( 3 ) For anionics, these micelles appear to be roughly spherical assemblages in which the hydrocarbon tails come together so that the polar groups ( the ionized ends ) face outward towards the aqueous continuous phase.

For example, the allotropes of carbon include diamond ( where the carbon atoms are bonded together in a tetrahedral lattice arrangement ), graphite ( where the carbon atoms are bonded together in sheets of a hexagonal lattice ), graphene ( single sheets of graphite ), and fullerenes ( where the carbon atoms are bonded together in spherical, tubular, or ellipsoidal formations ).

For the spherical Bessel functions the orthogonality relation is:

For example, carbon can be found as diamond, which has a tetrahedral structure around each carbon atom ; graphite, which has layers of carbon atoms with a hexagonal structure stacked on top of each other ; graphene, which is a single layer of graphite that is incredibly strong ; fullerenes, which have nearly spherical shapes ; and carbon nanotubes, which are tubes with a hexagonal structure ( even these may differ from each other in electrical properties ).

For example: some early medieval manuscripts of Macrobius include maps of the Earth, including the antipodes, zonal maps showing the Ptolemaic climates derived from the concept of a spherical Earth and a diagram showing the Earth ( labeled as globus terrae, the sphere of the Earth ) at the center of the hierarchically ordered planetary spheres.

( For example, in spherical coordinates, let radius r go to R² / r where R is the Earth's radius.

For a four-dimensional spherical uncharged black hole, the deformation of the horizon is similar to the type of deformation which describes the emission and absorption of particles on a string-theory world sheet.

For this reason spherical reference surfaces are frequently used in mapping programs.

For example a spherical polygon is drawn on the surface of a sphere, and its sides are arcs of great circles.

For this reason, the sphere appears in nature: for instance bubbles and small water drops are roughly spherical, because the surface tension locally minimizes surface area.

For example, the sum of the interior angles of a spherical triangle exceeds 180 degrees.

For Sweden men's national ice hockey team, the home arena is Ericsson Globe, one of the largest spherical building in the world, but it is also hosting concerts and other events.

For spherical symmetry there is no such distinction, it implies planes of reflection.

For this reason, the type of traversable wormhole they proposed, held open by a spherical shell of exotic matter, is referred to as a Morris-Thorne wormhole.

For purposes of spherical astronomy, which is concerned only with the directions to objects, it makes no difference whether this is actually the case, or if it is the Earth which rotates while the celestial sphere stands still.

For observers near sea level the difference between this geometrical horizon ( which assumes a perfectly flat, infinite ground plane ) and the true horizon ( which assumes a spherical Earth surface ) is imperceptible to the naked eye ( but for someone on a 1000-meter hill looking out to sea the true horizon will be about a degree below a horizontal line ).

For example, a polished spherical electrode 30 cm in diameter immersed in air at STP ( which has a breakdown voltage of about 30 kV / cm ) could be expected to develop a maximum voltage of about 450 kV.

For low values of the Reynolds number (< 1 ), which is true of most aerosol motion, Stokes ' law describes the force of resistance on a solid spherical particle in a fluid.

For example, an asymmetrical asteroid's light curve generally has more pronounced peaks, while a more spherical object's light curve will be flatter.

For example, the van der Waals interaction energy between spherical bodies of radii R < sub > 1 </ sub > and R < sub > 2 </ sub > and with smooth surfaces was approximated in 1937 by Hamaker ( using London's famous 1937 equation for the dispersion interaction energy between atoms / molecules as the starting point ) by:

For instance, a plane triangle has an angle sum of 180 °; an octant is a spherical triangle with three right angles, so its angle sum is 270 °, and its angle excess is 90 °.

For spherical and hyperbolic spatial geometries, the curvature gives a scale ( either by using the radius of curvature or its inverse ), a fact noted by Carl Friedrich Gauss in an 1824 letter to Franz Taurinus.

For a spherical mass of uniform density, the gravitational binding energy U is given by the formula

For a perfectly spherical droplet the apparent weight can be written as:

For weeks after the battle, bodies washed up along the Egyptian coast, decaying slowly in the intense dry heat.

For example, the rules of tournament bridge are governed by the World Bridge Federation, and by local bodies in various countries such as the American Contract Bridge League in the U. S., and the English Bridge Union in England.

For the study of the mechanical behavior of solids and fluids these are assumed to be continuous bodies, which means that the matter fills the entire region of space it occupies, despite the fact that matter is made of atoms, has voids, and is discrete.

For example, hundreds of individuals were found in Lake Callabonna with well-preserved lower bodies but crushed and distorted heads.

For these, asha was the course of everything observable, the motion of the planets and astral bodies, the progression of the seasons, the pattern of daily nomadic herdsman life, governed by regular metronomic events such as sunrise and sunset.

For that reason both types of bodies have advisory councils which have advisory and co-decision authorities.

For the most part, car bodies were now manufactured at Elizabeth, South Australia, with engines as before, confined to the Fishermans Bend plant in Port Melbourne, Victoria.

For example, some invertebrates are attracted to dead bodies.

For example, suppose there are two bodies of equal mass, one stationary and one approaching the other at a speed ( as in the figure ).

For small bodies, destabilization is actually far more likely.

For the case where the masses of two bodies are comparable, an exact Newtonian solution is still available, and qualitatively similar to the case of dissimilar masses, by centering the coordinate system on the center of mass of the two.

For smaller bodies particularly, light and stellar wind can cause significant perturbations to the attitude and direction of motion of the body, and over time can be significant.

For microscopic bodies, the extension of the system is much smaller than the coherence length, which gives rise to long-range entanglement and other nonlocal phenomena that are characteristic of quantum systems.

For two bodies known to be at the same temperature, if one seeks to decide if they will be in thermal equilibrium when put into thermal contact, it is not necessary to actually bring them into contact and measure any changes of their observable properties in time.

For example, in Israel marriage is governed by officially recognized religious bodies who each provide marriage services for their respected adherents, yet no form of civil marriage ( free of religion, for atheists, for example ) exists nor marriage by non recognized minority religions.

For that reason, the quartering of troops was cited as a grievance in the United States Declaration of Independence: < nowiki >< nowiki ></ nowiki > has combined with others to subject us to a jurisdiction foreign to our constitution, and unacknowledged by our laws ; giving his Assent to their Acts of pretended Legislation: ... For Quartering large bodies of armed troops among us.

" For my part ," he says, " I take my stand in human anatomy "; elsewhere he insists upon " the necessity, in each particular case, of an intelligent designing mind for the contriving and determining of the forms which organized bodies bear.

For example, an object with a mass of one kilogram has a weight of about 9. 8 newtons on the surface of the Earth, about one-sixth as much on the Moon, and very nearly zero when in deep space far away from all bodies imparting gravitational influence.

For example, colonies routinely find the maximum distance from all colony entrances to dispose of dead bodies.

For orbital spaceflights, spacecraft enter closed orbits around the Earth or around other celestial bodies.

For government agencies, external stakeholders include tax-payers, higher-level government agencies, and international lending bodies such as the International Monetary Fund, the World Bank, various economic agencies of the United Nations, and development banks.

For example, at a public meeting with VeriSign to air technical concerns about SiteFinder, numerous people, active in the IETF and other technical bodies, explained how they were surprised by VeriSign's changing the fundamental behavior of a major component of Internet infrastructure, not having obtained the customary consensus.

For example, the long-finned pilot whale secretes an enzymatic gel that rests on the outer surface of this animal and helps prevent other organisms from establishing colonies on the surface of these whales ' bodies.