The purpose of the following report is to demonstrate that with the mathematical tools of the 17th century, a proof to Fermat’s conjecture may have been possible. The whole procedure is based on planar geometry, which was perfectly known at the time. Moreover, the procedure does not exceed contemporary school mathematics.
Fermat´s last theorem has been a hot topic for mathematicians since it was originally published in Fermat’s "Arithmetica". Although Pierre de Fermat had claimed to have found an easy proof for his conjecture, he failed to disclose it. Over the past 350 years, mathematicians were unable to find this simple proof. So, over time, it was concluded that Fermat had made an error with his claim. Finally, in 1994 the British mathematician Andrew Wiles found a complex mathematical proof for Fermat’s conjecture.
Inhaltsverzeichnis (Table of Contents)
- Introduction
- Rules for Even, Odd and Rational Numbers
- Fermat's Equation
- Fermat's Triangle
- Hero's Triangle
- What are the Angles?
- Conclusion
- Triangle Area
- Summary
Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)
This report aims to demonstrate that a proof for Fermat's Last Theorem may have been possible using 17th-century mathematical tools, specifically planar geometry. The author explores whether the mathematical knowledge of that era was sufficient to justify Fermat's claim of having found a simple proof.
- Fermat's Last Theorem and its historical significance
- The limitations of 17th-century mathematics
- The use of planar geometry to prove Fermat's theorem
- The feasibility of Fermat's claim
Zusammenfassung der Kapitel (Chapter Summaries)
- Introduction: The report introduces Fermat's Last Theorem, its history, and the challenge of recreating Fermat's supposed proof. It also establishes mathematical notation and definitions for even, odd, and rational numbers.
- Rules for Even, Odd and Rational Numbers: This chapter outlines the rules for addition, subtraction, multiplication, and division of even, odd, and rational numbers. These rules will be applied to Fermat's equation in subsequent chapters.
- Fermat's Equation: This chapter presents Fermat's Last Theorem as a mathematical equation and analyzes its implications. It establishes the conditions for integers involved in the equation and explores contradictions arising from specific integer combinations.
Schlüsselwörter (Keywords)
The key topics and terms explored in this report include Pierre de Fermat, Fermat's Last Theorem, Andrew Wiles, planar geometry, 17th-century mathematics, and the feasibility of Fermat's claim.
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- Hans Georg Schrey (Autor:in), 2023, A 17th Century Approach to Fermat's Last Theorem, München, GRIN Verlag, https://www.grin.com/document/1396819
