The English aviation pioneer Frederick Lanchester (1868–1946) introduced many important contributions to aerodynamics. He analysed the motion of an aircraft under various consitions of lift and drag. He introduced the term **“phugoid”** to describe aircraft motion in which the aircraft alternately climbs and descends, varying about straight and level flight. This is one of the basic modes of aircraft dynamics, and is clearly illustrated by the flight of gliders.

## Archive for the 'Occasional' Category

### Inertial Oscillations and Phugoid Flight

Published July 13, 2017 Occasional Leave a CommentTags: Applied Maths, Fluid Dynamics, Geophysics

### Patterns in Poetry, Music and Morse Code

Published June 29, 2017 Occasional Leave a CommentTags: Arithmetic, History, Recreational Maths

Suppose we have to ascent a flight of stairs and can take only one or two steps at a time. How many different patterns of ascent are there? We start with the simplest cases. With one step there is only one way; with two, there are two: take two single steps or one double step. With three steps, there are three possibilities. We can now proceed in an inductive manner.

### The Beer Mat Game

Published June 22, 2017 Occasional Leave a CommentTags: Games, Recreational Maths

Alice and Bob, are enjoying a drink together. Sitting in a bar-room, they take turns placing beer mats on the table. The only rules of the game are that the mats must not overlap or overhang the edge of the table. The winner is the player who puts down the final mat. Is there a winning strategy for Alice or for Bob?

We start with the simple case of a circular table and circular mats. In this case, there is a winning strategy for the first player. Before reading on, can you see what it is?

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### A Remarkable Pair of Sequences

Published June 8, 2017 Occasional Leave a CommentTags: Number Theory

The terms of the two integer sequences below are equal for all such that , but equality is violated for this enormous value and, intermittently, for larger values of .

### Wavelets: Mathematical Microscopes

Published May 25, 2017 Occasional Leave a CommentTags: Applied Maths, Wave Motion

In the last post, we saw how Yves Meyer won the Abel Prize for his work with wavelets. Wavelets make it easy to analyse, compress and transmit information of all sorts, to eliminate noise and to perform numerical calculations. Let us take a look at how they came to be invented.

### Hearing Harmony, Seeing Symmetry

Published May 11, 2017 Occasional Leave a CommentTags: Geometry, Music

Musical notes that are simply related to each other have a pleasing effect when sounded together. Each tone has a characteristic rate of oscillation, or frequency. For example, Middle C on the piano oscillates 264 times per second or has a frequency of 264 Hz (Hertz). If the frequencies of two notes have a ratio of two small whole numbers, the notes are harmonically related and sound pleasant when played together.

### A Geometric Sieve for the Prime Numbers

Published April 27, 2017 Occasional Leave a CommentTags: Number Theory, Primes

In the time before computers (BC) various ingenious devices were invented for aiding the extensive calculations required in astronomy, navigation and commerce. In addition to calculators and logarithms, several *nomograms* were devised for specific applications, for example in meteorology and surveying.