相关论文: The Plimpton 322 Tablet and the Babylonian Method …
A mathematically and culturally natural modification of Evart Bruins' explanation of the genesis of the numbers on the Old Babylonian tablet Plimpton 322 gives an economical accounting for the "missing pairs" in his reconstruction. When the…
Pythagorean triples are the positive integer solutions to the Pythagoras equation for right triangles, a2+b2 = c2. They have been studied for many years, many centuries in fact. In this short paper we present a method for computing…
Recently it has been discovered that on a stone tablet over 3800 years old, the Plimpton-322 table, are carved the geometric relations that exist between the sides of 15 right triangles chosen in a very special way. Due to its property as a…
The right triangles represented in the Plimpton 322 data have integer sides $(a, b, d)$ with $a < b < d$, by inspecting the data we propose $b=M\,Q_{M}$ with $M,Q_{M}$ positive integers. In this way we present a new data-driven family of…
The method of generating Pythagorean triples is known for about 2000 years. Though the classical formulas produce all primitive triples they do not generate all possible triples, especially non-primitive triples. This paper presents a…
It is well-known that pythagorean triples can be represented by points of the unit circle with rational coordinates. These points form an abelian group, and we describe its structure. This structural description yields, almost immediately,…
Ratios and coefficients are used to simplify calculations. For geometric usage these values also called function values. Like in Egypt also in Babylon such a value system can be shown. The reconstructed calculation sequence, of the Plimpton…
In this note we present a survey on some classical and modern approaches on Pythagorean triples. Some questions are also posed in direction of some materials under review. In particular some non commutative and operator theoretical…
Some relations among Pythagorean triples are established. The main tool is a fundamental characterization of the Pythagorean triples through a chatetus which allows to determine relationships with Pythagorean triples having the same…
In this note we show that in addition to two integers forming a Pythagorean triple, there also exist two irrational numbers in terms of which this Pythagorean triple can also be obtained. We also put forward a relation between these two…
Late-Babylonian mathematics (450-100 BC), represented by some 60 cuneiform tablets from Babylon and Uruk, is incompletely known compared to its abundantly preserved, well-studied Old-Babylonian predecessor (1800-1600 BC). With the present…
In 1934 B. Berggren first discovered the surprising result that every Pythagorean triplet is the pre product of the triplet (3, 4, 5) presented as a column by a product of three matrices, that every triplet is obtained in this manner…
The bisection of trapezoids by transversal lines has many examples in Babylonian mathematics. In this article, we study a similar problem in Elamite mathematics, inscribed on a clay tablet held in the collection of the Louvre Museum and…
The paper presents a systematic construction of primitive Pythagorean triples. The order of enumeration on the set of primitive Pythagorean triples is defined. The order is based on the representation of a primitive Pythagorean triple by…
The Babylonian graph B has the positive integers as vertices and connects two if they define a Pythagorean triple. Triangular subgraphs correspond to Euler bricks. What are the properties of this graph? Are there tetrahedral subgraphs…
One of the greatest achievements of Greek mathematics is the proof that the square root of 2 is irrational. It has not been thought that the Babylonians appreciated the concept of irrationality and certainly that they did not prove that the…
The general formulas for finding the quantity of all primitive and nonprimitive triples generated by the given number x have been proposed. Also the formulas for finding the complete quantity of the representations of the integers as a…
The traditional construction of primitive Pythagorean triples by the formulas of two independent variables does not allow their ordering. The paper shows a new view on the construction of primitive Pythagorean triples. A method for…
Given a right triangle and two inscribed squares, we show that the reciprocals of the hypotenuse and the sides of the squares satisfy an interesting Pythagorean equality. This gives new ways to obtain rational(integer)right triangles from a…
In 1998, in the winter issue of the journal Mathematics and Computer education (see [1]), Monte Zerger posed the following problem. He had noticed the Pythagorean triple (216,630,666);(216)^2+(630)^2=(666)^2. Note that 216=6^3 and 666 is…