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  2. Parallel (geometry) - Wikipedia

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

    the distance between the two lines can be found by locating two points (one on each line) that lie on a common perpendicular to the parallel lines and calculating the distance between them. Since the lines have slope m , a common perpendicular would have slope −1/ m and we can take the line with equation y = − x / m as a common perpendicular.

  3. Concurrent lines - Wikipedia

    en.wikipedia.org/wiki/Concurrent_lines

    The de Longchamps point is the point of concurrence of several lines with the Euler line. Three lines, each formed by drawing an external equilateral triangle on one of the sides of a given triangle and connecting the new vertex to the original triangle's opposite vertex, are concurrent at a point called the first isogonal center .

  4. Non-Euclidean geometry - Wikipedia

    en.wikipedia.org/wiki/Non-Euclidean_geometry

    Simply replacing the parallel postulate with the statement, "In a plane, given a point P and a line l not passing through P, all the lines through P meet l", does not give a consistent set of axioms. This follows since parallel lines exist in absolute geometry, [21] but this statement says that there are no parallel lines. This problem was ...

  5. 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 ...

  6. Convergence of parallel lines - Wikipedia

    en.wikipedia.org/wiki/Convergence_of_parallel_lines

    Convergence of parallel lines can refer to: In everyday life, the vanishing point phenomenon; Non-Euclidean geometry in which Euclid's parallel postulate does not hold

  7. Parallel projection - Wikipedia

    en.wikipedia.org/wiki/Parallel_projection

    Parallel lines are mapped on parallel lines, or on a pair of points (if they are parallel to ). The ratio of the length of two line segments on a line stays unchanged. As a special case, midpoints are mapped on midpoints. The length of a line segment parallel to the projection plane remains unchanged. The length of any line segment is shortened ...

  8. Café wall illusion - Wikipedia

    en.wikipedia.org/wiki/Café_wall_illusion

    The café wall illusion (also known as the Münsterberg illusion or the kindergarten illusion) is a geometrical-optical illusion in which the parallel straight dividing lines between staggered rows with alternating dark and light rectangles (such as bricks or tiles) appear to be sloped, not parallel as they really are.

  9. Parallel curve - Wikipedia

    en.wikipedia.org/wiki/Parallel_curve

    A parallel of a curve is the envelope of a family of congruent circles centered on the curve. It generalises the concept of parallel (straight) lines. It can also be defined as a curve whose points are at a constant normal distance from a given curve. [1]