All articles A–Z
519,064 articles
Sphere of influence
A sphere of influence is a region where a powerful country dominates weaker states' foreign policies while excluding rival great powers, seen in imperial China after 1870.
Sphere packing
Sphere packing is the mathematical problem of arranging identical non-overlapping balls to maximize the fraction of space covered, known as the density, solved in dimensions 8 and 24 in 2016.
Sphere packing in dimensions 8 and 24
Sphere packing in dimensions 8 and 24 was solved in 2016 by Maryna Viazovska and colleagues, who proved the E₈ and Leech lattices are densest.
Sphere shaping precoding
Sphere shaping precoding is transmit-side signal processing that picks the codeword whose energy lies inside a sphere, pre-canceling interference in multiuser MIMO downlinks and in probabilistic amplitude shaping.
SPHERES
SPHERES is a testbed of three bowling-ball-sized free-flying satellites developed by MIT that has operated inside the International Space Station since 2006, demonstrating formation flying and autonomous docking in microgravity.
SPHEREx
SPHEREx is a NASA astrophysics space telescope launched in March 2025 that is conducting the first all-sky near-infrared spectral survey, imaging the entire sky in 102 infrared colors.
Spherical aberration
Spherical aberration is an optical defect in which light rays passing through different zones of a lens or mirror focus at different points, imaging one object point as a blurred disk.
Spherical cap
A spherical cap, also called a spherical dome, is the portion of a sphere cut off by a plane; when the plane passes through the center it is a hemisphere.
Spherical coordinate system
The spherical coordinate system, also called spherical coordinates, is a three-dimensional coordinate system that locates a point by its distance from an origin and two angles.
Spherical cow
The spherical cow, or spherical cow in a vacuum, is a humorous metaphor from a physics joke for the highly simplified models scientists build from complex real-world problems.
Spherical Earth
Spherical Earth, also called the sphericity of the Earth, is the model of Earth's figure as a sphere, argued from antiquity and refined into an oblate spheroid.
Spherical harmonics
Spherical harmonics, also written Ylm, are eigenfunctions of the Laplace-Beltrami operator on the sphere, introduced by Laplace in 1782 as a spherical analog of Fourier series.
Spherical measure
Spherical measure is a mathematical term for either the surface measure on the unit sphere, used for spherical averages, or a ball-covering outer measure close to Hausdorff measure.
Spherical mirror
A spherical mirror is a mirror whose reflecting surface forms part of a sphere, either concave or convex, used in geometric optics to form images of objects.
Spherical model
The spherical model is an exactly solvable model of a ferromagnet in statistical mechanics, introduced by Berlin and Kac in 1952 as a continuous-spin generalization of the Ising model.
Spherical multipole moments
Spherical multipole moments are the coefficients of the expansion of a potential, such as an electric or magnetic field, in powers of distance and spherical harmonics.
Spherical nucleic acid
Spherical nucleic acid (SNA) nanoparticles are nanostructures with a nanoparticle core surrounded by a dense shell of radially oriented DNA or RNA strands, first synthesized in 1996.
Spherical robot (manipulator)
A spherical robot, also called a polar robot, is an industrial manipulator with two rotary joints and one linear joint, used for welding and die casting.
Spherical tokamak
The spherical tokamak, also known as the spherical torus, is a compact fusion device with a cored-apple plasma shape that operates at unusually high plasma pressure.
Spherical Tokamak for Energy Production
Spherical Tokamak for Energy Production (STEP) is a UK Atomic Energy Authority program to build a prototype fusion power plant at West Burton, Nottinghamshire, by the 2040s.
Spherical trigonometry
Spherical trigonometry, or spherical trig, is the branch of trigonometry that deals with triangles drawn on a sphere, the basis of great-circle and celestial navigation.
Spherical wave
A spherical wave is a wave whose surfaces of constant phase are concentric spheres expanding from a point source, its amplitude decaying as 1/r, following the inverse-square law.
Spherical wrist
A spherical wrist is a robot wrist mechanism whose three revolute joint axes intersect at a single point, the wrist center, as in the Stanford manipulator.
Sphero (toy)
Sphero is a smartphone-controlled spherical robot toy first launched in 2011 by Orbotix, a Boulder, Colorado company that later took the Sphero name and expanded into educational robotics.
Spherocytosis
Hereditary spherocytosis (Minkowski-Chauffard disease), congenital spherocytic hemolytic anemia: inherited red cell membrane protein defects (ANK1, spectrin, band 3) causing spherical fragile red cells, anemia, jaundice, splenomegaly; treated by splenectomy.
Spheroid
A spheroid, also called an ellipsoid of revolution, is a quadric surface made by rotating an ellipse, giving oblate or prolate shapes like Earth or a rugby ball.
Spheroid body myopathy
Spheroid body myopathy, a rare autosomal dominant myofibrillar myopathy (OMIM 609200, ORPHA 268129) caused by MYOT myotilin mutations, marked by proximal weakness and spheroid body inclusions on muscle biopsy.
Spheroidal carbonaceous particles
Spheroidal carbonaceous particles are carbon-rich fly-ash particles produced only by industrial coal and oil combustion, which accumulate in sediments as unambiguous markers of fossil-fuel pollution.
Spheroidal wave functions
Spheroidal wave functions are the special functions that arise when the wave equation is separated in spheroidal coordinates, reducing to Legendre functions when the spheroidal parameter vanishes.
Spheromak
A spheromak is a compact toroid of magnetized plasma that holds both poloidal and toroidal magnetic fields from internal currents, studied for compact magnetic confinement fusion.