Pythagorean triangles of equal areas
The main intent in this paper is to find triples of Rational Pythagorean Triangles (abbr. RPT) having equal areas. A new method of solving a2+ab+b2=c2 is to set a=y−1, b=y+1, y∈N−{0,1} and get Pell's equation c2−3y2=1. To solve a2−ab−b2=c2, we set a=12(y+1), b=y−1, y≥2, y∈N and get a correspond...
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| Format: | Article |
| Language: | English |
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Wiley
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171288000948 |
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| _version_ | 1849413152501923840 |
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| author | Malvina Baica |
| author_facet | Malvina Baica |
| author_sort | Malvina Baica |
| collection | DOAJ |
| description | The main intent in this paper is to find triples of Rational Pythagorean Triangles (abbr. RPT) having equal areas. A new method of solving a2+ab+b2=c2 is to set a=y−1, b=y+1, y∈N−{0,1} and get Pell's equation c2−3y2=1. To solve a2−ab−b2=c2, we set a=12(y+1), b=y−1, y≥2, y∈N and get a corresponding Pell's equation. The infinite number of solutions in Pell's equation gives rise to an infinity of solutions to a2±ab+b2=c2. From this fact the following theorems are proved. |
| format | Article |
| id | doaj-art-5c4b7bafd68f4240b3e2143b22a1ae75 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1988-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-5c4b7bafd68f4240b3e2143b22a1ae752025-08-20T03:34:13ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251988-01-0111476978010.1155/S0161171288000948Pythagorean triangles of equal areasMalvina Baica0Department of Mathematics and Computer Science, The University of Wisconsin, Whitewater 53190, Wisconsin , USAThe main intent in this paper is to find triples of Rational Pythagorean Triangles (abbr. RPT) having equal areas. A new method of solving a2+ab+b2=c2 is to set a=y−1, b=y+1, y∈N−{0,1} and get Pell's equation c2−3y2=1. To solve a2−ab−b2=c2, we set a=12(y+1), b=y−1, y≥2, y∈N and get a corresponding Pell's equation. The infinite number of solutions in Pell's equation gives rise to an infinity of solutions to a2±ab+b2=c2. From this fact the following theorems are proved.http://dx.doi.org/10.1155/S0161171288000948rational Pythagorean triangles (abbr. RPT)perimeter of the RPTPell's (Euler's) equationFibonacci sequence. |
| spellingShingle | Malvina Baica Pythagorean triangles of equal areas International Journal of Mathematics and Mathematical Sciences rational Pythagorean triangles (abbr. RPT) perimeter of the RPT Pell's (Euler's) equation Fibonacci sequence. |
| title | Pythagorean triangles of equal areas |
| title_full | Pythagorean triangles of equal areas |
| title_fullStr | Pythagorean triangles of equal areas |
| title_full_unstemmed | Pythagorean triangles of equal areas |
| title_short | Pythagorean triangles of equal areas |
| title_sort | pythagorean triangles of equal areas |
| topic | rational Pythagorean triangles (abbr. RPT) perimeter of the RPT Pell's (Euler's) equation Fibonacci sequence. |
| url | http://dx.doi.org/10.1155/S0161171288000948 |
| work_keys_str_mv | AT malvinabaica pythagoreantrianglesofequalareas |