## Archive for September, 2021

### The Spine of Pascal’s Triangle

We are all familiar with Pascal’s Triangle, also known as the Arithmetic Triangle (AT). Each entry in the AT is the sum of the two closest entries in the row above it. The ${k}$-th entry in row ${n}$ is the binomial coefficient ${\binom{n}{k}}$ (read ${n}$-choose-${k}$), the number of ways of selecting ${k}$ elements from a set of ${n}$ distinct elements.

### Embedding: Reconstructing Solutions from a Delay Map

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In mechanical systems described by a set of differential equations, we normally specify a complete set of initial conditions to determine the motion. In many dynamical systems, some variables may easily be observed whilst others are hidden from view. For example, in astronomy, it is usual that angles between celestial bodies can be measured with high accuracy, while distances to these bodies are much more difficult to find and can be determined only indirectly.

### Earth System Models simulate the changing climate

Image credit: NASA.

The climate is changing, and we need to know what changes to expect and how soon to expect them. Earth system models, which simulate all relevant components of the Earth system, are the primary means of anticipating future changes of our climate [TM219 or search for “thatsmaths” at irishtimes.com].

### The Signum Function may be Continuous

Abstract: Continuity is defined relative to a topology. For two distinct topological spaces ${(X,\mathcal{O}_1)}$ and ${(X,\mathcal{O}_2)}$ having the same underlying set ${X}$ but different families of open sets, a function may be continuous in one but discontinuous in the other. Continue reading ‘The Signum Function may be Continuous’

### The Social Side of Mathematics

On a cold December night in 1976, a group of mathematicians assembled in a room in Trinity College Dublin for the inaugural meeting of the Irish Mathematical Society (IMS). Most European countries already had such societies, several going back hundreds of years, and it was felt that the establishment of an Irish society to promote the subject, foster research and support teaching of mathematics was timely [TM218 or search for “thatsmaths” at irishtimes.com].