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Conical spiral with an archimedean spiral as floor projection Floor projection: Fermat's spiral Floor projection: logarithmic spiral Floor projection: hyperbolic spiral. In mathematics, a conical spiral, also known as a conical helix, [1] is a space curve on a right circular cone, whose floor projection is a plane spiral.
In general, a conical surface consists of two congruent unbounded halves joined by the apex. Each half is called a nappe, and is the union of all the rays that start at the apex and pass through a point of some fixed space curve. [2] Sometimes the term "conical surface" is used to mean just one nappe. [3]
A conic is the curve obtained as the intersection of a plane, called the cutting plane, with the surface of a double cone (a cone with two nappes).It is usually assumed that the cone is a right circular cone for the purpose of easy description, but this is not required; any double cone with some circular cross-section will suffice.
Coordinate surfaces of the conical coordinates. The constants b and c were chosen as 1 and 2, respectively. The red sphere represents r = 2, the blue elliptic cone aligned with the vertical z-axis represents μ=cosh(1) and the yellow elliptic cone aligned with the (green) x-axis corresponds to ν 2 = 2/3.
If we discard the origin, we can divide all coefficients by their sum to see that a conical combination is a convex combination scaled by a positive factor. In the plane, the conical hull of a circle passing through the origin is the open half-plane defined by the tangent line to the circle at the origin plus the origin.
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It is the shape, a cone frustum, that gives the washer its characteristic spring. The "Belleville" name comes from the inventor Julien Belleville who in Dunkerque, France, in 1867 patented a spring design which already contained the principle of the disc spring. [1] [3] The real inventor of Belleville washers is unknown.
On the other end, a cone shape is also spring-loaded and is used to locate the center of a previously drilled hole. This style of edge finder is considered to be the most accurate, and its accuracy can be further improved through the use of a collet. In proper setups, a repeatability of 0.0002 in (0.0051 mm) or better can be obtained.