相关论文: A new and elementary proof of Newton's "favorite" …

We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.

This article provides a simple proof of the quadratic formula, which also produces an efficient and natural method for solving general quadratic equations. The derivation is computationally light and conceptually natural, and has the…

Iterating Newton's method symbolically for the general quadratic yields a rational function, the numerator and denominator of which are polynomials with highly composite coefficients.

We give a new proof of Lucas' Theorem in elementary number theory.

The classical quadratic formula and some of its lesser known variants for solving the quadratic equation are reviewed. Then, a new formula for the roots of a quadratic polynomial is presented.

An interpretation of selected parts of Newton's Principia, with modern notation and methods. Keplers Laws are derived from an inverse square law using Newton's methods.

In this note we prove that the version of Newton algorithm with line search we used in [2] converges quadratically.

In this paper, we derive the quadratic formula as a consequence of constructively proving the existence of standard and factored forms for general form real quadratic functions. Emphasis is put on connections to graphing of corresponding…

Inspired by a recent preprint of N. Curien, we provided what may be a new and elementary proof of the Law of Large Numbers.

I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.

We give a new simpler proof of a theorem of Jayne and Rogers.

Newton's "superb theorem" for the gravitational inverse-square-law force states that a spherically symmetric mass distribution attracts a body outside as if the entire mass were concentrated at the center. This theorem is crucial for…

A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.

An error analysis for some Newton-Cotes quadrature formulae is presented. Peano-like error bounds are obtained. They are generally, but not always, better than the usual Peano bounds.

An technically interesting proof of a known theorem.

It is shown that quadrature formulas in many different applications can be derived from rational approximation of the Cauchy transform of a weight function. Since rational approximation is now a routine technology, this provides an easy new…

We discuss several existing proofs of the value of a quartic integral and present a new proof that evolved from rational Landen transformations.

In this note we generalise a method of Perott to give new proofs that there are infinitely many prime numbers.

An elementary derivation of the Newton "inverse square law" from the three Kepler laws is proposed. Our proof, thought essentially for first-year undergraduates, basically rests on Euclidean geometry. It could then be offered even to…

A new transparent proof of the well known good compactification theorem for the complex torus $(\Bbb C^*)^n$ is presented. This theorem provides a powerful tool in enumerative geometry for subvarieties in the complex torus. The paper also…