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Connected Mathematics is a comprehensive mathematics program intended for U.S. students in grades 6–8.The curriculum design, text materials for students, and supporting resources for teachers were created and have been progressively refined by the Connected Mathematics Project (CMP) at Michigan State University with advice and contributions from many mathematics teachers, curriculum ...
Consider the following problem. Suppose that a tangent vector to the sphere S is given at the north pole, and we are to define a manner of consistently moving this vector to other points of the sphere: a means for parallel transport. Naively, this could be done using a particular coordinate system. However, unless proper care is applied, the ...
The "nine dots" puzzle. The puzzle asks to link all nine dots using four straight lines or fewer, without lifting the pen. The nine dots puzzle is a mathematical puzzle whose task is to connect nine squarely arranged points with a pen by four (or fewer) straight lines without lifting the pen or retracing any lines.
Movements to any directions: blue: wheel drive direction; red: vehicle moving direction. a) Moving straight ahead, b) Moving sideways, c) Moving diagonally, d) Moving around a bend, e) Rotation, f) Rotation around the central point of one axle. A Mecanum wheel is an omnidirectional wheel design for a land-based vehicle to move in any direction.
In mathematics, connectedness [1] is used to refer to various properties meaning, in some sense, "all one piece". When a mathematical object has such a property, we say it is connected; otherwise it is disconnected. When a disconnected object can be split naturally into connected pieces, each piece is usually called a component (or connected ...
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In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. It is closely related to the concepts of open set and interior . Intuitively speaking, a neighbourhood of a point is a set of points containing that point where one can move some amount in any direction away from ...
Equivalently, geodesics are curves that locally take the shortest path between two points. They are the generalization of straight lines in Euclidean space to arbitrary Riemannian manifolds. An ant living in a Riemannian manifold walking straight ahead without making any effort to accelerate or turn would trace out a geodesic.