Thomas Britz
Dear Readers, welcome to the first issue of the 62nd volume of Parabola!
Ian Jung
We derive a recurrence relation of the Riemann zeta function at even natural numbers by first establishing a recurrence for \(F_n\).
Soham Dutta and Nandita Sen
We provide a surprising spin-off of the AM-GM-HM Inequality and other inequalities for complex numbers with a fixed modulus.
Artem E. Atamanchuk and Zdravko F. Starc
This article examines the fundamental principles of the method of mathematical induction and its application to mathematical problems.
Fabian Schmitt and Christopher C. Tisdell
We explore the possibilities for using the finite double-edged straightedge at its full potential, and explore several different opportunities to resolve some of the tension between theory and practice in the learning, teaching and practising of constructive geometry. In particular, this extra feature will mean that we can remove the use of a compass.
Seung Won (Daniel) Oh
This article proposes an alternative to the usual approach for reducing the cubic equation to a quadratic equation.
Sawyer Jacobson and Jeffery Zhang
The paper presents a derived algorithm for estimating graphical minimal surfaces through the use of mean curvature flow. Simulations are provided, demonstrating the effectiveness of the numerical approach.
Onur Örnek
We discuss two fundamental questions that often arise when considering random binary strings, namely the waiting time and location until a fixed pattern appears.
Md Sadikur Rahman and Tandra Sarkar
We establish an alternative proof of the sum and square sum identities for consecutive tetrahedral numbers using the Cauchy Residue Theorem.
Marc Jornet Sanz
We study the mental-calculation theory behind square roots and its deep connection with mathematics, giving later relations with other tasks such as division or cube roots.
Mohammed Ilyas Dehbi
This note establishes a novel, non-differential approach for finding the local maxima and minima of polynomials.
Pranav Kudumula
Where are my manners? Let me introduce myself. I am Pranav, a 12-year-old eighth grader who seems to spend most of his time doing recreational and contest mathematics instead of going to school. In this note, I'm going to share a short result in number theory that I found while goofing around (hey, that rhymes!).
Md Sadikur Rahman
We present simple geometric proofs of the limits \[
\lim_{x \to 0} \frac{\sin x}{x} = 1\qquad\text{and}\qquad
\lim_{x \to 0} \frac{1 - \cos x}{x} = 0
\]
Andi Du
We give a new proof of the Soddy-Gosset Theorem by using linear algebra, and we give some applications of the theorem.
Artem E. Atamanchuk
A new family of weighted integral inequalities generated by logarithmic derivatives is constructed and investigated in this work. The obtained results substantially extend classical estimates by allowing one to account for the influence of a weight function on the nature of integral relations.
David Angell, Mikhail Isaev and Sin Keong Tong
Q1791 Consider an ``old--fashioned'' 12-hour clock face having an hour hand, minute hand and second hand. Is there any time at which the three hands are equally spaced around the clock face? If so, then find all such times.
David Angell, Mikhail Isaev and Sin Keong Tong
Q1783 Let \(x\) be a positive integer. Prove that if \(x^2\) is the difference of two consecutive (integer) cubes, then \(x\) is the sum of two consecutive (integer) squares.