The color of amethyst has been demonstrated to result from substitution by irradiation of trivalent iron ( Fe < sup > 3 +</ sup >) for silicon in the structure, in the presence of trace elements of large ionic radius, and, to a certain extent, the amethyst color can naturally result from displacement of transition elements even if the iron concentration is low.

The CsCl structure is preferred because Cs < sup >+</ sup > has an ionic radius of 174 pm and 181 pm.

Solving the hydrostatic equation then leads to a model white dwarf which is a polytrope of index 3 / 2 and therefore has radius inversely proportional to the cube root of its mass, and volume inversely proportional to its mass.

Thus a circular geosynchronous orbit has a radius of 42164 km ; 42164 / 6378. 1

and the moment of inertia is larger when the body has an increased radius, the speed of rotation may be increased by moving the body into a compact shape, and reduced by opening out into a straight position.

Using the ratio test it is possible to show that this power series has an infinite radius of convergence, and so defines e < sup > z </ sup > for all complex z.

The transit method reveals the radius of a planet, and it has the benefit that it sometimes allows a planet's atmosphere to be investigated through spectroscopy.

On a geostationary view Alpha Centauri has a speed many times greater than c as the rim speed of an object moving in a circle is a product of the radius and angular speed.

The points on the two branches that are closest to each other are called the vertices ; they are the points where the curve has its smallest radius of curvature.

As of 2011, this island has a radius of roughly, and a high point of about above sea level, growing each year.

Lithium has a diagonal relationship with magnesium, an element of similar atomic and ionic radius.

A mandolin typically has a hollow wooden body with a tailpiece that holds one end of the strings, a floating bridge, a neck with a flat ( or slight radius ) fretted fingerboard, a nut, and mechanical tuning machines to accommodate metal strings.

With the aid of empirical correlation method, a divalent metallic radius of ( 0. 194 ± 0. 010 ) nm has been estimated.

Since it has only a tiny fraction of its parent's radius ( and therefore its moment of inertia is sharply reduced ), a neutron star is formed with very high rotation speed, and then gradually slows down.

Alternatively, 5 ml from a neutron star of radius 20 km radius ( average density ) has a mass of about 400 million metric tons, or about the mass of all humans .</ ref > The resulting force of gravity is so strong that if an object were to fall from a height of one meter it would only take one microsecond to hit the surface of the neutron star, and would do so at around 2000 kilometers per second, or 7. 2 million kilometers per hour.

* The particle horizon ( the boundary of the observable universe ) has a radius of about 14. 0 Gpc ( 45. 7 billion light-years ).

) In modern mathematics, this formula can be derived using integral calculus, i. e. disk integration to sum the volumes of an infinite number of circular disks of infinitesimally small thickness stacked centered side by side along the x axis from where the disk has radius r ( i. e. ) to where the disk has radius 0 ( i. e. ).

A great circle is a circle on the sphere that has the same center and radius as the sphere, and consequently divides it into two equal parts.

The curve has a radius that might be a short as on a child's board or as large as on a racer's board.

Tungsten has also been used in Dense Inert Metal Explosives, which use it as dense powder to reduce collateral damage while increasing the lethality of explosives within a small radius.

Felix Kopstein states that `` when the snake reaches its maturity it has already reached about its maximal length '', but goes on to cite the reticulate python as an exception, with maximum length approximately three times that at maturity.

It has been stated that settled cathodoluminescent phosphor screens may have a limiting resolution of 60 Af at high voltage values of approximately 20 Aj.

In contrast, the largest North American community north of the circle, Sisimiut ( Greenland ), has approximately 5, 000 inhabitants, while between Canada and the USA, Barrow, Alaska is the largest settlement with circa 4, 000 inhabitants.

Rovaniemi ( in Finland ), which lies slightly south of the line, has a population of approximately 58, 000, and is the largest settlement in the immediate vicinity of the Arctic Circle.

Argon has approximately the same solubility in water as oxygen and is 2. 5 times more soluble in water than nitrogen.

About half of Armenia's area of approximately has an elevation of at least, and only 3 % of the country lies below.

For example, the full moon has an angular diameter of approximately 0. 5 °, when viewed from Earth.

This has cooled it down to approximately 1 K, as deduced by astronomical observation, which is the lowest natural temperature ever recorded.

Archaeology has uncovered remains at the site dating to approximately 3000 BC.

It has been estimated that during his entire career Aalto designed over 500 individual buildings, approximately 300 of which were built, the vast majority of which are in Finland.

Although there has been considerable revision of this phylum ( the order Haemosporidia now has 17 genera rather than 9 ) it seems likely these numbers are still approximately correct.

Aon has approximately 600 offices worldwide, serving 120 countries with 61, 000 employees.

Starting in approximately the 1970s into the present day analytical chemistry has progressively become more inclusive of biological questions ( bioanalytical chemistry ), whereas it had previously been largely focused on inorganic or small organic molecules.

Altair possesses an extremely rapid rate of rotation ; it has a rotational period of approximately 9 hours.

The human brain has been estimated to contain approximately 100 trillion synapses ; even the brain of a fruit fly contains several million.

At room temperature and pressure, barium has a body-centered cubic structure, with a barium – barium distance of 503 picometers, expanding with heating at a rate of approximately 1. 8 /° C.

Loving-kindness living: Boaz and Ruth are models of an altruism for which the word " loving-kindness " has been coined ( approximately translating Hebrew hesed ).

While the brown bear's range has shrunk and it has faced local extinctions, it remains listed as a least concern species by the IUCN with a total population of approximately 200, 000.

More than a million pre-college students around the world use BJU textbooks, and the Press has approximately 2, 500 titles in print.

As of the early 21st century, Christianity has approximately 2. 2 billion adherents.

Chad has a total of 33, 400 km of roads of which approximately 500 km are paved.

The privatized national pension system ( AFP ) has encouraged domestic investment and contributed to an estimated total domestic savings rate of approximately 21 % of GDP.