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The graph (bottom, in red) of the signed distance between the points on the xy plane (in blue) and a fixed disk (also represented on top, in gray) A more complicated set (top) and the graph of its signed distance function (bottom, in red).
Another way to generalize it is (even in 2D) to consider a variable distance, e.g. parametrized by another curve. [22] One can for example stroke (envelope) with an ellipse instead of circle [22] as it is possible for example in METAFONT. [26] An envelope of ellipses forming two general offset curves above and below a given curve
This is so the majority of time in each cycle is allotted for the work-intensive stroke. These quick-return mechanisms are often referred to as offset. [6] Examples of offset mechanisms include: Cutting machines; Package-moving devices; With offset mechanisms, it is very important to understand how and to what degree the offset affects the time ...
The denominator of this expression is the distance between P 1 and P 2. The numerator is twice the area of the triangle with its vertices at the three points, (x 0,y 0), P 1 and P 2. See: Area of a triangle § Using coordinates.
Other specific graphs that are unit distance graphs include the Petersen graph, [10] the Heawood graph, [11] the wheel graph (the only wheel graph that is a unit distance graph), [3] and the Moser spindle and Golomb graph (small 4-chromatic unit distance graphs). [12]
Kalai linked additional posts by Jordan Ellenberg and Noam Elkies, with Elkies and (separately) de Grey proposing a Polymath project to find non-4-colorable unit distance graphs with fewer vertices than the one in de Grey's construction. [6] As of 2021, the smallest known unit distance graph with chromatic number 5 has 509 vertices. [7]
In general, a distance matrix is a weighted adjacency matrix of some graph. In a network, a directed graph with weights assigned to the arcs, the distance between two nodes of the network can be defined as the minimum of the sums of the weights on the shortest paths joining the two nodes (where the number of steps in the path is bounded). [2]
An early graphing calculator was designed in 1921 by electrical engineer Edith Clarke. [1] [2] [3] The calculator was used to solve problems with electrical power line transmission. [4] Casio produced the first commercially available graphing calculator in 1985. Sharp produced its first graphing calculator in 1986, with Hewlett Packard ...