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Conical Helix
In mathematics, a conical spiral, also known as a conical helix, is a space curve on a right circular cone, whose Orthographic projection, floor projection is a plane spiral. If the floor projection is a logarithmic spiral, it is called ''conchospiral'' (from conch). Parametric representation In the x-y-plane a spiral with parametric representation : x=r(\varphi)\cos\varphi \ ,\qquad y=r(\varphi)\sin\varphi a third coordinate z(\varphi) can be added such that the space curve lies on the cone with equation \;m^2(x^2+y^2)=(z-z_0)^2\ ,\ m>0\; : * x=r(\varphi)\cos\varphi \ ,\qquad y=r(\varphi)\sin\varphi\ , \qquad \color \ . Such curves are called conical spirals. They were known to Pappos. Parameter m is the slope of the cone's lines with respect to the x-y-plane. A conical spiral can instead be seen as the orthogonal projection of the floor plan spiral onto the cone. Examples : 1) Starting with an ''archimedean spiral'' \;r(\varphi)=a\varphi\; gives the conical spiral ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat's Spiral
A Fermat's spiral or parabolic spiral is a plane curve with the property that the area between any two consecutive full turns around the spiral is invariant. As a result, the distance between turns grows in inverse proportion to their distance from the spiral center, contrasting with the Archimedean spiral (for which this distance is invariant) and the logarithmic spiral (for which the distance between turns is proportional to the distance from the center). Fermat spirals are named after Pierre de Fermat. Their applications include curvature continuous blending of curves, modeling phyllotaxis, plant growth and the shapes of certain spiral galaxy, spiral galaxies, and the design of variable capacitors, solar power reflector arrays, and cyclotrons. Coordinate representation Polar The representation of the Fermat spiral in polar coordinates is given by the equation r=\pm a\sqrt for . The parameter a is a scaling factor affecting the size of the spiral but not its shape. The tw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neptunea - Links&rechts Gewonden
''Neptunea'' is a genus of large sea snails, marine gastropod mollusks in the subfamily Neptuneinae of the family Buccinidae, the true whelks.Bouchet, P.; Gofas, S. (2010). ''Neptunea'' Röding, 1798. In: Bouchet, P.; Gofas, S.; Rosenberg, G. (2010) World Marine Mollusca database. Accessed through: World Register of Marine Species at http://www.marinespecies.org/aphia.php?p=taxdetails&id=137710 on 2010-11-02 Species According to the World Register of Marine Species (WoRMS), the following species with valid names are included within the genus ''Neptunea'': *'' Neptunea acutispiralis'' *'' Neptunea alabaster'' *'' Neptunea alexeyevi'' *'' Neptunea amianta'' *'' Neptunea angulata'' *'' Neptunea antarctocostata'' *'' Neptunea antiqua'' *'' Neptunea arthritica'' *'' Neptunea aurigena'' *'' Neptunea behringiana'' *'' Neptunea borealis'' *'' Neptunea bulbacea'' *'' Neptunea communis'' *'' Neptunea constricta'' *'' Neptunea contraria'' *'' Neptunea convexa'' *'' Nep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-similarity
In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity is a typical property of fractals. Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant; it can be continually magnified 3x without changing shape. The non-trivial similarity evident in fractals is distinguished by their fine structure, or detail on arbitrarily small scales. As a counterexample, whereas any portion of a straight line may resemble the whole, further detail is not revealed. Peitgen ''et al.'' explain the concept as such: Since mathematically, a fractal may sho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
