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A Pythagorean triple is an ordered triple of integers (a,b,c) = (0,0,0) such that a² +b² = c². It is well known that the set P of all Pythagorean triples has an intrinsic structure of commutative monoid with respect to a suitable binary operation, (P,*). In this article, we will introduce the "commensurability" relation R among Pythagorean triples, and we will see that it induces a group quotient, P/R, which is isomorphic with the direct product of infinite (countable) copies of C∞, the infinite cyclic group, and a cyclic group of order 4. As an application, we will see that the acute angles of Pythagorean triangles are irrational when measured in degrees. [ABSTRACT FROM AUTHOR]

Therefore Graph HT ht is a right triangle. Well, obviously if they are the same in the corresponding locations (so Graph HT ht generalizes), then they will be congruent. The general case ( I n i > 6) can be easily derived from the hexagons adjoining a suitable ( I n i - 4)-gon (see Graph HT ht in Figure 7). [Extracted from the article]