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The grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal. It is a special case of the slope, where zero indicates horizontality. A larger number indicates higher or steeper degree of "tilt".
Remark 1: The 2-points–2-tangents property of a parabola is an affine version of the 3-point degeneration of Pascal's theorem. Remark 2: The 2-points–2-tangents property should not be confused with the following property of a parabola, which also deals with 2 points and 2 tangents, but is not related to Pascal's theorem.
F 8 is a degree-three field extension of F 2, so the points of the Fano plane may be identified with F 8 ∖ {0}. The symmetry group may be written PGL(3, 2) = Aut(P 2 F 2). Similarly, PSL(2, 7) = Aut(P 1 F 7). There is a relation between the underlying objects, P 2 F 2 and P 1 F 7 called the Cat's Cradle map. Color the seven lines of the Fano ...
The golden ratio φ and its negative reciprocal −φ −1 are the two roots of the quadratic polynomial x 2 − x − 1. The golden ratio's negative −φ and reciprocal φ −1 are the two roots of the quadratic polynomial x 2 + x − 1. The golden ratio is also an algebraic number and even an algebraic integer. It has minimal polynomial
March equinox. The March equinox[ 7][ 8] or northward equinox[ 9] is the equinox on the Earth when the subsolar point appears to leave the Southern Hemisphere and cross the celestial equator, heading northward as seen from Earth. The March equinox is known as the vernal equinox (spring equinox) in the Northern Hemisphere and as the autumnal ...
If, for example, the (absolute) slope at point BB in the diagram is equal to 2, to produce one more packet of butter, the production of 2 guns must be sacrificed. If at AA , the marginal opportunity cost of butter in terms of guns is equal to 0.25, the sacrifice of one gun could produce four packets of butter, and the opportunity cost of guns ...
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.
This also means that the slope depends on the units of measurement and will change if the units change (e.g., dollars per pound versus dollars per ounce) while the elasticity is a simple number, independent of the units (e.g., 1.2). This is a major advantage of elasticities.