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  2. Parallel (geometry) - Wikipedia

    en.wikipedia.org/wiki/Parallel_(geometry)

    parallel, if they do not intersect in the plane, but converge to a common limit point at infinity (ideal point), or; ultra parallel, if they do not have a common limit point at infinity. [17] In the literature ultra parallel geodesics are often called non-intersecting. Geodesics intersecting at infinity are called limiting parallel.

  3. Slope - Wikipedia

    en.wikipedia.org/wiki/Slope

    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.

  4. Line (geometry) - Wikipedia

    en.wikipedia.org/wiki/Line_(geometry)

    For a convex quadrilateral with at most two parallel sides, the Newton line is the line that connects the midpoints of the two diagonals. [7] For a hexagon with vertices lying on a conic we have the Pascal line and, in the special case where the conic is a pair of lines, we have the Pappus line. Parallel lines are lines in the same plane that ...

  5. Hillslope evolution - Wikipedia

    en.wikipedia.org/wiki/Hillslope_evolution

    During most of the 20th century three models of hillslope evolution were widely diffused: slope decline, slope replacement and parallel slope retreat. Until the 1950s models of hillslope form evolution were central in geomorphology. The modern understanding is that the evolution of slopes is much more complex than the classical models of ...

  6. Line at infinity - Wikipedia

    en.wikipedia.org/wiki/Line_at_infinity

    Also, if any pair of lines do not intersect at a point on the line, then the pair of lines are parallel. Every line intersects the line at infinity at some point. The point at which the parallel lines intersect depends only on the slope of the lines, not at all on their y-intercept. In the affine plane, a line extends in two opposite directions.

  7. Arrangement of lines - Wikipedia

    en.wikipedia.org/wiki/Arrangement_of_lines

    However, parallel (non-crossing) pairs of lines are less restricted in hyperbolic line arrangements than in the Euclidean plane: in particular, the relation of being parallel is an equivalence relation for Euclidean lines but not for hyperbolic lines. [51] The intersection graph of the lines in a hyperbolic arrangement can be an arbitrary ...

  8. I'm a lifelong skier. There are 6 mistakes I always see ... - AOL

    www.aol.com/im-lifelong-skier-6-mistakes...

    I'm an experienced skier who has been to more than a dozen ski resorts around the world. I often see beginners make mistakes such as holding up lines, tailgating, and zooming down slopes. Wearing ...

  9. Parallel postulate - Wikipedia

    en.wikipedia.org/wiki/Parallel_postulate

    If the sum of the interior angles α and β is less than 180°, the two straight lines, produced indefinitely, meet on that side. In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry.