Pythagorean Triangles (eBook)

Waclaw Sierpinski (Autor)

eBook Download: EPUB

2013
128 Seiten
Dover Publications (Verlag)
978-0-486-17483-9 (ISBN)

Infos

This classic text, written by a distinguished mathematician and teacher, focuses on a fundamental theory of geometry. Topics include all types of Pythagorean triangles.

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The Pythagorean Theorem is one of the fundamental theorems of elementary geometry, and Pythagorean triangles — right triangles whose sides are natural numbers — have been studied by mathematicians since antiquity. In this classic text, a brilliant Polish mathematician explores the intriguing mathematical relationships in such triangles.Starting with "e;primitive"e; Pythagorean triangles, the text examines triangles with sides less than 100, triangles with two sides that are successive numbers, divisibility of one of the sides by 3 or by 5, the values of the sides of triangles, triangles with the same arm or the same hypotenuse, triangles with the same perimeter, and triangles with the same area. Additional topics include the radii of circles inscribed in Pythagorean triangles, triangles in which one or more sides are squares, triangles with natural sides and natural areas, triangles in which the hypotenuse and the sum of the arms are squares, representation of triangles with the help of the points of a plane, right triangles whose sides are reciprocals of natural numbers, and cuboids with edges and diagonals expressed by natural numbers.

Inhalt

1. Pythagorean triangles. Primitive pythagorean triangles2. Obtaining primitive pythagorean triangles3. Pythagorean triangles with sides 4. Pythagorean triangles two sides of which are successive numbers5. Divisibility by 3 or by 5 of one of the sides of a pythagorean triangle6. The values of the sides of pythagorean triangles7. Pythagorean triangles with the same arm or the same hypotenuse8. Pythagorean triangles with the same perimeter9. Pythagorean triangles with the same area9a. The radii of circles inscribed in pythagorean triangles10. Pythagorean triangles in which one or more sides are squares11. Triangles with natural sides and natural areas. Triangles with natural areas and sides which are successive numbers. Rational triangles12. Pythagorean triangles in which the hypotenuse and the sum of the arms are squares13. Representation of pythagorean triangles with the help of the points of a plane14. Right triangles the sides of which are reciprocals of natural numbers15. Cuboids with edges and diagonals expressed by natural numbers

Produkt-Details

• Erscheint lt. Verlag: 10.4.2013
• Reihe/Serie: Dover Books on Mathematics
• Zusatzinfo: none
• Sprache: englisch
• Maße: 140 x 140 mm
• Gewicht: 150 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: Geometry • Greek mathematics • Pythagoras • Pythagorean triangles • triangles
• ISBN-10: 0-486-17483-2 / 0486174832
• ISBN-13: 978-0-486-17483-9 / 9780486174839