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  2. 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.

  3. Buffon's needle problem - Wikipedia

    en.wikipedia.org/wiki/Buffon's_needle_problem

    The aneedle lies across a line, while the bneedle does not. In probability theory, Buffon's needle problemis a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon:[1] Suppose we have a floormade of parallelstrips of wood, each the same width, and we drop a needleonto the floor.

  4. Parallel postulate - Wikipedia

    en.wikipedia.org/wiki/Parallel_postulate

    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. It states that, in two-dimensional geometry: If a line segment intersects two straight lines forming two interior angles on the same side that are less than two right ...

  5. Affine geometry - Wikipedia

    en.wikipedia.org/wiki/Affine_geometry

    e. In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting" [ 1 ][ 2 ]) the metric notions of distance and angle. As the notion of parallel lines is one of the main properties that is independent of any metric, affine geometry is often considered as the study of parallel lines.

  6. Intercept theorem - Wikipedia

    en.wikipedia.org/wiki/Intercept_theorem

    Intercept theorem. The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a common starting point are intercepted by a pair of parallels.

  7. Vanishing point - Wikipedia

    en.wikipedia.org/wiki/Vanishing_point

    A vanishing point is a point on the image plane of a perspective rendering where the two-dimensional perspective projections of mutually parallel lines in three-dimensional space appear to converge. When the set of parallel lines is perpendicular to a picture plane, the construction is known as one-point perspective, and their vanishing point ...

  8. Line (geometry) - Wikipedia

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

    e. In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature, an idealization of such physical objects as a straightedge, a taut string, or a ray of light. Lines are spaces of dimension one, which may be embedded in spaces of dimension two, three, or higher.

  9. Poncelet–Steiner theorem - Wikipedia

    en.wikipedia.org/wiki/Poncelet–Steiner_theorem

    To draw the parallel (h) to a diameter g through any given point P. Chose auxiliary point C anywhere on the straight line through B and P outside of BP. (Steiner) In the branch of mathematics known as Euclidean geometry, the Poncelet–Steiner theorem is one of several results concerning compass and straightedge constructions having additional restrictions imposed on the traditional rules.

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