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Integer-distance straight line embeddings are known to exist for cubic graphs. [ 3 ] Sachs (1983) raised the question of whether every graph with a linkless embedding in three-dimensional Euclidean space has a linkless embedding in which all edges are represented by straight line segments, analogously to Fáry's theorem for two-dimensional ...
The Simson line LN (red) of the triangle ABC with respect to point P on the circumcircle. In geometry, given a triangle ABC and a point P on its circumcircle, the three closest points to P on lines AB, AC, and BC are collinear. [1] The line through these points is the Simson line of P, named for Robert Simson. [2]
A plumb bob, plumb bob level, or plummet, is a weight, usually with a pointed tip on the bottom, suspended from a string and used as a vertical direction as a reference line, or plumb-line. It is a precursor to the spirit level and used to establish a vertical datum. It is typically made of stone, wood, or lead, but can also be made of other ...
The line may be straight or curved, but must not touch or cross itself or any other line. The new spot cannot be placed on top of one of the endpoints of the new line. Thus the new spot splits the line into two shorter lines. No spot may have more than three lines attached to it.
For each pair of lines, there can be only one cell where the two lines meet at the bottom vertex, so the number of downward-bounded cells is at most the number of pairs of lines, () /. Adding the unbounded and bounded cells, the total number of cells in an arrangement can be at most n ( n + 1 ) / 2 + 1 {\displaystyle n(n+1)/2+1} . [ 5 ]
WASHINGTON — With Donald Trump heading back to the White House, a growing band of younger, more energetic House Democrats is challenging seasoned veterans for powerful congressional posts ...
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