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 
Archive for September, 2021
The Spine of Pascal’s Triangle
Published September 30, 2021 Occasional ClosedTags: Arithmetic, Number Theory
Embedding: Reconstructing Solutions from a Delay Map
Published September 23, 2021 Occasional ClosedTags: Mechanics, Topology
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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.
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Earth System Models simulate the changing climate
Published September 16, 2021 Irish Times ClosedTags: biology, Climate Modelling, Geophysics
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].
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Abstract: Continuity is defined relative to a topology. For two distinct topological spaces 
Continue reading ‘The Signum Function may be Continuous’
The Social Side of Mathematics
Published September 2, 2021 Irish Times ClosedTags: Education, Ireland
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].
ThatsMaths 