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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 ...
Given some point in a topological space , the union of any collection of connected subsets such that each contains will once again be a connected subset. The connected component of a point in is the union of all connected subsets of that contain ; it is the unique largest (with respect to ) connected subset of that contains .
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 ...
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.
In two dimensions, a circle is not simply connected, but a disk and a line are. Spaces that are connected but not simply connected are called non-simply connected or multiply connected. A sphere is simply connected because every loop can be contracted (on the surface) to a point. The definition rules out only handle-shaped holes. A sphere (or ...
Can each house be connected to each utility, with no connection lines crossing? Two views of the utility graph, also known as the Thomsen graph or K 3 , 3 {\displaystyle K_{3,3}} The classical mathematical puzzle known as the three utilities problem or sometimes water, gas and electricity asks for non-crossing connections to be drawn between ...
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