"The power of two" is a Royal Institution (Ri) mathematics "master-class". It is a two-and-a half-hour interactive learning session, which, with varying degree of coverage and depth, has been run with students from Year 5 to Year 11, and for teachers. The master class focuses on an historical episode--the Josephus…

A student noticed an interesting fact about the base two numerals for perfect numbers. Mathematical explanations for some questions are given. (MNS)

Through the importance of the number three in our culture and the strange preference for a ternary pattern of our nature one can perceive how and why number theory degraded to numerology. The strong preference of our minds for simple patterns can be read as the key to understanding not only the development of numerology, but also why scientists…

Presented are the mathematical explanation of the algorithm for representing rational numbers in base two, paper-and-pencil methods for producing the representation, some patterns in these representations, and pseudocode for computer programs to explore these patterns. (MNS)

Discusses the relationship between the world of mathematics and the real world through a consideration of Mitsumasa Anno's exploration of the two different yet connected worlds in five picture books. (SR)

An analysis of the rabbit problem reveals some of the fascinating properties of the Fibonacci numbers. (MP)

The Euclidean algorithm for finding the greatest common divisor is presented. (MNS)

An algebraic development of the Fibonnaci sequence, appropriate for use in beginning algebra classes, is presented. (SD)

Playing with number patterns can lead students to discover some divisibility tests. (JT)

Advocated is developing intuitive ideas of limits whenever the opportunity arises in elementary mathematics. Examples are given for geometry, fractions, sequences and series, areas, probability, graphing, and the golden section. (MNS)

The problem of determining the number of squares on a checkerboard is extended to finding the number of rectangles on an n x n board and finding the total numbers of cubes and rectangular solids in an n x n x n cube. (DT)