Pythagorean Triangles (Dover Books on Mathematics)
| Author | : | |
| Rating | : | 4.56 (501 Votes) |
| Asin | : | 0486432785 |
| Format Type | : | paperback |
| Number of Pages | : | 128 Pages |
| Publish Date | : | 2015-03-26 |
| Language | : | English |
DESCRIPTION:
In this classic text, a brilliant Polish mathematician explores the intriguing mathematical relationships in such triangles.Starting with "primitive" 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. 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. 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.
A Compendium of Facts about Pythagorean Triangles watzizname A pythagorean triangle (PT) is a right triangle (i. e. a triangle which has a right angle) the lengths of the sides of which are all 'natural numbers' (i.e. positive integers) The smallest and best known PT is (4, 3, 5).Chapter 1, section 1.2 begins: In a pythagorean triangle (as in any right triangle) the biggest side is obviously the hypoteneuse; the other two sides, called arms, contain the right angle. If these (i. e. their lengths) are x and y and the hypoteneuse is z