Steinig, J.: "A proof of Lagrange's theorem on periodic continued fractions", Arch. Math 59, 21-23 (1992).J. Steinig, `A proof of Lagrange's theorem on periodic continued fractions', Arch. Math. (Basel) 59 (1992), no. 1, 21-23....
We present an elementary proof of the Lagrange multiplier theorem for optimization problems with equality constraints in normed linear spaces. Most proofs in the literature rely on advanced concepts and results, such as the implicit function theorem and the Lyusternik theorem. By contrast, the proof...
Cody L. PattersonPaul Christian DawkinsHolly ZoltAnthony TucciKristen LewKathleen Melhuish
Machine-proof of mathematical theorems is a key component of the foundational theory of artificial intelligence. Lagrange's Theorem in group theory, which reveals the crucial relationship between a finite group and its subgroups, plays a significant role in understanding group structures and properties....
We present an elementary proof of the Lagrange multiplier theorem for optimization problems with equality constraints in normed linear spaces. Most proofs in the literature rely on advanced concepts and results, such as the implicit function theorem and the Lyusternik theorem. By contrast, the proof...
Thomson's theorem of electrostatics, which states the electric charge on a set of conductors distributes itself on the conductor surfaces to minimize the electrostatic energy, is reviewed in this letter. The proof of Thomson's theorem, based on a variational principle, is derived for a set of...
of the fundamental theorem of algebra (FTA). But there were no fewer than six attempts to prove the FTA before Gauss. We'll take a look at some of these pre-Gaussian proofs and show that Lagrange was the first to provide a complete and rigorous proof of the Fundamental Theorem of ...
Jeff Suzuki, Lagrange's proof of the fundamental theorem of algebra, MAA Monthly 113(8) (Oct. 2006), 705-714.Suzuki J., Lagrange's proof of the Fundamental Theorem of Algebra, Amer. Math. Monthly 113 (2006), 705-714.J. Suzuki, Lagrange's Proof of the Fundamental Theorem of Algebra,...
Tretyakov, S.E. Wright, A short elementary proof of the lagrange multiplier theorem, Optim. Lett., 6 (2012) 1597-1601.Brezhneva, O., Tret'vakov, A.A., Wright, S.E., A short elementary proof of the Lagrange multi- plier theorem, Optim. Lett. (2012) 6:1597-1601....