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  2. Distance between two parallel lines - Wikipedia

    en.wikipedia.org/wiki/Distance_between_two...

    the distance between the two lines is the distance between the two intersection points of these lines with the perpendicular line y = − x / m . {\displaystyle y=-x/m\,.} This distance can be found by first solving the linear systems

  3. Buffon's needle problem - Wikipedia

    en.wikipedia.org/wiki/Buffon's_needle_problem

    The farthest this end of the needle can move away from this line horizontally in its region is t. The probability that the farthest end of the needle is located no more than a distance l cos θ away from the line (and thus that the needle crosses the line) out of the total distance t it can move in its region for 0 ≤ θ ≤ ⁠ π / 2 ⁠ is ...

  4. Parallel (geometry) - Wikipedia

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

    Line art drawing of parallel lines and curves. In geometry, parallel lines are coplanar infinite straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. Parallel curves are curves that do not touch each other or intersect and keep a fixed minimum distance. In three ...

  5. 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]

  6. 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 ...

  7. Pascal's theorem - Wikipedia

    en.wikipedia.org/wiki/Pascal's_theorem

    In projective geometry, Pascal's theorem (also known as the hexagrammum mysticum theorem, Latin for mystical hexagram) states that if six arbitrary points are chosen on a conic (which may be an ellipse, parabola or hyperbola in an appropriate affine plane) and joined by line segments in any order to form a hexagon, then the three pairs of ...

  8. 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

  9. Arrangement of lines - Wikipedia

    en.wikipedia.org/wiki/Arrangement_of_lines

    The number of vertices is smaller when some lines are parallel, or when some vertices are crossed by more than two lines. [4] An arrangement can be rotated, if necessary, to avoid axis-parallel lines. After this step, each ray that forms an edge of the arrangement extends either upward or downward from its endpoint; it cannot be horizontal.

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