The Gömböc is tangible proof of mathematical theory, developed by Gábor Domokos and Péter Várkonyi from the Budapest University Technology and Economics, about the stability of solid objects. The Gömböc is a three-dimensional, homogenous, convex object that has exactly one stable and one unstable equilibrium, or balance point; if you put it down on a flat surface it will reorient itself until it reaches the one stable equilibrium point.

The mathematicians have chosen to gift one of the Gömböc pieces to the University with the unique serial number 1824, in honour of the University’s 200 anniversary which is being celebrated throughout 2024. Gömböc 1824 stands at 180mm tall and is made from plexiglass. It will be exhibited in the Mathematics Department located in the Alan Turing Building.

Gömböc 1824 was presented to the University at a ceremony on 10 October, by H.E. Ferenc Kumin, ambassador of Hungary, and was accepted by Professor Martin Shroder , Vice-President and Dean of the Faculty of Science and Engineering and Professor Andrew Hazel , Head of the Department of Mathematics. The ambassador also had the chance to have lunch with Hungarian staff and students at the University and took a tour of the robotics lab.

Since its discovery in 2007, many Gömböc pieces have been donated to renowned institutions worldwide, including Harvard University, the Beijing Institute of Mathematical Sciences, the Pompidou Centre and The University of Tokyo.

There are few Gömböc pieces in the UK; The University of Oxford, The University of Cambridge, Windsor Castle, The Crown Estate, University College London and Academia Europaea are the only institutions which currently have a Gömböc on display. The University of Manchester’s Gömböc 1824 is the first Gömböc to be gifted to an institution in the North of England.

Professor Andrew Hazel, Head of the Department of Mathematics, said: "It is somewhat unusual to have a mathematical object whose proof of existence can be realised in such a tangible way. The Gömböc is visually interesting and stimulates discussion between staff, students and visitors."

We are thrilled to accept Gömböc 1824. Being included among other prestigious institutions who have been gifted a Gömböc is a true honour; and it holds a special significance in this bicentenary year of the University.

Although discovered in Hungary, the Gömböc has connections to The University of Manchester. Some of the early research on the statics of solid bodies was pioneered by Sir Horace Lamb, who studied Mathematics at Owens College and was a Professor of Physics at the University between 1885 and 1920. Lamb wrote the influential textbook

*Statics, Including Hydrostatics and the Elements of the Theory of Elasticity,*which describes methods that can be adapted to analyse the stability of the Gömböc.

The Gömböc is also relevant for current research being undertaken at the University. Researchers working on granular flows and particle dynamics used the Gömböc as a test shape for computer codes, to verify the stability calculations used to analyse piles of grains.

H.E. Ferenc Kumin, ambassador of Hungary, said: "It is with great pride that we present the G1824, a remarkable embodiment of Hungarian ingenuity and problem-solving, in honour of The University of Manchester’s foundation. More than a scientific marvel, for us, Professor Domokos’ Gömböc represents Hungarian thinking and creative problem solving."

Having a Gömböc at the University of Manchester symbolises the creative depth that unites great minds across borders, celebrating the pioneering spirit of a world-leading institution renowned for ground-breaking discoveries.

## History of the Gömböc

In geometry, a body with a single stable resting position is called*monostatic;*the term

*mono-monostatic*has been coined to describe a body which additionally has only one unstable point of balance.

The weight of the Gömböc is distributed evenly; and no simpler homogeneous shape exists with these properties. In fact, it is not possible for a convex, homogenous, solid three-dimensional object to have fewer than two equilibria.

The question of whether it is possible to construct a three-dimensional body which is mono-monostatic, homogenous and convex, was posed by Russian mathematician Vladimir Igorevich Arnold at a conference in 1995, in Hamburg.

In 2007, Gábor Domokos and Péter Várkonyi proved Arnold’s conjecture correct and created the first physical example, which became known as the Gömböc. The discovered mono-monostatic shape is the most sphere-like shape, apart from the sphere itself; its name is a diminutive form of

*gömb,*meaning ’sphere’ in Hungarian.

Gömböc-like shapes can be seen in nature. Biological evolution developed a similar shape in the form of the shell of the Indian Star Tortoise , which self-rights when turned upside down. Domokos and Várkonyi spent time studying tortoises in Hungary, attempting to explain the shape and function of their shells.

After its creation in 2007, a series of individual Gömböc models were launched. Each individual Gömböc carries its own unique serial number, between 1 and the current year, and has only been produced once.

The first individually numbered Gömböc model (Gömböc 001) was presented by Domokos and Várkonyi as a gift to Vladimir Igorevich Arnold on his 70 birthday in 2007; Professor Arnold later donated Gömböc 001 to the Steklov Institute of Mathematics, where it is currently on exhibit.