Vibrating strings and infinite series

Time to dive into some mathematics again – today we celebrate the birth of British mathematician Brook Taylor (18 Aug 1685 – 29 Dec 1731).

Taylor is best known for ‘Taylor’s Theorem’ and the ‘Taylor series’, a mathematical method for expanding functions into infinite series. In 1715, he published a groundbreaking work ”Methodus Incrementorum Directa et Inversa“, which introduced a new branch of mathematics that became known as the ‘calculus of finite differences’.

Using finite differences, Taylor was able to mathematically express the movement of a vibrating string, reduced to mechanical principles.

The above work also contained what became known as Taylor’s Theorem – this blog is neither the time or place to even try and go into the details of the theorem, but suffice to say it is a pretty significant mathematical construct. Despite being introduced in his 1715 publication, it wasn’t until almost 60 years later that it’s value was fully recognised – in 1772 the great mathematician Joseph-Louis Lagrange termed it ‘the main foundation of differential calculus’.

Besides being one of the great mathematicians of all time, Brook Taylor was also a keen artist, with one of his particular interests being the principles of perspective – he wrote an essay called “Linear Perspective” on this subject, which also included the first general introduction of the concept of vanishing points.

So to celebrate this day, how about strumming a guitar while staring off into the vanishing distance… or painting perspectives while listening to some soothing guitar (the Majestic Silver Strings, perhaps)… 🙂

Sounds like a good day to me!