functions A(r), E(r), and E(r)/(the 4th root of r). A method is devised for computing A(r) on a digital computer for all values of r which are perfect squares in the closed interval (1,4 time 10 to the 10th power). The method is then utilized in a computer program, and A(r) is evaluated. Knowing A(r), approximate evaluations of E(r) and E(r)/(the 4th root of r) are readily obtained. The results of all computations are given in tabulated form. | |
| 650 | 7 | |a Algebra |2 dtict | |
| 650 | 7 | |a Computer programming |2 dtict | |
| 650 | 7 | |a Crystal lattices |2 dtict | |
| 650 | 7 | |a Geometry |2 dtict | |
| 650 | 7 | |a Number theory |2 dtict | |
| 650 | 7 | |a Numerical methods and procedures |2 dtict | |
| 830 | 0 | |a Applied Mathematics and Statistics Laboratory <Stanford, Calif.>: Technical report |v 17 |w (DE-604)BV006665053 |9 17 | |
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Record in the Search Index
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| id | DE-604.BV009931007 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:43:25Z |
| institution | BVB |
| language | English |
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| owner_facet | DE-91G DE-BY-TUM |
| physical | 64 S. |
| publishDate | 1961 |
| publishDateSearch | 1961 |
| publishDateSort | 1961 |
| record_format | marc |
| series | Applied Mathematics and Statistics Laboratory <Stanford, Calif.>: Technical report |
| series2 | Applied Mathematics and Statistics Laboratory <Stanford, Calif.>: Technical report |
| spelling | Mitchell, Harry L. Verfasser aut Numerical experiments on the number of lattice points in a circle by Harry Lawrence Mitchell Stanford, California 1961 64 S. txt rdacontent n rdamedia nc rdacarrier Applied Mathematics and Statistics Laboratory <Stanford, Calif.>: Technical report 17 A lattice point is any point in the plane having integer Cartesian coordinates. If C is a circle in the plane, the lattice points of C are those lattice points on the boundary or in the interior of C. If C is a circle of radius (square root of r), and if C is centered at (0,0), A(r) denotes the number of lattice points of C and E(r) denotes the difference between A(r) and one-half the circumference of C. Numerical information is considered for the functions A(r), E(r), and E(r)/(the 4th root of r). A method is devised for computing A(r) on a digital computer for all values of r which are perfect squares in the closed interval (1,4 time 10 to the 10th power). The method is then utilized in a computer program, and A(r) is evaluated. Knowing A(r), approximate evaluations of E(r) and E(r)/(the 4th root of r) are readily obtained. The results of all computations are given in tabulated form. Algebra dtict Computer programming dtict Crystal lattices dtict Geometry dtict Number theory dtict Numerical methods and procedures dtict Applied Mathematics and Statistics Laboratory <Stanford, Calif.>: Technical report 17 (DE-604)BV006665053 17 |
| spellingShingle | Mitchell, Harry L. Numerical experiments on the number of lattice points in a circle Applied Mathematics and Statistics Laboratory <Stanford, Calif.>: Technical report Algebra dtict Computer programming dtict Crystal lattices dtict Geometry dtict Number theory dtict Numerical methods and procedures dtict |
| title | Numerical experiments on the number of lattice points in a circle |
| title_auth | Numerical experiments on the number of lattice points in a circle |
| title_exact_search | Numerical experiments on the number of lattice points in a circle |
| title_full | Numerical experiments on the number of lattice points in a circle by Harry Lawrence Mitchell |
| title_fullStr | Numerical experiments on the number of lattice points in a circle by Harry Lawrence Mitchell |
| title_full_unstemmed | Numerical experiments on the number of lattice points in a circle by Harry Lawrence Mitchell |
| title_short | Numerical experiments on the number of lattice points in a circle |
| title_sort | numerical experiments on the number of lattice points in a circle |
| topic | Algebra dtict Computer programming dtict Crystal lattices dtict Geometry dtict Number theory dtict Numerical methods and procedures dtict |
| topic_facet | Algebra Computer programming Crystal lattices Geometry Number theory Numerical methods and procedures |
| volume_link | (DE-604)BV006665053 |
| work_keys_str_mv | AT mitchellharryl numericalexperimentsonthenumberoflatticepointsinacircle |