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The bottom example depicts a real lens with spherical surfaces, which produces spherical aberration: The different rays do not meet after the lens in one focal point. The further the rays are from the optical axis, the closer to the lens they intersect the optical axis (positive spherical aberration). (Drawing is exaggerated.)
The intersection of two convex cones in the same vector space is again a convex cone, but their union may fail to be one. The class of convex cones is also closed under arbitrary linear maps . In particular, if C {\displaystyle C} is a convex cone, so is its opposite − C {\displaystyle -C} , and C ∩ − C {\displaystyle C\cap -C} is the ...
Convex fluting was probably intended to imitate plant forms. [2] Minoan and Mycenaean architecture used both, but Greek and Roman architecture used the concave style almost exclusively. [3] Fluting was very common in formal ancient Greek architecture, and compulsory in the Greek Doric order. It was optional for the Ionic and Corinthian orders ...
In geometry, the convex hull, convex envelope or convex closure [1] of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset.
A: The bottom of a concave meniscus. B: The top of a convex meniscus. In physics (particularly fluid statics), the meniscus (pl.: menisci, from Greek ' crescent ') is the curve in the upper surface of a liquid close to the surface of the container or another object, produced by surface tension.
Convex analysis - the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex minimization. Convex combination - a linear combination of points where all coefficients are non-negative and sum to 1. All convex combinations are within the convex hull of the given points.
The chamber is connected by a second pipe to the bottom of the central column, where a hole in the column exposes the pipe to (the contents of) the bowl of the cup. [ 1 ] When the cup is filled, liquid rises through the second pipe up to the chamber at the top of the central column, following Pascal's principle of communicating vessels .
Convex geometry is a relatively young mathematical discipline. Although the first known contributions to convex geometry date back to antiquity and can be traced in the works of Euclid and Archimedes, it became an independent branch of mathematics at the turn of the 20th century, mainly due to the works of Hermann Brunn and Hermann Minkowski in dimensions two and three.