What is the circularity? To me (and again I may be wrong) it’s instantiated in the section below from the Wikipedia article.
Johnson and Jackson’s abstract adds that the book with the largest known collection of proofs for the theorem – Elisha Loomis’s The Pythagorean Proposition – “flatly states that ‘there are no trigonometric proofs because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean theorem’.” And since that particular field of study was discovered, mathematicians have maintained that any alleged proof of the Pythagorean theorem which uses trigonometry constitutes a logical fallacy known as circular reasoning, a term used when someone tries to validate an idea with the idea itself. Legions of schoolchildren have learned the notation summarizing the theorem in their geometry classes: a 2+b 2=c 2.Īs mentioned in the abstract of Johnson and Jackson’s 18 March mathematical society presentation, trigonometry – the study of triangles – depends on the theorem. The 2,000-year-old theorem established that the sum of the squares of a right triangle’s two shorter sides equals the square of the hypotenuse – the third, longest side opposite the shape’s right angle.
Now this is somewhat above my pay grade, but perhaps a mathematician will weigh in.
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