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In geometry, Playfair's axiom is an axiom that can be used instead of the fifth postulate of Euclid (the parallel postulate): In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.[1] It is equivalent to Euclid's parallel postulate in the context of Euclidean geometry [2] and ...
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.
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 ...
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.
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.
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.
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