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4 days ago · In 1847, Gabriel Lamé outlined a proof of Fermat's Last Theorem based on factoring the equation x p + y p = z p in complex numbers, specifically the cyclotomic field based on the roots of the number 1. His proof failed, however, because it assumed incorrectly that such complex numbers can be factored uniquely into primes
4 days ago · Conversely, if we can prove that A + B = C for three similar figures without using the Pythagorean theorem, then we can work backwards to construct a proof of the theorem. For example, the starting center triangle can be replicated and used as a triangle C on its hypotenuse, and two similar right triangles ( A and B ) constructed on ...
Sep 9, 2024 · In physical theories prior to that of special relativity, mass and energy were viewed as distinct entities. Furthermore, the energy of a body at rest could be assigned an arbitrary value. In special relativity, however, the energy of a body at rest is determined to be mc2. Thus, each body of rest mass m possesses mc2 of “rest ...
Sep 8, 2024 · How to prove that limit of sin x / x = 1 as x approaches 0 ? Area of the small blue triangle $\color{blue}{OAB}$ is $\displaystyle A(\color{blue}{OAB})=\frac{1\cdot\sin x}{2}=\color{blue}{\frac{\sin x}{2}}$
5 days ago · In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample mean converges to a standard normal distribution. This holds even if the original variables themselves are not normally distributed.
2 days ago · The most common method for proving conjectures is direct proof. This method will be used to prove the lattice problem above. Prove that the number of segments connecting an \(n\times n\) lattice is \(2n(n+1)\).
Sep 12, 2024 · Mathematical Proofs: Euler’s theorem is a general case for proofs enabling modular arithmetic, divisibility tests and number theory identities and it provides clear and convincing mathematical arguments that are the foundation of rigorous mathematical analysis.
