An Attractive Spinning Toy: the Phi-TOP

It is fascinating to watch a top spinning. It seems to defy gravity: while it would topple over if not spinning, it remains in a vertical position as long as it is spinning rapidly. There are many variations on the simple top. The gyroscope has played a vital role in navigation and in guidance and … Continue reading An Attractive Spinning Toy: the Phi-TOP →

Some Fundamental Theorems of Maths

Every branch of mathematics has key results that are so important that they are dubbed fundamental theorems. The customary view of mathematical research is that of establishing the truth of propositions or theorems by rigorous deduction from axioms and definitions. Mathematics is founded upon axioms, basic assumptions that are taken as true. Logical reasoning is … Continue reading Some Fundamental Theorems of Maths →

Maths and Poetry: Beauty is the Link

Mathematicians are not renowned for their ability to reach the deepest recesses of the human soul. This talent is usually associated with great artists and musicians, and a good poet can move us profoundly with a few well-chosen words [TM173 or search for “thatsmaths” at irishtimes.com]. William Rowan Hamilton, whose work we celebrate during Maths Week, was … Continue reading Maths and Poetry: Beauty is the Link →

The Wonders of Complex Analysis

If you love mathematics and have never studied complex function theory, then you are missing something wonderful. It is one of the most beautiful branches of maths, with many amazing results. Don't be put off by the name: complex does not mean complicated. With elementary calculus and a basic knowledge of imaginary numbers, a whole … Continue reading The Wonders of Complex Analysis →

Emergence of Complex Behaviour from Simple Roots

It is exhilarating to watch a large flock of birds swarming in ever-changing patterns. Swarming is an emergent behaviour, resulting from a set of simple rules followed by each individual animal, bird or fish, without any centralized control or leadership. A murmuration of starlings is a breathtaking sight, with thousands of birds moving in harmony, … Continue reading Emergence of Complex Behaviour from Simple Roots →