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. … Continue reading Patterns in Poetry, Music and Morse Code
Month: June 2017
The Beer Mat Game
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 … Continue reading The Beer Mat Game
Fractal Complexity of Finnegans Wake
Tomorrow we celebrate Bloomsday, the day of action in Ulysses. Most of us regard Joyce's singular book as a masterpiece, even if we have not read it. In contrast, Finnegans Wake is considered by some as a work of exceptional genius, by others as impenetrable bafflegab [See TM117 or search for “thatsmaths” at irishtimes.com]. Sentence Length … Continue reading Fractal Complexity of Finnegans Wake
A Remarkable Pair of Sequences
The terms of the two integer sequences below are equal for all $latex {n}&fg=000000$ such that $latex {1<n<777{,}451{,}915{,}729{,}368}&fg=000000$, but equality is violated for this enormous value and, intermittently, for larger values of $latex {n}&fg=000000$. Hypercube Tic-Tac-Toe The simple game of tic-tac-toe, or noughts and crosses, has been generalized in several ways. The number of cells in … Continue reading A Remarkable Pair of Sequences
Beautiful Patterns in Maths and Music
The numerous connections between mathematics and music have long intrigued practitioners of both. For centuries scholars and musicians have used maths to analyze music and also to create it. Many of the great composers had a deep understanding of the mathematical principles underlying music. Johann Sebastian Bach was the grand master of structural innovation and … Continue reading Beautiful Patterns in Maths and Music
ThatsMaths 