Fermat’s Last Theorem Fermat observed , if x n +y n = z n where n>2 has any whole number solutions. With its help we establish the Pythagorean Theorem and Carnot's Theorem. He believed that there were no such solutions and also believed that he found proof that showed that there were no whole number solutions. remained. Global Journal of Advanced Research on Classical and Modern Geometries ISSN: 2284-5569, Vol.2, Issue 1, pp.20-25 A CONCISE ELEMENTARY PROOF FOR THE PTOLEMY’S THEOREM Fermat's Last Theorem. [4] H. Lee, Another Proof of the Erdos [5] O.Shisha, On Ptolemy’s Theorem, International Journal of Mathematics and Mathematical Sciences, 14.2(1991) p.410. 1 23 PTOLEMY’S THEOREM – A New Proof Dasari Naga Vijay Krishna † Abstract: In this article we present a new proof of Ptolemy’s theorem using a metric relation of circumcenter in a different approach.. Ptolemy used a theorem on cyclic quadrilaterals (now called Ptolemy’s Theorem) in much the same way we use the addition formulas for the sine and cosine in order to produce his table. This is an expository note on Ptolemy’s Theorem and its converse, giving a more algebraic proof of these results. Ptolemys Theorem - YouTube ytimg.com. File:Ptolemy Theorem az.svg - Wikimedia Commons wikimedia.org. 12 No. 1 Introduction and main lemma We start by recalling Ptolemy’s theorem, a classical result and we present one of its proofs, which we ¨ – Mordell Theorem, Forum Geometricorum, 1(2001) pp.7 – 8. We show that 4 points in the plane lie on a circle or straight line if and only if they satisfy Ptolemy’s … DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE, THE OPEN UNIVERSITY OF SRI LANKA(OUSL), NAWALA, NUGEGODA, SRI LANKA. which is the Pythagoras' theorem for $\Delta BDC.$ This means, Ptolemy's theorem is more powerful than Pythagoras' theorem! Ptolemy's Theorem gives a relationship between the side lengths and the diagonals of a cyclic quadrilateral; it is the equality case of Ptolemy's Inequality.Ptolemy's Theorem frequently shows up as an intermediate step in problems involving inscribed figures. Journal of Mathematical Sciences & Mathematics Education Vol. Let's take a look at one more application. Ptolemy's theorem is a powerful result. He hinted inside a book he was reading that he found the proof. Combined with the Law of Sines, Ptolemy's theorem serves to prove the addition and subtraction formulas for the sine function. Ptolemy's theorem - Wikipedia wikimedia.org. It has a short proof in complex numbers. Ptolemy's theorem - Wikipedia wikimedia.org. PTOLEMY’S THEOREM AND ITS CONVERSE RICHARD G. SWAN Abstract. Ptolemy's theorem also provides easy derivations for … The theorem is named after the Greek astronomer and mathematician Ptolemy (Claudius Ptolemaeus). We therefore called it Ptolemy’s sine lemma. 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