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The Moulton plane.Lines sloping down and to the right are bent where they cross the y-axis.. In incidence geometry, the Moulton plane is an example of an affine plane in which Desargues's theorem does not hold.
The slope number of a graph of maximum degree d is clearly at least ⌈ / ⌉, because at most two of the incident edges at a degree-d vertex can share a slope. More precisely, the slope number is at least equal to the linear arboricity of the graph, since the edges of a single slope must form a linear forest, and the linear arboricity in turn is at least ⌈ / ⌉.
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
l = slope length α = angle of inclination. The grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line is either the elevation angle of that surface to the horizontal or its tangent. It is a special case of the slope, where zero indicates horizontality. A ...
the slope field is an array of slope marks in the phase space (in any number of dimensions depending on the number of relevant variables; for example, two in the case of a first-order linear ODE, as seen to the right). Each slope mark is centered at a point (,,, …,) and is parallel to the vector
Sutherland points out that in the early chapters Trollope describes the Proudies as intending to spend as much time as possible in London, leaving the field clear for Slope to act on his own in Barchester with the action easily contained in a single-volume novel: in Chapter IV, Slope thinks to himself that, in the Proudies' anticipated absences ...
Slope mass rating (SMR) is a rock mass classification scheme developed by Manuel Romana [1] [2] [3] to describe the strength of an individual rock outcrop or slope. The system is founded upon the more widely used RMR scheme, [4] which is modified with quantitative guidelines to the rate the influence of adverse joint orientations (e.g. joints dipping steeply out of the slope).
Slope stability refers to the condition of inclined soil or rock slopes to withstand or undergo movement; the opposite condition is called slope instability or slope failure. The stability condition of slopes is a subject of study and research in soil mechanics , geotechnical engineering , and engineering geology .