Volume 56
, Issue 1

2020

welcome to the first Parabola issue of this decade! We welcome Arnaud Brothier who is joining David Angell as Problem Editor.
Welcome Arnaud and welcome, dear Reader!

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.

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.

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.

A fresh comic for your amusement!

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?

Q1605 Calculate the constant term when the expression

$\big(1 + x + \frac{1}{x}\big)^{10}$

is expanded and like terms collected.