It has a short proof in complex numbers. Combined with the Law of Sines, Ptolemy's theorem serves to prove the addition and subtraction formulas for the sine function. 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's theorem also provides easy derivations for … The proof of this lemma is based on the well-known, yet rarely used, Ptolemy’s theorem. 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. The theorem is named after the Greek astronomer and mathematician Ptolemy (Claudius Ptolemaeus). 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. This is an expository note on Ptolemy’s Theorem and its converse, giving a more algebraic proof of these results. Aaboe, 1964 and Berggren, 1986, and Katz, 1998 all contain excellent Ptolemy's theorem - Wikipedia wikimedia.org. 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 Ptolemy's Theorem Ptolemy's Theorem is a relation in Euclidean geometry between the four sides and two diagonals of a cyclic quadrilateral (i.e., a quadrilateral whose vertices lie on a common circle). 12 No. Fermat's Last Theorem. Science’s gain history’s loss. remained. 1 Introduction and main lemma We start by recalling Ptolemy’s theorem, a classical result and we present one of its proofs, which we [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. Ptolemy's theorem is a powerful result. PTOLEMY’S THEOREM AND ITS CONVERSE RICHARD G. SWAN Abstract. Ptolemys Theorem - YouTube ytimg.com. He believed that there were no such solutions and also believed that he found proof that showed that there were no whole number solutions. DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE, THE OPEN UNIVERSITY OF SRI LANKA(OUSL), NAWALA, NUGEGODA, SRI LANKA. Fermat’s Last Theorem Fermat observed , if x n +y n = z n where n>2 has any whole number solutions. File:Ptolemy Theorem az.svg - Wikimedia Commons wikimedia.org. Journal of Mathematical Sciences & Mathematics Education Vol. We show that 4 points in the plane lie on a circle or straight line if and only if they satisfy Ptolemy’s … Let's take a look at one more application. We therefore called it Ptolemy’s sine lemma. Ptolemy's Theorem relates the diagonals of a quadrilateral inscribed in a circle to its side lengths. Trigonometric Identities. With its help we establish the Pythagorean Theorem and Carnot's Theorem. He hinted inside a book he was reading that he found the proof. Proof of Ptolemy’s Theorem | Advanced Math Class at ... wordpress.com. ¨ – Mordell Theorem, Forum Geometricorum, 1(2001) pp.7 – 8. which is the Pythagoras' theorem for $\Delta BDC.$ This means, Ptolemy's theorem is more powerful than Pythagoras' theorem! Ptolemy's theorem - Wikipedia wikimedia.org. Theorem | Advanced Math Class at... wordpress.com the Pythagoras ' theorem for $ BDC.... 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