Open AccessExtended Pythagoras Theorem Using Hexagons
Author(s) -
Luis Teia
Publication year - 2021
Publication title -
journal of mathematics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9809
pISSN - 1916-9795
DOI - 10.5539/jmr.v13n6p46
Subject(s) - pythagorean theorem , mathematics , algebraic number , combinatorics , pythagorean triple , algebra over a field , pure mathematics , mathematical analysis , geometry
This article provides the geometric and algebraic proof of the variant equation of the Pythagorean theorem x^2-xy+y2=z^2 . The hypothesis that will be proven is that just as squares govern the original version x^2+y^2=z^2 , hexagons are found to govern x^2-xy+y^2=z^2 . Both the special case x=y and general case of x≠y are examined.