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  2. Nine dots puzzle - Wikipedia

    en.wikipedia.org/wiki/Nine_dots_puzzle

    Thus a single line can be drawn connecting all nine dots—which would appear as three lines in parallel on the paper, when flattened out. [18] It is also possible to fold the paper flat , or to cut the paper into pieces and rearrange it, in such a way that the nine dots lie on a single line in the plane (see fold-and-cut theorem ).

  3. Parallel (geometry) - Wikipedia

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

    Since these are equivalent properties, any one of them could be taken as the definition of parallel lines in Euclidean space, but the first and third properties involve measurement, and so, are "more complicated" than the second. Thus, the second property is the one usually chosen as the defining property of parallel lines in Euclidean geometry ...

  4. 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 ...

  5. 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 ...

  6. 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.

  7. 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]

  8. Geometry - Wikipedia

    en.wikipedia.org/wiki/Geometry

    A curve is a 1-dimensional object that may be straight (like a line) or not; curves in 2-dimensional space are called plane curves and those in 3-dimensional space are called space curves. [ 52 ] In topology, a curve is defined by a function from an interval of the real numbers to another space. [ 49 ]

  9. 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 .

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