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Using the basic properties of the base-b representation of rational numbers, we will give an elementary proof of Gauss's lemma: Every real root of a monic polynomial with integer coefficients is either an integer or irrational. The paper offers a new perspective in understanding the meaning of ‘irrational numbers’ from a deeper perspective, and a good occasion to improve the student's skills with point of view on number systems. [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]

In this paper, we will show a characterization for pairs of commensurable diagonals of regular n-gons. This result gives a positive answer to a recent question. [ABSTRACT FROM AUTHOR]