Where can the idea of the Gömböc be applied?
In case of many mathematical discoveries the route to applications often takes many years. Although the Gömböc is a very recent result, applications in biology and geology are already very promising. Some turtles have evidently developed Gömböc-like shells to facilitate self-righting. The theory behind the Gömböc may help to provide a useful, new classification for pebble shapes. Beyond scientific applications, the Gömböc aroused the interest of major industrial companies in various industries.
Why is the Gömböc expensive?
Although the Gömböc has no moving parts, the geometry has to be manufactured to unprecedented precision: a Gömböc of 10 cm diameter has tolerances far less than 0.1mm. This precision presents a formidable challenge even to state-of-art precision technologies. Nevertheless, as more pieces are produced, we expect the price to drop.
Is there only one Gömböc shape?
No, in fact, there are infinitely many Gömböc shapes. However, the overwhelming majority of these shapes could never be manufactured because these shapes are much too close to the sphere. Currently we manufacture two different shapes ( 8005 and 8205 ). Both are quite similar and have a substantial deviation from the sphere.
Does the behavior of the Gömböc depend on the size or the material?
In theory, it does not depend as long as the material is homogeneous. In practice the mass of the Gömböc plays a role: heavier objects have a better chance to overcome small surface imperfections.