Year 2020 - Volume 56
2020 - Present

Thomas Britz

Dear Reader, welcome to this issue of Parabola!
It is my pleasure to dedicate this issue to Bruce Henry, to whom I - and Parabola - owe much. It also my pleasure to welcome Parabola's newest Problem Editor, Sin Keong, a life-long expert in Parabola problems.

Fibonacci numbers are well-known and well-studied, as are the related Lucas numbers. In this article, we present a geometric interpretation of these interrelated sequences and their unique properties.

Ashwin Sivakumar

This paper describes a recursive fraction operation which in interesting ways seems leads to irrational numbers and Fibonacci numbers. The Reader is invited to join this exploration.

Thomas Britz

In this article, it is my pleasure to share with you, dear Reader, some less-known facts about Fibonacci numbers. These include some brief but interesting history and some fun and challenging counting problems.

Mike Chapman and Robert Schneider

A fresh comic for your amusement!

David Angell and Arnaud Brothier

Q1616 Fourteen circular counters of identical size are available; 9 of them are red and 5 are blue. In how many ways can they be arranged into a stack of 14 counters, if there cannot be more than 3 adjacent counters of the same colour?

David Angell

Q1605 Calculate the constant term when the expression (1+x+1x)10 is expanded and like terms collected.

Thomas Britz

welcome to this issue of Parabola! This theme of this issue is the “natural” numbers.

Stephen Bewlay and Long Yin Felicina Chau

We look at number triples that almost - but not quite - satisfy Pythagoras' Theorem: the quasi-Pythagorean triads.

A. Anas Chentouf

Nearly a century and a half since its introduction, Sylvester's sequence continues to be relevant as it is the focus of open conjectures.

Timothy Hume

This article provides a brief introduction to aliquot sums and presents a proof of a beautiful identity that these sums satisfy.

Arya R. Kondur

In this paper, we prove theorems that simplify the famous Sierpinski Number Problem. We also develop a method for prime numbers that would aid the current sequential searching techniques.

Thomas Britz and Imaginary Co-author

This note briefly gives advice on how to write a Parabola article - or any mathematical article.

Mike Chapman and Robert Schneider

An odd comic about even numbers.

David Angell and Arnaud Brothier

Q1622 Find the sum of the digits of

where the last term on the right hand side has 999 digits, all equal to 1

David Angell and Arnaud Brothier

Thomas Britz

Dear Reader, welcome to this issue of Parabola!
It is my pleasure to dedicate this issue to Bruce Henry, to whom I - and Parabola - owe much. It also my pleasure to welcome Parabola's newest Problem Editor, Sin Keong, a life-long expert in Parabola problems.

Randell Heyman

The number $1+\sqrt{2}$ $1 + \sqrt{2}$ has an interesting property. When we calculate the numbers

$1+\sqrt{2}$ $1 + \sqrt{2}$, $\left(1+\sqrt{2}{\right)}^{2}$ $(1 + \sqrt{2})^2$, $\left(1+\sqrt{2}{\right)}^{3}$ $(1 + \sqrt{2})^3$, $\dots$ $\ldots$,

they seem to get closer and closer to integers.

Jennifer Lew

In this paper, I will share how to use and optimize Monte Carlo Integration to solve a real-world problem.

Eric Gao

This paper analyzes game in which the player knows possible payoffs and their possible moves but does not know the game mechanisms. We analyse how learning is acheived, not by learning game mechanisms, but by players geting better at guessing their way through repetitions, based on their prior results.

Arqam Patel

Consider the algorithm CARA: take a number, count the number of letters in its spelling to get a new number, and repeat. For example,

15 (fifteen) → 7 (seven) → 5 (five) → 4 (four) → 4 (four) → ··· We show that all such sequences end in the number 4.

Timothy Hume

In this article we present brief summaries of some mathematical articles which readers may be interested in. If this list of readings proves popular, it may become a regular feature in Parabola.

Mike Chapman, Max Schneider and Robert Schneider

An odd comic about even numbers.

David Angell, Arnaud Brothier and Sin Keong Tong

Q1639 What is the largest integer that cannot be expressed as 99a+100b+101c , where a , b , and c are non–negative integers?

David Angell, Arnaud Brothier and Sin Keong Tong