Concentric objects

In the Euclidean plane, two circles that are concentric necessarily have different radii from each other.{{citation|title=Surveyor Reference Manual|first1=George M.|last1=Cole|first2=Andrew L.|last2=Harbin|publisher=www.ppi2pass.com|year=2009|isbn=9781591261742|url=https://books.google.com/books?id=bFun4fjl4P0C&pg=SA2-PA6|at=§2, p. 6}}.

However, circles in three-dimensional space may be concentric, and have the same radius as each other, but nevertheless be different circles. For example, two different meridians of a terrestrial globe are concentric with each other and with the globe of the earth (approximated as a sphere). More generally, every two great circles on a sphere are concentric with each other and with the sphere.{{citation|title=The American universal geography;: or, A view of the present state of all the kingdoms, states, and colonies in the known world, Volume 1|first=Jedidiah|last=Morse|edition=6th|publisher=Thomas & Andrews|year=1812|page=19|url=https://books.google.com/books?id=J_5AAAAAcAAJ&pg=PA19}}.

By Euler's theorem in geometry on the distance between the circumcenter and incenter of a triangle, two concentric circles (with that distance being zero) are the circumcircle and incircle of a triangle if and only if the radius of one is twice the radius of the other, in which case the triangle is equilateral.{{citation |author=Dragutin Svrtan and Darko Veljan |title=Non-Euclidean versions of some classical triangle inequalities |publisher=Forum Geometricorum |volume=12 |year=2012 |pages=197–209 |url=http://forumgeom.fau.edu/FG2012volume12/FG201217index.html |website=forumgeom.fau.edu}}{{rp|p. 198}}

The circumcircle and the incircle of a regular n-gon, and the regular n-gon itself, are concentric. For the circumradius-to-inradius ratio for various n, see Bicentric polygon#Regular polygons. The same can be said of a regular polyhedron's insphere, midsphere and circumsphere.

The region of the plane between two concentric circles is an annulus, and analogously the region of space between two concentric spheres is a spherical shell.{{citation|title=New Horizons in Geometry|volume=47|series=Dolciani Mathematical Expositions|first=Tom|last=Apostol|author-link=Tom Apostol|publisher=Mathematical Association of America|year=2013|isbn=9780883853542|page=140|url=https://books.google.com/books?id=PUVvwfjhjvMC&pg=PA140}}.

For a given point c in the plane, the set of all circles having c as their center forms a pencil of circles. Each two circles in the pencil are concentric, and have different radii. Every point in the plane, except for the shared center, belongs to exactly one of the circles in the pencil. Every two disjoint circles, and every hyperbolic pencil of circles, may be transformed into a set of concentric circles by a Möbius transformation.{{citation|title=Complex Numbers and Geometry|series=MAA Spectrum|first=Liang-shin|last=Hahn|publisher=Cambridge University Press|year=1994|isbn=9780883855102|page=142|url=https://books.google.com/books?id=s3nMMkPEvqoC&pg=PA142}}.{{citation|title=Geometry|first1=David A.|last1=Brannan|first2=Matthew F.|last2=Esplen|first3=Jeremy J.|last3=Gray|publisher=Cambridge University Press|year=2011|isbn=9781139503709|pages=320–321|url=https://books.google.com/books?id=UlrmKjIjrzQC&pg=PA320}}.

The ripples formed by dropping a small object into still water naturally form an expanding system of concentric circles.{{citation|title=Waves and Ripples in Water, Air, and Æther: Being a Course of Christmas Lectures Delivered at the Royal Institution of Great Britain|first=Sir John Ambrose|last=Fleming|author-link=John Ambrose Fleming|publisher=Society for Promoting Christian Knowledge|year=1902|page=20|url=https://books.google.com/books?id=BiRJAAAAIAAJ&pg=PA20}}. Evenly spaced circles on the targets used in target archery{{citation|title=Archery: Steps to Success|first1=Kathleen|last1=Haywood|first2=Catherine|last2=Lewis|publisher=Human Kinetics|year=2006|isbn=9780736055420|page=xxiii|url=https://books.google.com/books?id=-EFySHOgGmIC&pg=PR23}}. or similar sports provide another familiar example of concentric circles.

Coaxial cable is a type of electrical cable in which the combined neutral and earth core completely surrounds the live core(s) in system of concentric cylindrical shells.{{citation|title=Fiber Optics Standard Dictionary|first=Martin|last=Weik|publisher=Springer|year=1997|isbn=9780412122415|page=124|url=https://books.google.com/books?id=s56JS2WkXE4C&pg=PA124}}.

Johannes Kepler's Mysterium Cosmographicum envisioned a cosmological system formed by concentric regular polyhedra and spheres.{{citation|title=Geometry and Its Applications|first=Walter A.|last=Meyer|edition=2nd|publisher=Academic Press|year=2006|isbn=9780080478036|page=436|url=https://books.google.com/books?id=ez6H5Ho6E3cC&pg=PA436}}.

Concentric circles have been used on firearms surfaces as means of holding lubrication or reducing friction on components, similar to jewelling.{{citation|url=https://americanhandgunner.com/handguns/behind-enemy-lines-sterling-haydens-registered-magnum/|title=Behind Enemy Lines: Sterling Hayden's Registered Magnum|magazine=American Handgunner|first=Dave|last=Elliot|year=2018}}

Concentric circles are also found in diopter sights, a type of mechanic sights commonly found on target rifles. They usually feature a large disk with a small-diameter hole near the shooter's eye, and a front globe sight (a circle contained inside another circle, called tunnel). When these sights are correctly aligned, the point of impact will be in the middle of the front sight circle.

File:2006-01-14 Surface waves.jpg|Ripples in water

File:Histology of a Pacinian corpuscle.jpg|Histology of a Pacinian corpuscle, in a typical expanding circular pattern.

File:Wooden Piling - dendrochronolgy.jpg|Tree rings, as can be used for tree-ring dating

{{div col}}

• Centered cube number
• Homoeoid
• Focaloid
• Circular symmetry
• Magic circle (mathematics)
• Osculating circle
• Spiral

{{div col end}}

{{reflist}}

• Geometry: [http://www.mathopenref.com/concentric.html Concentric circles demonstration] With interactive animation

Category:Corrosion prevention

Category:Geometric centers

Category:Visual motifs