The self-balancing shape you're asking about is the Gömböc, a unique convex, three-dimensional body with just one stable and one unstable point of equilibrium, meaning it always returns to the same resting spot, like a turtle shell or roly-poly toy. Discovered by Hungarian mathematicians Gábor Domokos and Péter Várkonyi, the Gömböc inspired the understanding of real-world self-righting animals like tortoises and is a fascinating mathematical curiosity that can be produced as a physical object.
Meet the Gömböc, a shape that exists at the very edge of mathematical possibility. It has only two equilibrium points: one stable, one unstable. No matter how you set it down, it will always right itself, but only after wobbling, hesitating, and resisting before finding its balance again.
The self- balancing mechanism is achieved through a feedback control system that stabilizes the robot on its two wheels using a combination of gyroscopic and accelerometer data. A proportional-integral-derivative (PID) controller is employed to maintain stability and ensure smooth navigation along the path.
A gömböc (Hungarian: [ˈɡømbøt͡s]) is any member of a class of convex, three-dimensional and homogeneous bodies that are mono-monostatic, meaning that they have just one stable and one unstable point of equilibrium when resting on a flat surface.
In geometry, the rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has a total of 62 faces: 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, with 60 vertices, and 120 edges.
The arc (think: circle) is the strongest structural shape, and in nature, the sphere is the strongest 3-d shape. The reason being is that stress is distributed equally along the arc instead of concentrating at any one point. Storage silos, storage tanks, diving helmets, space helmets, gas tanks, bubbles, planets, etc.
Self-balancing scooters operate on the same principles as a human standing upright. When you lean forward, the scooter detects the shift and accelerates the wheels to prevent a fall. Conversely, leaning backward signals the motors to slow down or reverse.
The inventor Louis Brennan (1852-1932) built this working model in about 1907 to demonstrate his ideas for a single-tracked rail vehicle stabilised by two linked gyroscopes. Brennan's daughter became a guinea-pig and was enlisted to help him conduct tests and demonstrations to prove the stability of his invention.
An AVL tree (Georgy Adelson-Velsky and Landis' tree, named after the inventors) is a self-balancing binary search tree.
(geometry) A polygon with a googol number of sides (virtually indistinguishable from a circle)
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.
A 300-Year-Old Mystery Solved: The First Shape That Can't Pass Through Itself. The 'Noperthedron,' the new shape that has solved a 300-year-old mathematical mystery. Courtesy of Jisse Steininger and Sergey Yurkevich.
sphere-since a sphere has no edges and, as a result, no corners. It has a single curved face that wraps around.
What is the Most Calming Shape? The soothing essence of the perfect circle brings a sense of balance and calmness, its seamless symmetry radiating a timeless tranquility for a serene visual experience.
Gigagon. The gigagon is a polygon with a billion sides.
In early 2024, the monorail was dismantled as part of park renovations. Due to rising maintenance costs including difficulty to procure parts, a decision was made to permanently close the monorail in 2024.
Shonan Monorail is the first public transportation system by SAFEGE suspended monorail in Japan. The initial service section was started with business distance of 4.7km and 5 stations between Ofuna and Nishi Kamakura in March 1970 that was the year when Osaka Expo was held.
As noted above the Maglev trains are capable of traveling at speeds nearly twice as fast as the bullet trains. However, the use of such extreme speeds in commercial travel seems unlikely. Whereas Maglev trains travel at speeds of up to 400 or 600kph, bullet trains travel at a modest 320kph.
A self-balancing scooter (also hoverboard, self-balancing board, electric scooter board, or swegway) is a self-balancing personal transporter consisting of two motorized wheels connected to a pair of articulated pads on which the rider places their feet.
Advantages of Self- Balancing Ledger
Speedy detection of errors is possible. Balancing is done quickly and thus saves time, labour and money. The system helps reducing fraud. Final Accounts can be prepared easily and quickly.
10 Tips to Achieve Life Balance
The triangle. It distributes weight evenly across all three sides, making it unbreakable.
In geometry, the nonconvex great rhombicosidodecahedron is a nonconvex uniform polyhedron, indexed as U67. It has 62 faces (20 triangles, 30 squares and 12 pentagrams), 120 edges, and 60 vertices. It is also called the quasirhombicosidodecahedron.
The triangle is considered the strongest shape because it distributes weight evenly on all three sides. This even distribution of weight allows for greater stability and can withstand heavy loads without collapsing.