Characterizations of Pythagorean Triangles in Relation to Special Dhuruva Numbers of Orders Four and Six

The fascinating branch of mathematics is the theory of numbers in which Pythagorean triangles have been a matter of interest to various mathematicians and to lovers of mathematics because it is a treasure house in which the search for many hidden connections is a treasure hunt. A careful observer of patterns may note that there are many fascinating patterns of numbers namely, Jarasandha numbers, polygonal numbers, pyramidal numbers, Nasty numbers, Dhuruva numbers and so on.

This chapter discusses on obtaining varieties of patterns of Pythagorean triangles in connection with special Dhuruva numbers of orders 4 and 6. Specifically, Pythagorean triangles, each with a leg represented by the six digits Dhuruva number 631764 are obtained. The number of primitive Pythagorean triangles, non- primitive Pythagorean triangles and Pythagorean triangles with special characterizations are exhibited. Further, the process of obtaining pairs of Pythagorean triangles, where, in each pair, the difference between their perimeters represented by the four digits Dhuruva number 6174 is illustrated. In addition, the number of pairs of primitive and non-primitive Pythagorean triangles is presented.