# Curves in Honour of Leibniz’s Tercentenary

## Curves in Honour of Leibniz’s Tercentenary

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http://www.gresham.ac.uk/lectures-and-events/curves-in-honour-of-leibniz...

4.00pm: Dr. Snezana Lawrence (University of Bath)

*Hold on to your chairs! – the mathematics of whirls, spirals, and curves*

Curves have been studied throughout the history of mathematics, and Archimedean curve is one of the most famous among them. This lecture will explore the history of, and ways in which curves are generated, looking at both their practical and aesthetic applications. Archimedes had made curves already famous in his book *On Spirals*, written around 225 BC. The way Archimedes described, and employed spirals, is rich in both context and meaning. We will here explore some of these aspects of curves by him and by other mathematicians, and demonstrate their ways of generation. Thus a practical, historical, and mathematical survey, this talk will take you on a whistle tour of classical curves and spirals, beginning with the famous Archimedean spiral.

4.45pm: Prof Kenneth Falconer (University of St Andrews)

** Fractal curves: from the esoteric to the ubiquitous** The lecture will consider the origins of certain `fractal’ curves that were constructed in the late 1800s/early 1900s to provide specific examples or counter-examples and which were regarded as 'pathological’ oddities. For example, Riemann and Weierstrass constructed continuous curves that were nowhere differentiable, and von Koch's ‘snowflake’ curve exhibited a similar phenomenon. We will go on to see how, following the work of Mandelbrot and others, such curves are now regarded as members of a vast family of interesting and naturally occurring curves and fractal objects.

5.30: refreshments

6.00pm: Gresham Lecture: Prof Jan Van Maanen (University of Utrecht) Mathematics and diplomacy: *Leibniz (1646-1716) and the curve of quickest descent.*

Not only is mathematics challenging. Mathematicians are also often challenging each other. The search for the quickest slide between two points in a vertical plane is such a challenge. It was launched 1695 by Johann Bernoulli and became famous as the Brachysto-chrone (shortest-time) problem. The launch in a journal article, repeated in Bernoulli's New Year wish for 1696, resulted in a long-lasting quarrel between Johann and his elder brother Jacob Bernoulli. Other mathematicians, among whom Isaac Newton, got involved. This year’s tercentenary of the death of Gottfried Leibniz puts Leibniz in the limelight. He deserves this in his own right, because his involvement reveals interesting mathematics as well as friendly diplomacy. With his letters and publications about the Brachystochrone Leibniz hoped to reconcile the two Bernoulli brothers, the first students of his new calculus, whom he valued highly.

More details in due course.