The Beauty of Geometrical Curves

The path traced out by a given point on the rim of a circle as you roll it along a straight line is a beautiful curve called a cycloid, whose appeal to mathematicians has had it dubbed “the Helen of Geometry”. This curve is known in geometry as a roulette, which is a curve you get by rolling one curve along another, and there are many more with an amazing range of applications, from clockwork toys to nuclear reactors.

This lecture provided a guided tour of the beauty of geometrical curves.

This is part of the series:

Geometry: The Mathematics of Art



Professor Sarah Hart


Sarah Hart is the first woman Professor of Geometry at Gresham College, and was appointed in 2020. She is Professor of Mathematics and until recently was Head of Mathematics and Statistics at Birkbeck, University of London.

She studied at Oxford and Manchester, gaining her PhD in 2000. Postdoctoral research and teaching followed, including a prestigious Engineering and Physical Sciences Research Council Fellowship, before she was appointed to a lectureship at Birkbeck in 2004. She has been Professor of Mathematics there since 2013. In 2021 she began a three-year term as President of the British Society for the History of Mathematics.

Sarah is an active researcher, publishing mainly in the area of pure mathematics known as group theory, which has many applications both inside and outside of mathematics, for example in coding theory and cryptography. She is passionate about communicating mathematics and is a sought-after public speaker. She is particularly interested in the links between mathematics, culture and creativity: many of her public lectures and talks in schools are on this topic, especially on mathematics and art.

In 2020-21, Professor Hart will be lecturing on Mathematics in Music and Writing, part of a three-year exploration of Mathematics, Culture and Creativity.

Professor Hart’s lecture series is as follows:

2021/22 Geometry: The Mathematics of Art

2020/21 Mathematics in Music and Writing

All lectures by the Gresham Professors of Geometry can be found here.

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