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Doubling the cube is the construction, using only a straightedge and compass, of the edge of a cube that has twice the volume of a cube with a given edge. This is impossible because the cube root of 2, though algebraic, cannot be computed from integers by addition, subtraction, multiplication, division, and taking square roots.
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 ...
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land' and μέτρον (métron) 'a measure') [1] is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. [2]
A straightedge or straight edge is a tool used for drawing straight lines, or checking their straightness. If it has equally spaced markings along its length, it is usually called a ruler . Straightedges are used in the automotive service and machining industry to check the flatness of machined mating surfaces.
Straight edge grew out of hardcore punk in the late 1970s and early 1980s and was partly characterized by shouted rather than sung vocals. [16] Straight-edge individuals of this early era often associated with the original punk ideals such as individualism, disdain for work and school, and live-for-the-moment attitudes. [9]
Projective geometry can also be seen as a geometry of constructions with a straight-edge alone, excluding compass constructions, common in straightedge and compass constructions. [2] As such, there are no circles, no angles, no measurements, no parallels, and no concept of intermediacy (or "betweenness"). [3]
However, the universe could be finite, even if its curvature is flat. An easy way to understand this is to consider two-dimensional examples, such as video games where items that leave one edge of the screen reappear on the other. The topology of such games is toroidal and the geometry is flat. Many possible bounded, flat possibilities also ...