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In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a pair of compasses.
A truncated hexagon, t{6}, is a dodecagon, {12}, alternating two types (colors) of edges. An alternated hexagon, h{6}, is an equilateral triangle, {3}. A regular hexagon can be stellated with equilateral triangles on its edges, creating a hexagram. A regular hexagon can be dissected into six equilateral triangles by adding a center point.
Moser's worm problem (also known as mother worm's blanket problem) is an unsolved problem in geometry formulated by the Austrian-Canadian mathematician Leo Moser in 1966. The problem asks for the region of smallest area that can accommodate every plane curve of length 1.
In Tractatus de configurationibus qualitatum et motuum, [1] the 14th-century philosopher and mathematician Nicole Oresme introduces the concept of curvature as a measure of departure from straightness; for circles he has the curvature as being inversely proportional to the radius; and he attempts to extend this idea to other curves as a continuously varying magnitude.
Euclidean geometry has two fundamental types of measurements: angle and distance. The angle scale is absolute, and Euclid uses the right angle as his basic unit, so that, for example, a 45-degree angle would be referred to as half of a right angle. The distance scale is relative; one arbitrarily picks a line segment with a certain nonzero ...
Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, [a] which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental ...
A track geometry car (also known as a track recording car) is an automated track inspection vehicle on a rail transport system used to test several parameters of the track geometry without obstructing normal railroad operations. Some of the parameters generally measured include position, curvature, alignment of the track, smoothness, and the ...
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry . Analytic geometry is used in physics and engineering , and also in aviation , rocketry , space science , and spaceflight .