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The gömböc's shape helped to explain the body structure of some tortoises and their ability to return to an equilibrium position after being placed upside down. [ 2 ] [ 3 ] [ 4 ] Copies of the first physically constructed example of a gömböc have been donated to institutions and museums, and the largest one was presented at the World Expo ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Between the two is a local maximum . A ball located at this point, ball 3, is in equilibrium but unstable; the slightest disturbance will cause it to move to one of the stable points. Light switch, a bistable mechanism. In a dynamical system, bistability means the system has two stable equilibrium states. [1]
In mathematics, the method of dominant balance approximates the solution to an equation by solving a simplified form of the equation containing 2 or more of the equation's terms that most influence (dominate) the solution and excluding terms contributing only small modifications to this approximate solution.
For convex two-dimensional shapes, the centroid can be found by balancing the shape on a smaller shape, such as the top of a narrow cylinder. The centroid occurs somewhere within the range of contact between the two shapes (and exactly at the point where the shape would balance on a pin).
The curve of fastest descent is not a straight or polygonal line (blue) but a cycloid (red).. In physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), [1] or curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead slides ...
In contrast to this, in a logarithmic spiral these distances, as well as the distances of the intersection points measured from the origin, form a geometric progression. The Archimedean spiral has two arms, one for θ > 0 and one for θ < 0. The two arms are smoothly connected at the origin. Only one arm is shown on the accompanying graph.
Then an edge of the alpha-shape is drawn between two members of the finite point set whenever there exists a generalized disk of radius 1/α that has the two points on its boundary and that contains none of the point set in its interior. If α = 0, then the alpha-shape associated with the finite point set is its ordinary convex hull.