# Hanne Kekkonen

Assistant Professor of Mathematics and Statistics

EEMCS, Delft University of Technology

Delft, Netherlands

I'm a mathematician interested in visualising topological shapes and using them to introduce otherwise difficult to grasp mathematical concepts to the general public. I was originally attracted to mathematical art by the possibilities offered by 3D-printing. However, I quickly realised that many printable shapes can also be crocheted. I create shapes from several different medium nowadays, but I still find crocheting the easiest way of making complex shapes. Recently, I have been experimenting on combining crocheting and plaster to create rigid, yet mathematically exact shapes. This method was used for creating the hyperbolic chalk 'board'.

Heresy

25 x 50 x 45 cm

Crocheted yarn, glue, plaster, wood, polystyrene, paint, chalk

2020

Demonstrating hyperbolic, spherical and Euclidean (flat) geometry with chalk surfaces.

At school we learn certain things as fundamental truths: the angles of a triangle add up to 180°, a line has only one parallel line through a given point, and the circumference of a circle is 2πr. However, these facts are true only on flat surfaces.

A sphere has constant positive curvature which affects the geometry: all triangles add up to more than 180°, there are no parallel lines and circles are shorter.

A surface having constant negative curvature is called hyperbolic. On a hyperbolic plane triangles add up to less than 180°, a line has infinitely many parallels through a given point and circles are longer than 2πr.

At school we learn certain things as fundamental truths: the angles of a triangle add up to 180°, a line has only one parallel line through a given point, and the circumference of a circle is 2πr. However, these facts are true only on flat surfaces.

A sphere has constant positive curvature which affects the geometry: all triangles add up to more than 180°, there are no parallel lines and circles are shorter.

A surface having constant negative curvature is called hyperbolic. On a hyperbolic plane triangles add up to less than 180°, a line has infinitely many parallels through a given point and circles are longer than 2πr.