By:  Fatima Durrani – Social Development and Policy Major 2020

(Student, School of Arts, Humanities and Social Sciences, Habib University)


Dr. Glen Van Brummelen is an internationally acclaimed Canadian historian of mathematics specializing in historical applications of mathematics to astronomy. On the 7 of August, Dr. Brummelen brought to Habib University his rich and wide berth of knowledge of Mathematics and Astronomy and presented it to an audience of over fifty students, mathematics enthusiasts and professors in a DSSE Public Lecture. This lecture, titled ‘FROM THE HEAVENS TO THE EARTH: THE MERCURIAL TALE OF SPHERICAL TRIGONOMETRY’ was an in-depth summary of his renowned book- first one, to be accurate- with the same title (The Mathematics of the Heavens and the Earth: The Early History of Trigonometry). His book has enjoyed extreme success in the academic circles and is a further testament to his mastery in this arena.

The lecture was focused on trigonometry and the deviation of its current form from its medieval roots.  True to the professionalism of a historian, Dr. Brummelen served the audience with an accurate account of the birth of Trigonometry, giving complete credit to Indian and Muslim scholars where due. This information was new for most students in the audience and roused a huge round of applause. Being a mathematician, the lecture also consisted of a lot of interesting equation solving. From the ancient Y1K theorem and its very interesting inception by four Muslim scholars from different parts of the World to talking about the immense importance of the angle 180, the lecture was very enchanting and full of new information.  A dominant and recurring topic in this lecture was the discussion regarding spherical trigonometry in terms of its validity in astronomy and even in navigation. Spherical trigonometry is the branch of spherical geometry that deals with the relationships between trigonometric functions of the sides and angles of the spherical polygons defined by a number of intersecting great circles on the sphere. The importance of spherical trigonometry lies in its deep entanglement with Navigation and astronomy. Dr. Brummelen presented a thorough account of John Napier’s great leaps in this very diverse field. A lot of emphasis was also placed on comparing and contrasting the characteristics of plane and spherical geometry. This discussion was followed by rounds of audience interaction regarding right angles, triangles and the surface of the earth and its relationship with angles. Dr. Brummelen covered a very wide ground of the history of trigonometry in this ninety-minute long lecture, from the shape of the hemisphere according to medieval findings and the dull impression of trigonometry today on students and teachers both.

This insightful session was followed by a brief questions and answer session that received a very good response from the audience. The session ended on a very good note with Dr. Moiz– the organizer of this esteemed lecture, a continuation of the DSSE Lecture Series– inviting Dr. Shahid Hussain, a professor in the Computer Science department at Habib to present Dr. Brummelen with a gift as a token of the appreciation of the Habib University’s  gratitude for the extension of his knowledge into an enriching 90 minutes.