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The following are examples of [[orders of magnitude]] for different [[length]]s.
[[Image:Triangle.EulerLine.svg|thumb|right|300px|Euler's line (red) is a straight line through the centroid (orange), orthocenter (blue), circumcenter (green) and center of the nine-point circle (red).]]


{| align="right"
In [[geometry]], the '''Euler line''', named after [[Leonhard Euler]], is a [[line (mathematics)|line]] determined from any [[triangle]] that is not [[equilateral triangle|equilateral]]; it passes through several important points determined from the triangle. It passes through the [[orthocenter]], the [[circumcenter]], the [[centroid]], the [[Exeter point]] and the center of the [[nine-point circle]] of the triangle.
|
|}
{| class="wikitable" border=1 cellpadding=3px
! rowspan=2 | Section !! colspan=2 | Range ([[meter|m]]) !! rowspan=2 | Unit !! rowspan=2 | Example Items
|-
! ≥ !! <
|-
| Planck area || [[#lt 1E-15|？]] || 10<sup>−35</sup> || || [[Quantum foam]]
|-
| [[#Subatomic|Subatomic]] || [[#lt 1E-15|10<sup>−35</sup>]] || 10<sup>−15</sup> || [[attometre|am]] || [[electron]], [[quark]], [[String (physics)|string]]
|-
| rowspan=3 | [[#Atomic and cellular|Atomic and cellular]] || [[#1E-15|10<sup>−15</sup>]] || 10<sup>−12</sup> || [[femtometre|fm]] || [[atomic nucleus]], [[proton]], [[neutron]]
|-
| [[#1E-12|10<sup>−12</sup>]] || 10<sup>−9</sup> || [[picometre|pm]] || [[wavelength]] of [[gamma ray]]s and [[X-ray]]s, [[hydrogen]] atom
|-
| [[#1E-9|10<sup>−9</sup>]] || 10<sup>−6</sup> || [[nanometre|nm]] || [[DNA]] [[helix]], [[virus]], wavelength of [[optical spectrum]]
|-
| rowspan=4 | [[#Human scale|Human scale]] || [[#1E-6|10<sup>−6</sup>]] || 10<sup>−3</sup> || [[micrometre|µm]] || [[bacterium]], [[fog]] water droplet, human hair<ref name="Physics Factbook">
According to ''The [[Physics]] Factbook'', the [[diameter]] of human hair ranges from 17 to 181 µm. {{cite web|url=http://hypertextbook.com/facts/1999/BrianLey.shtml|title=Width of a Human Hair|last=Ley|first=Brian|work=The Physics Factbook|year=1999}}</ref>
|-
| [[#1E-3|10<sup>−3</sup>]] || 10<sup>0</sup> || [[millimetre|mm]] || [[mosquito]], [[golf ball]], [[football (association football)|football]]
|-
| [[#1E0|10<sup>0</sup>]] || 10<sup>3</sup> || [[metre|m]] || [[human being]], [[association football#Pitch|football field]], [[Eiffel Tower]]
|-
| [[#1E3|10<sup>3</sup>]] || 10<sup>6</sup> || [[kilometre|km]] || [[Mount Everest]], length of [[Panama Canal]], larger [[asteroid]]
|-
| rowspan=7 | [[#Astronomical|Astronomical]] || [[#1E6|10<sup>6</sup>]] || 10<sup>9</sup> || [[megametre|Mm]] || the [[Moon]], Earth, one [[light-second]]
|-
| [[#1E9|10<sup>9</sup>]] || 10<sup>12</sup> || [[gigametre|Gm]] || [[Sun]], one [[light-minute]], Earth's orbit
|-
| [[#1E12|10<sup>12</sup>]] || 10<sup>15</sup> || [[terametre|Tm]] || orbits of [[outer planets]], [[Solar System]]
|-
| [[#1E15|10<sup>15</sup>]] || 10<sup>18</sup> || [[petametre|Pm]] || one [[light-year]]; distance to [[Proxima Centauri]]
|-
| [[#1E18|10<sup>18</sup>]] || 10<sup>21</sup> || [[exametre|Em]] || [[spiral arm|galactic arm]]
|-
| [[#1E21|10<sup>21</sup>]] || 10<sup>24</sup> || [[zettametre|Zm]] || [[Milky Way]], distance to [[Andromeda Galaxy]]
|-
| [[#1E24|10<sup>24</sup>]] || <math>10^{10^{10^{122}}}</math><ref name="exponents" group=note/> || [[yottametre|Ym]] || [[Huge-LQG]], [[Hercules-Corona Borealis Great Wall]], [[visible universe]]
|}


==Detailed list==
Euler showed in 1765 that in any triangle, the orthocenter, circumcenter and centroid are [[Line (geometry)|collinear]]. This property is also true for the nine-point center, although it had not been defined in Euler's time. In equilateral triangles, these four points coincide, but in any other triangle they do not, and the Euler line is determined by any two of them. The center of the nine-point circle lies midway along the Euler line between the orthocenter and the [[circumcenter]], and the distance from the centroid to the circumcenter is half that from the centroid to the orthocenter.
To help compare different orders of magnitude, the following list describes various lengths between 1.6{{E|−35}}&nbsp;meters and <math>10^{10^{10^{122}}}</math>meters.


===Subatomic===
Other notable points that lie on the Euler line are the [[de Longchamps point]], the [[Schiffler point]], the [[Exeter point]] and the [[far-out point]]. However, the [[incenter]] lies on the Euler line only for [[isosceles triangle]]s.
{| class="wikitable" border=1 cellpadding=3px
! Factor ([[metre|m]])
! Multiple
! Value
! Item
|-
<div id="lt 1E-15"/>
|[[1 yoctometer|10<sup>−35</sup>]]
| 1 [[Planck Length]]
|0.0000000000162&nbsp;ym&nbsp;(1.62{{E|−35}}&nbsp;m)
|[[Planck length]]; typical scale of hypothetical [[loop quantum gravity]] or size of a hypothetical [[String (physics)|string]] and of [[branes]]; according to [[string theory]] lengths smaller than this do not make any [[physics|physical]] sense.<ref name="Burgess_and_Quevedo">{{cite news | author=[[Cliff Burgess]] |author2=[[Fernando Quevedo]]  | title=The Great Cosmic Roller-Coaster Ride | url= | type=print | work=[[Scientific American]] | publisher=Scientific American, Inc. | page=55 | date=November 2007 |accessdate=2008-06-27 }}</ref> [[Quantum foam]] is thought to exist at this level.
|-
|[[1 yoctometre|10<sup>−24</sup>]]
|1 [[yoctometer]] (ym)
|20 ym (2 × 10<sup>&minus;23</sup> meters)
|effective [[Cross section (physics)|cross section]] radius of 1 [[MeV]] [[neutrino]]s<ref>{{cite web |author=Carl R. Nave |url=http://hyperphysics.phy-astr.gsu.edu/hbase/particles/cowan.html#c1 |title=Cowan and Reines Neutrino Experiment |accessdate=2008-12-04}} (6.3 × 10<sup>&minus;44</sup> cm<sup>2</sup>, which gives an effective radius of about 2 × 10<sup>&minus;23</sup> m)</ref>
|-
|rowspan=3|[[1 zeptometre|10<sup>−21</sup>]]
|rowspan=3|1 [[zeptometer]] (zm)
|
|[[Preons]], hypothetical particles proposed as subcomponents of quarks and leptons; the upper bound for the width of a [[cosmic string]] in string theory.
|-
|7 zm (7 × 10<sup>&minus;21</sup> meters)
| effective cross section radius of high energy [[neutrino]]s<ref name="NaveN3">{{cite web |author=Carl R. Nave |url=http://hyperphysics.phy-astr.gsu.edu/hbase/particles/neutrino3.html#c2 |title=Neutron Absorption Cross-sections |accessdate=2008-12-04}} (area for 20 GeV about 10 × 10<sup>&minus;42</sup> m<sup>2</sup> gives effective radius of about 2 × 10<sup>&minus;21</sup> m; for 250 GeV about 150 × 10<sup>&minus;42</sup> m<sup>2</sup> gives effective radius of about 7 × 10<sup>&minus;21</sup> m)</ref>
|-
|310 zm (3.10 × 10<sup>&minus;19</sup> meters)
|[[de Broglie wavelength]] of [[protons]] at the [[Large Hadron Collider]] (4 TeV as of 2012)
|-
|rowspan=3|[[1 attometre|10<sup>−18</sup>]]
|rowspan=3|1 [[attometer]] (am)
|rowspan=3|
|upper limit for the size of [[quark]]s and [[electron]]s
|-
|sensitivity of the [[LIGO]] detector for [[gravitational wave]]s
|-
|upper bound of the typical size range for "fundamental [[String (physics)|strings]]"<ref name="Burgess_and_Quevedo"/>
|-
|rowspan=1|10<sup>−17</sup>
|rowspan=1|10 am
|rowspan=1|
| range of the [[weak force]]
|-
|}


===Atomic and cellular===
Let ''A'', ''B'', ''C'' denote the vertex angles of the reference triangle, and let ''x'' : ''y'' : ''z'' be a variable point in [[trilinear coordinates]]; then an equation for the Euler line is
<!-- No more than three examples per row: choose examples from a range of sizes, and add extra examples to the sub-articles instead -->


{| class="wikitable" border=1 cellpadding=3px
:<math>\sin 2A \sin(B - C)x + \sin 2B \sin(C - A)y + \sin 2C \sin(A - B)z = 0.\,</math>
!Factor ([[metre|m]])
!Multiple
!Value
!Item
<div id="1E-15"/>
|-
|rowspan=3|[[1 femtometre|10<sup>−15</sup>]]
|rowspan=3|1 [[femtometer]] (fm)
|1.5 fm
|size of an 11 MeV [[proton]]<ref name="Nav">{{cite web |author=Carl R. Nave |url=http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/crosec.html |title= Scattering Cross Section |accessdate=2009-02-10}}
(diameter of the [[Cross section (physics)|Scattering Cross Section]] of an 11 MeV [[proton]] with a target proton)<!-- To verify, use online form with these figures: Z=1 KE=11 A=1 and obtain cross section of 1.758 fm^2; use Area=Pi*R^2 to derive diameter (2R) --></ref>
|-
|2.81794 fm
|[[classical electron radius]]<ref>[[National Institute of Standards and Technology|NIST]]. [http://physics.nist.gov/cgi-bin/cuu/Value?re CODATA Value:    classical electron radius]. Retrieved 2009-02-10</ref>
|-
|
|scale of the [[atomic nucleus]]<ref name="Burgess_and_Quevedo"/><ref>{{cite web |title=The Scale of the Universe |url=http://cass.ucsd.edu/public/tutorial/scale.html |author=H. E. Smith |publisher=[[University of California, San Diego|UCSD]] |quote=~10<sup>-13</sup>cm |accessdate=2009-02-10}}</ref>
|-
|rowspan=1|[[10 femtometers|10<sup>−14</sup>]]
|rowspan=1|10 fm
|
|
|-
|rowspan=1|10<sup>−13</sup>
|rowspan=1|100 fm
|
|
<div id="1E-12"/>
|-
|rowspan=3|[[1 picometre|10<sup>−12</sup>]]
|rowspan=3|1 [[picometer]] (pm)
|...
|longest [[wavelength]] of [[gamma ray]]s
|-
|2.4 pm
|[[Compton wavelength]] of [[electron]]
|-
|5 pm
|wavelength of shortest [[X-ray]]s
|-
|rowspan=3|[[10 picometres|10<sup>−11</sup>]]
|rowspan=3|10 pm
|25 pm
|radius of [[hydrogen atom]]
|-
|31 pm
|radius of [[helium]] atom
|-
|53 pm
|[[Bohr radius]]
|-
|rowspan=3|[[100 picometres|10<sup>−10</sup>]]
|rowspan=3|[[100 picometres|100 pm]]
|100 pm (0.1&nbsp;nm)
|1 [[Angstrom|Ångström]] (also [[covalent radius]] of [[sulfur]] atom<ref>{{cite web |author=Mark Winter |title=WebElements Periodic Table of the Elements / Sulfur / Radii |url=http://www.webelements.com/sulfur/atom_sizes.html |year=2008 |accessdate=2008-12-06}}</ref>)
|-
|154 pm (0.154&nbsp;nm)
|length of a typical [[covalent bond]] ([[carbon|C]]–C).
|-
|500 pm (0.50&nbsp;nm)
|width of [[protein]] [[alpha helix|α helix]]
<div id="1E-9"/>
|-
|rowspan=3|[[1 nanometre|10<sup>−9</sup>]]
|rowspan=3|1 [[nanometer]] (nm)
|1&nbsp;nm
|diameter of a [[carbon nanotube]]<ref>{{Cite journal |first=E. |last=Flahaut |author2=Bacsa R |author3=Peigney A |author4=Laurent C.  |year=2003 |title=Gram-Scale CCVD Synthesis of Double-Walled Carbon Nanotubes |journal=Chemical Communications |volume=12 | pages=1442–1443 |url=http://www.rsc.org/Publishing/Journals/CC/article.asp?doi=b301514a |doi=10.1039/b301514a |accessdate=2008-11-14 |pmid=12841282 |issue=12}}</ref>
|-
|2.5&nbsp;nm
|Smallest [[microprocessor]] [[transistor]] [[Gate (transistor)|gate]] oxide thickness (as of Jan 2007)
|-
|6–10&nbsp;nm
|thickness of [[cell membrane]]
|-
|rowspan=3|[[10 nanometres|10<sup>−8</sup>]]
|rowspan=3|10&nbsp;nm
|10&nbsp;nm
|thickness of [[cell wall]] in [[Gram staining|gram]]-negative [[bacteria]]{{Citation needed|date=February 2009}}
|-
|40&nbsp;nm
|extreme [[ultraviolet]] wavelength
|-
|90&nbsp;nm
|[[HIV|Human immunodeficiency virus (HIV)]] (generally, [[virus]]es range in size from 20&nbsp;nm to 450&nbsp;nm)
|-
|rowspan=3|[[100 nanometres|10<sup>−7</sup>]]
|rowspan=3|100&nbsp;nm
|121.6&nbsp;nm
|wavelength of the [[Lyman-alpha line]]<ref name="ber">Cohn, J. [[University of California, Berkeley]] [http://astro.berkeley.edu/~jcohn/lya.html Lyman alpha systems and cosmology]. Retrieved 2009-02-21</ref>
|-
|380–435&nbsp;nm
|wavelength of [[violet (color)|violet]] light—see [[color]] and [[optical spectrum]]<ref name="hyp">[http://hyperphysics.phy-astr.gsu.edu/hbase/vision/specol.html#c1 Color]</ref>
|-
|625–740&nbsp;nm
|wavelength of red light<ref name="hyp"/>
|}


===Human scale===
Another particularly useful way to represent the Euler line is in terms of a parameter t.  Starting with the circumcenter (with trilinears <math>\cos A : \cos B : \cos C</math>) and the orthocenter (with trilinears <math>\sec A : \sec B : \sec C = \cos B \cos C : \cos C \cos A : \cos A \cos B)</math>, every point on the Euler line, except the orthocenter, is given as
<!-- No more than three examples per row: choose examples from a range of sizes, and add extra examples to the sub-articles instead; prefer examples that are well-cited and well-known throughout the world -->


{| class="wikitable" border=1 cellpadding=3px
:<math>\cos A + t \cos B \cos C : \cos B + t \cos C \cos A : \cos C + t \cos A \cos B\,</math>
!Factor ([[metre|m]])
!Multiple
!Value
!Item
<div id="1E-6"/>
|-
|rowspan=3|[[1 micrometre|10<sup>−6</sup>]]
|rowspan=3|1 [[micrometer]] (µm)
|1&nbsp;µm
|also called one [[micron]]
|-
|1–3&nbsp;µm
|particle size that a [[surgical mask]] removes at 80–95% efficiency{{Citation needed|date=December 2008}}
|-
|6-8&nbsp;µm
|diameter of a [[red blood cell]]<ref>{{Cite web | url=http://www.wadsworth.org/chemheme/heme/microscope/rbc.htm | title=Through the Microscope: Blood Cells - Life's Blood | publisher=Wadsworth Center, New York State Department of Health | accessdate=2011-09-13 }}</ref>
|-
|rowspan=3|[[10 micrometres|10<sup>−5</sup>]]
|rowspan=3|10&nbsp;µm
|10&nbsp;µm
|typical size of a fog, mist or cloud water droplet. Chip [[10 µm process]] in 1971.
|-
|12&nbsp;µm
|width of [[acrylic fibre]]
|-
|25.4&nbsp;µm
|1/1000&nbsp;inch, commonly referred to as one [[Thou (unit of length)|thou]] or one [[Thou (unit of length)|mil]]
|-
|rowspan=3|[[1 myriometre|10<sup>−4</sup>]]
|rowspan=3|100&nbsp;µm
|100&nbsp;µm
|average width of a strand of human hair<ref name="Physics Factbook"/>
|-
|200&nbsp;µm
|typical length of ''[[Paramecium|Paramecium caudatum]]'', a ciliate protist
|-
|750&nbsp;µm
|maximum diameter of ''[[Thiomargarita namibiensis]]'', the largest bacterium ever discovered
|-
<div id="1E-3"/>
|-
|rowspan=3|[[1 millimetre|10<sup>−3</sup>]]
|rowspan=3|1 [[millimeter]] (mm)
|2.54&nbsp;mm
|1/10th inch; distance between pins in [[dual in-line package|DIP]] (dual-inline-package) electronic components
|-
|5&nbsp;mm
|length of average red [[ant]]
|-
|7.62&nbsp;mm
|common military ammunition size
|-
|rowspan=3|[[1 centimetre|10<sup>−2</sup>]]
|rowspan=3|1 [[centimeter]] (cm)
|1.5&nbsp;cm
|length of a large [[mosquito]]
|-
|2.54&nbsp;cm
|1 [[inch]]
|-
|4.267&nbsp;cm
|diameter of a [[golf ball]]
|-
|rowspan=3|[[1 decimetre|10<sup>−1</sup>]]
|rowspan=3|1 [[decimeter]] (dm)
|10&nbsp;cm
|wavelength of the highest [[Ultra high frequency|UHF]] radio frequency, 3&nbsp;GHz
|-
|30.48&nbsp;cm
|1 [[foot (length)|foot]]
|-
|91.44&nbsp;cm
|1 [[yard]]
<div id="1E0"/>
|-
|rowspan=3|[[1 metre|10<sup>0</sup>]]
|rowspan=3|1 [[meter]]
| 1 m
|wavelength of the lowest [[Ultra high frequency|UHF]] and highest [[Very high frequency|VHF]] radio frequency, 300&nbsp;MHz
|-
|1.7 m (5 feet 7&nbsp;inches)
|average height of a human
|-
|8.38 m
|The length of a London Bus ([[Routemaster]])
|-
|rowspan=3|[[1 decametre|10<sup>1</sup>]]
|rowspan=3|1 [[decameter]] (dam)
|10 m
|wavelength of the lowest [[Very high frequency|VHF]] and highest [[shortwave]] radio frequency, 30&nbsp;MHz
|-
|33 m
|length of longest [[blue whale]] measured, the largest animal<ref>{{Cite web | url=http://nationalzoo.si.edu/Animals/AnimalRecords/ | title=Animal Records | publisher=Smithsonian National Zoological Park | accessdate=2007-05-29 }}</ref>
|-
|93.47 m
|height of the [[Statue of Liberty]] (foundation of pedestal to torch)
|-
|rowspan=3|[[1 hectometre|10<sup>2</sup>]]
|rowspan=3|1 [[hectometer]] (hm)
|100 m
|wavelength of the lowest [[shortwave]] radio frequency and highest [[medium wave]] radio frequency, 3&nbsp;MHz
|-
|137 m (147 m)
|height (present and original) of the [[Great Pyramid of Giza]]
|-
|979 m
|height of the [[Salto Angel]], the world's highest free-falling waterfall ([[Venezuela]])
<div id="1E3"/>
|-
|rowspan=4|[[1 kilometre|10<sup>3</sup>]]
|rowspan=4|1 [[kilometer]] (km)
|1&nbsp;km
|wavelength of the lowest [[medium wave]] radio frequency, 300&nbsp;kHz
|-
|1609 m
|1 [[mile|international mile]]
|-
|1852 m
|1 [[nautical mile]]<br>&nbsp;
|-
|8848 m
|height of the highest mountain on earth, [[Mount Everest]]
|-
|rowspan=3|[[1 myriametre|10<sup>4</sup>]]<!-- Please consider renaming the obsolete term myriametre to [[10 kilometres (order of magnitude)]] -->
|rowspan=3|10&nbsp;km
|10.911&nbsp;km
|depth of deepest part of the ocean, [[Mariana Trench]]
|-
|13&nbsp;km
|narrowest width of the [[Strait of Gibraltar]], separating Europe and Africa
|-
|90&nbsp;km
|width of the [[Bering Strait]]
|-
|rowspan=3|[[100 kilometres|10<sup>5</sup>]]
|rowspan=3|100&nbsp;km
|111&nbsp;km
|distance covered by one degree of [[latitude]] on Earth's surface
|-
|163&nbsp;km
|length of the [[Suez Canal]]
|-
|974.6&nbsp;km
|greatest diameter<ref>{{cite journal|first=P. C.|last=Thomas|author2=Parker, J. Wm. |author3=McFadden, L. A. |author4= et al. |title=Differentiation of the asteroid Ceres as revealed by its shape|year=2005|journal=Nature|volume=437|pages=224&ndash;226|doi=10.1038/nature03938| bibcode=2005Natur.437..224T|pmid=16148926|issue=7056}}</ref> of the dwarf planet<ref name="Asteroid-planet?" group=note>The exact [[Solar System#Terminology|category]] (asteroid, dwarf planet or planet) to which particular solar system objects belong, has been subject to some revision since the discovery of [[extrasolar planet]]s and [[Trans-Neptunian object|trans-Neptunian]] objects</ref> [[Ceres (dwarf planet)|Ceres]]
|}


===Astronomical===
for some ''t''.
{| class="wikitable" border=1 cellpadding=3px
!Factor ([[metre|m]])
!Multiple
!Value
!Item
<div id="1E6"/>
|-
|rowspan=7|[[1 megametre|10<sup>6</sup>]]
|rowspan=7|1,000&nbsp;km = 1 [[megameter]] (Mm)
|2,390&nbsp;km
|diameter of dwarf planet [[Pluto]], formerly the smallest [[planet]] category<ref name="Asteroid-planet?" group=note/> of our solar system
|-
|3,480&nbsp;km
|diameter of the [[Moon]]
|-
|5,200&nbsp;km
|typical distance covered by the winner of the [[24 Hours of Le Mans]] automobile endurance race
|-
|6,400&nbsp;km
|length of the [[Great Wall of China]]
|-
|6,600&nbsp;km
|approximate length of the two longest rivers, the [[Nile]] and the [[Amazon River|Amazon]]
|-
|7,821&nbsp;km
|length of the [[Trans-Canada Highway]]
|-
|9,288&nbsp;km
|length of the [[Trans-Siberian Railway]], longest in the world
<div id="1E7"/>
|-
|rowspan=2|[[10 megametres|10<sup>7</sup>]]
|rowspan=2|10,000&nbsp;km
|12,756&nbsp;km
|equatorial diameter of the Earth
|-
|40,075&nbsp;km
|length of the Earth's [[equator]]
<div id="1E8"/>
|-
|rowspan=3|[[100 megametres|10<sup>8</sup>]]
|rowspan=3|100,000&nbsp;km
|142,984&nbsp;km
|diameter of [[Jupiter]]
|-
|299,792.458&nbsp;km
|distance travelled by light in one second
|-
|384,000&nbsp;km = 384 Mm
|[[Moon]]'s orbital distance from Earth
<div id="1E9"/>
|-
|rowspan=2|[[1 gigametre|10<sup>9</sup>]]
|rowspan=2|1 million km = 1 [[gigameter]] (Gm)
|1,390,000&nbsp;km = 1.39&nbsp;Gm
|diameter of the [[Sun]]
|-
|4,200,000 &nbsp;km = 4.2&nbsp;Gm
|greatest mileage ever recorded by a car (A 1966 [[Volvo P1800|Volvo P-1800S]], still driving)
<div id="1E10"/>
|-
| [[10 gigametres|10<sup>10</sup>]]
| 10 million km
|18 million km
|approximately one [[light-minute]]
<div id="1E11"/>
|-
| rowspan=2 | [[100 gigametres|10<sup>11</sup>]]
| rowspan=2 | 100 million km
|150 million&nbsp;km = 150&nbsp;Gm
|1 [[astronomical unit]] (AU); mean distance between Earth and Sun
|-
|~ 900 Gm
|optical diameter of [[Betelgeuse]] (~600 × Sun)
<div id="1E12"/>
|-
|rowspan=6|[[1 terametre|10<sup>12</sup>]]
|rowspan=6|1000 million km = 1 [[terameter]] (Tm)
|1.4 {{E|9}}&nbsp;km
|orbital distance of [[Saturn]] from Sun
|-
|1.96 {{E|9}}&nbsp;km
|estimated optical diameter of [[VY Canis Majoris]] (1420 × Sun)
|-
|2.3 {{E|9}}&nbsp;km
|estimated optical diameter of [[NML Cygni]] (1650 × Sun)
|-
|2.37 {{E|9}}&nbsp;km
|median point of the optical diameter of [[UY Scuti]], as of 2014 the [[List of largest known stars|largest known star]]
|-
|5.9 {{E|9}}&nbsp;km = 5.9&nbsp;Tm
|orbital distance of Pluto from Sun
|-
|~ 7.5 {{E|9}}&nbsp;km = 7.5&nbsp;Tm
|outer boundary of the [[Kuiper belt]], inner boundary of the [[Oort cloud]] (~ 50 AU)
<div id="1E13"/>
|-
|rowspan=3|[[10 terametres|10<sup>13</sup>]]
|rowspan=3|10 Tm
|
|diameter of our [[Solar System]] as a whole<ref name="Burgess_and_Quevedo"/>
|-
|16.25{{E|9}}&nbsp;km = 16.25&nbsp;Tm
|distance of the [[Voyager 1]] spacecraft from Sun ({{As of|2009|alt=as of Feb 2009}}), the farthest man-made object so far<ref>[http://heavens-above.com/solar-escape.asp Spacecraft escaping the Solar System<!-- Bot generated title -->]</ref>
|-
|62.03{{E|9}}&nbsp;km = 62.03&nbsp;Tm
|estimated radius of the [[event horizon]] of the [[supermassive black hole]] in [[NGC 4889]], the largest known black hole to date
<div id="1E14"/>
|-
|[[100 terametres|10<sup>14</sup>]]
|100 Tm
|1.8{{E|11}}&nbsp;km = 180&nbsp;Tm
|size of the [[debris disk]] around the star [[51 Pegasi]] <ref>[http://esciencenews.com/articles/2009/09/24/twin.keck.telescopes.probe.dual.dust.disks Twin Keck telescopes probe dual dust disks]</ref> <div id="1E15"/>
|-
|rowspan=2|[[1 petametre|10<sup>15</sup>]]
|rowspan=2|1 [[petameter]] (Pm)
|~ 7.5 {{E|12}}&nbsp;km = 7.5&nbsp;Pm
|supposed outer boundary of the Oort cloud (~ 50,000 AU)
|-
|9.46{{E|12}}&nbsp;km = 9.46&nbsp;Pm<br> = 1 [[light year]]
|distance traveled by light in one year; at its current speed, Voyager 1 would need 17,500 years to travel this distance
<div id="1E16"/>
|-
|rowspan=3|[[10 petametres|10<sup>16</sup>]]
|rowspan=3|10 Pm
|3.2616 light-years<br>(3.0857{{E|13}}&nbsp;km = 30.857&nbsp;Pm)
|1 [[parsec]]
|-
|4.22 light-years = 39.9&nbsp;Pm
|distance to nearest star ([[Proxima Centauri]])
|-
|4.37 light-years = 41.3&nbsp;Pm
|as of March 2013, distance to nearest discovered [[extrasolar planet]] ([[Alpha Centauri Bb]])
<div id="1E17"/>
|-
|rowspan=2|[[100 petametres|10<sup>17</sup>]]
|rowspan=2|100 Pm
|20.4 light-years = 193&nbsp;Pm
|as of October 2010, distance to nearest discovered extrasolar planet with potential to support life as we know it ([[Gliese 581 d]])
|-
|65 light-years = 6.15{{E|17}}&nbsp;m = 615&nbsp;Pm
|approximate radius of humanity's radio bubble, caused by high-power TV broadcasts leaking through the atmosphere into outer space
<div id="1E18"/>
|-
|rowspan=1|[[1 exametre|10<sup>18</sup>]]
|rowspan=1|1 [[exameter]] (Em)
|200 light-years = 1.9&nbsp;Em
|distance to nearby [[solar twin]] ([[HIP 56948]]), a star with properties virtually identical to our Sun <ref>{{cite web | last = Shiga | first = David | url = http://space.newscientist.com/article/dn12725-suns-twin-an-ideal-hunting-ground-for-alien-life.html | title = Sun's 'twin' an ideal hunting ground for alien life | publisher = New Scientist | accessdate = 2007-10-03 }}</ref>
<div id="1E19"/>
|-
|[[10 exametres|10<sup>19</sup>]]
|10 Em
|1,000 light-years = 9.46 Em or 9.46 × 10<sup>15</sup> km
|average thickness of [[Milky Way Galaxy]]<ref>{{cite web |last=Christian |first=Eric |last2=Samar |first2=Safi-Harb |title=How large is the Milky Way? |url=http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/980317b.html |accessdate=2008-11-14}}</ref> (1000 to 3000 ly by [[Hydrogen line|21&nbsp;cm observations]]<ref>{{cite web |last=Duncan |first=Martin |title=Physics 216 – Introduction to Astrophysics |chapter=16 |url=http://www.physics.queensu.ca/~phys216/ch16B.pdf |year=2008 |accessdate=2008-11-14}}</ref>)
<div id="1E20"/>
|-
|rowspan=2|[[100 exametres|10<sup>20</sup>]]
|100 Em
|12,000 light-years = 113.5 Em or 1.135 × 10<sup>17</sup> km
|thickness of [[Milky Way Galaxy]]'s gaseous disk<ref>{{cite web|url=http://news.smh.com.au/milky-way-fatter-than-first-thought/20080220-1tbv.html |title=Milky Way fatter than first thought |accessdate=2008-11-14 |date=2008-02-20 |work=[[The Sydney Morning Herald]] |publisher=[[Australian Associated Press]]}}</ref>
|-
|950 Em
|100,000 light-years
|diameter of galactic disk of [[Milky Way Galaxy]]<ref name="Burgess_and_Quevedo"/>
<div id="1E21"/>
|-
|rowspan=5|[[1 zettametre|10<sup>21</sup>]]
|rowspan=5|1 [[zettameter]] (Zm)
|-
|50 [[kiloparsecs]]
|distance to [[Supernova 1987a|SN 1987A]], the most recent naked eye supernova
|-
|52 kiloparsecs = 1.62{{E|21}}&nbsp;m = 1.62&nbsp;Zm
|distance to the [[Large Magellanic Cloud]] (a [[dwarf galaxy]] [[orbit]]ing the [[Milky Way]])
|-
| 54 kiloparsecs = 1.66&nbsp;Zm
|distance to the [[Small Magellanic Cloud]] (another dwarf galaxy orbiting the Milky Way)
|-
| 200 kiloparsecs = 6.15&nbsp;Zm
|diameter of the low surface brightness disc halo of the giant spiral galaxy [[Malin 1]]
<div id="1E22"/>
|-
|rowspan=4|[[10 zettametres|10<sup>22</sup>]]
|rowspan=4|10 Zm
| 13.25&nbsp;Zm = 1.4 million light years<br>= 600 kiloparsecs
| radius of the diffuse stellar halo of [[IC 1101]], one of the largest known galaxies
|-
| 24&nbsp;Zm = 2.5 million light-years<br>= 770 kiloparsecs
|distance to [[Andromeda Galaxy]]
|-
|3.26 million light-years<br>=30.8&nbsp;Zm = 1 megaparsec
|1 [[megaparsec]]
|-
|50&nbsp;Zm (1.6&nbsp;Mpc)
|diameter of [[Local Group]] of [[galaxy|galaxies]]
<div id="1E23"/>
|-
|[[100 zettametres|10<sup>23</sup>]]
|100 Zm
|300–600&nbsp;Zm = 10–20 [[megaparsecs]]
|distance to [[Virgo cluster]] of [[galaxy|galaxies]]
<div id="1E24"/>
|-
|rowspan=4|[[1 yottametre|10<sup>24</sup>]]
|rowspan=4|1 [[yottameter]] (Ym)
|200 million light-years<br>= 1.9&nbsp;Ym = 61 megaparsecs
|diameter of the [[Local Supercluster]] and the largest voids and filaments.
|-
|300 million light-years<br>= 2.8&nbsp;Ym = 100 megaparsecs
|[[Observable universe#End of Greatness|End of Greatness]]
|-
|550 million light-years<br>~170 megaparsecs ~5&nbsp;Ym
|diameter of the enormous [[Horologium Supercluster]] <ref>http://www.atlasoftheuniverse.com/superc/hor.html The Horologium Supercluster</ref>
<div id="1E25"/>
|-
|1 billion light-years<br>= 9.46&nbsp;Ym =306 megaparsecs
|diameter of the [[Pisces–Cetus Supercluster Complex]], the supercluster complex where we live.
|-
|rowspan=3|[[10 yottametres|10<sup>25</sup>]]
|rowspan=3|10 Ym
|1.37 billion light years<br>= 1.3{{E|25}}&nbsp;m = 13&nbsp;Ym
|Length of the [[Sloan Great Wall]], a giant wall of galaxies ([[galactic filament]]).<ref>[http://arxiv.org/abs/astro-ph/0310571 J. R. Gott III ''et al.'', ''Astrophys. J.'', '''624''', 463 (2005).] Figure 8 &ndash; "Logarithmic Maps of the Universe" &ndash; is available as a poster from [http://www.astro.princeton.edu/~mjuric/universe/ the homepage of Mario Juric.]</ref>
|-
|3.26 billion light years<br>=30.8&nbsp;Ym = 1 gigaparsec
|1 [[gigaparsec]]
|-
|4 billion light years<br>=37.84&nbsp;Ym
|Length of the [[Huge-LQG]], a group of 73 [[quasar]]s
|-
<div id="1E26/>
|-
|rowspan=3|[[100 yottametres|10<sup>26</sup>]]
|rowspan=3|100 Ym
|1{{E|10}} light-years<br>= 9.5{{E|25}}&nbsp;m = 95&nbsp;Ym
|estimated [[Distance measures (cosmology)|light travel distance]] to certain [[quasars]]<br>


length of the [[Hercules-Corona Borealis Great Wall]], a colossal wall of galaxies, the largest and the most massive structure in the observable universe as of 2014
Examples:
|-
* [[centroid]] = <math>\cos A + \cos B \cos C : \cos B + \cos C \cos A : \cos C + \cos A \cos B</math>
|13.42 billion light years<br>=1.27{{E|26}}&nbsp;m = 127&nbsp;Ym
* [[nine-point center]] = <math>\cos A + 2 \cos B \cos C : \cos B + 2 \cos C \cos A : \cos C + 2 \cos A \cos B</math>
|Estimated [[Distance measures (cosmology)|light travel distance]] to [[UDFj-39546284]], the [[List of the most distant astronomical objects|most distant object]] ever observed
* [[De Longchamps point]] = <math>\cos A - \cos B \cos C : \cos B - \cos C \cos A : \cos C - \cos A \cos B</math>
|-
* [[Euler infinity point]] = <math>\cos A - 2 \cos B \cos C : \cos B - 2 \cos C \cos A : \cos C - 2 \cos A \cos B</math>
|9.2{{E|10}} light years<br>= 8.7{{E|26}}&nbsp;m = 870&nbsp;Ym
|approx. diameter ([[comoving distance]]) of the [[visible universe]]<ref name="Burgess_and_Quevedo"/>
|-
<div id="1E27/>
|-
|[[1000 yottametres|10<sup>27</sup>]]
|1000 Ym
<!-- previous version of this entry reported diameter as radius -->
|130 billion light years<br>= 1.2{{E|27}}&nbsp;m = 1200&nbsp;Ym
|lower bound of the (possibly infinite) radius of the universe, if it is a [[3-sphere]], according to one estimate using the [[WMAP]] data at 95% confidence.<ref>http://arxiv.org/abs/astro-ph/0605709v2 How Many Universes Do There Need To Be?</ref> It equivalently implies that there are at minimum 21 [[particle horizon]]-sized volumes in the universe.
<!-- The article this entry is based on has been withdrawn by the author, specifically due to an error in the lower-bound estimate itself
|-
|~400 billion light years<br>= 3.8{{E|27}}&nbsp;m = 3800&nbsp;Ym
|Lower bound of the homogeneous universe derived from the [[Planck spacecraft]] <ref>[http://arxiv.org/abs/1304.1181 data]</ref>
-->
|-
|<math>10^{10^{115}}</math><ref name="exponents" group=note>10<sup>115</sup> is 1 followed by 115 zeroes, or a [[googol]] multiplied by a quadrillion. 10<sup>10<sup>115</sup></sup> is 1 followed by a quadrillion googol zeroes. 10<sup>10<sup>10<sup>122</sup></sup></sup>is 1 followed by 10<sup>10<sup>122</sup></sup> (a [[googolplex]]<sup>10 sextillion</SUP>) zeroes. These numbers are so vast that they are essentially the same in whatever units we could use to list them.</ref>
|<math>10^{10^{115}}</math> Ym
|<math>10^{10^{115}}</math> megaparsecs<br>= <math>10^{10^{115}}</math>&nbsp;m<br>= <math>10^{10^{115}}</math>Ym
|According to the laws of probability, the distance one must travel until one encounters a volume of space identical to our [[observable universe]] with conditions identical to our own.<ref name="TegmarkPUstaple">"Parallel universes. Not just a staple of science fiction, other universes are a direct implication of cosmological observations.", Tegmark M., Sci Am. 2003 May;288(5):40-51.</ref><ref>{{cite journal |author1=Max Tegmark |journal=In "Science and Ultimate Reality: from Quantum to Cosmos", honoring John Wheeler's 90th birthday. J. D. Barrow, P.C.W. Davies, & C.L. Harper eds. Cambridge University Press (2003) |title=Parallel Universes |year=2003 |arxiv=astro-ph/0302131|bibcode = 2003astro.ph..2131T }}</ref>
|-
|<math>10^{10^{10^{122}}}</math><ref name="exponents" group=note/>
|<math>10^{10^{10^{122}}}</math> Ym
|<math>10^{10^{10^{122}}}</math> Mpc<br>= <math>10^{10^{10^{122}}}</math>&nbsp;m<br>= <math>10^{10^{10^{122}}}</math>Ym
|size of universe after [[cosmological inflation]], implied by one resolution of the No-Boundary Proposal<ref>http://arxiv.org/abs/hep-th/0610199 "Susskind's Challenge to the Hartle-Hawking No-Boundary Proposal and Possible Resolutions "</ref>
|}


==See also==
==See also==
* [[List of examples of lengths]]
*[[Gossard perspector]]
* [[Metric_prefix#List_of_SI_prefixes|List of metric prefixes]]
*[[Central line (geometry)|Central line]]
* [[List of semiconductor scale examples]]
* [[Earth's location in the universe]]
* ''[[Powers of Ten (film)|Powers of Ten]]'', a 1968 short documentary film which depicts the relative scale of the Universe in factors of ten.


==Notes==
== References ==
{{reflist|group=note}}


==References==
*{{cite journal
{{reflist|30em}}
| author = Euler, Leonhard
| authorlink = Leonhard Euler
| title = Solutio facilis problematum quorundam geometricorum difficillimorum
| journal = Novi Commentarii academiae scientarum imperialis Petropolitanae
| volume = 11
| year = 1767
| pages = 103–123
| url = http://math.dartmouth.edu/~euler/pages/E325.html
| id = <!--Enestrom number-->E325}} Reprinted in ''Opera Omnia'', ser. I, vol. XXVI, pp.&nbsp;139–157, Societas Scientiarum Naturalium Helveticae, Lausanne, 1953, {{MR|0061061}}.


==External links==
*{{cite journal
* [http://www.vendian.org/howbig/ How Big Are Things?] displays orders of magnitude in successively larger rooms
| author = Kimberling, Clark
* [http://microcosm.web.cern.ch/Microcosm/P10/english/welcome.html Powers of Ten] Travel across the Universe. Altering perspective by changing scale by just a few powers of ten (interactive) {{dead link|date=May 2013}}
| title = Triangle centers and central triangles
* [http://www.shekpvar.net/~dna/Publications/Cosmos/cosmos.html Cosmos &ndash; an Illustrated Dimensional Journey from microcosmos to macrocosmos] &ndash; from Digital Nature Agency {{dead link|date=May 2013}}
| journal = Congressus Numerantium
* [http://htwins.net/scale2/ Scale of the universe]- interactive guide to length magnitudes
| volume = 129
| year = 1998
| pages = i–xxv, 1–295}}


{{Orders of magnitude wide}}
== External links ==
{{Units of length used in Astronomy}}
* [http://www.cut-the-knot.org/triangle/altEuler.shtml Altitudes and the Euler Line] and [http://www.cut-the-knot.org/triangle/EulerLine.shtml Euler Line and 9-Point Circle] at [[cut-the-knot]]
* [http://faculty.evansville.edu/ck6/tcenters/class/eulerline.html Triangle centers on the Euler line], by Clark Kimberling.
* [http://www.mathopenref.com/eulerline.html An interactive applet showing several triangle centers that lies on the Euler line].
* {{mathworld | title = Euler Line | urlname = EulerLine}}
* [http://demonstrations.wolfram.com/EulerLine/ "Euler Line"] by Eric Rowland, the [[Wolfram Demonstrations Project]], 2007.
* [http://dynamicmathematicslearning.com/ninepointconic.html Nine-point conic and Euler line generalization] at [http://dynamicmathematicslearning.com/JavaGSPLinks.htm Dynamic Geometry Sketches] Generalizes nine-point circle to a nine-point conic with an associated generalization of the Euler line.
* [http://dynamicmathematicslearning.com/furtherEuler.html A further Euler line generalization] at [http://dynamicmathematicslearning.com/JavaGSPLinks.htm Dynamic Geometry Sketches] Generalizes the Euler line further by disassociating it from the nine-point conic (see above).


[[Category:Length]]
[[Category:Triangle geometry]]
[[Category:Orders of magnitude|Length]]
 
[[Category:Orders of magnitude (length)|*]]
[[ar:مستقيم أويلر]]
[[Category:Lists by length]]
[[bg:Ойлерова права]]
[[ca:Recta d'Euler]]
[[cs:Eulerova přímka]]
[[de:Eulersche Gerade]]
[[es:Recta de Euler]]
[[fr:Droite d'Euler]]
[[ko:오일러선]]
[[it:Retta di Eulero]]
[[he:ישר אוילר]]
[[hu:Euler-egyenes]]
[[nl:Rechte van Euler]]
[[ja:オイラー線]]
[[km:បន្ទាត់អយល័រ]]
[[pms:Reta d'Euler]]
[[pl:Prosta Eulera]]
[[pt:Reta de Euler]]
[[ro:Dreapta lui Euler]]
[[ru:Прямая Эйлера]]
[[sq:Drejtëza e Eulerit]]
[[sl:Eulerjeva premica]]
[[sr:Ојлерова права]]
[[fi:Eulerin suora]]
[[ta:ஆய்லர் கோடு]]
[[uk:Лінія Ейлера]]
[[vi:Đường thẳng Euler]]
[[zh:歐拉線]]

Revision as of 16:59, 10 August 2014

Euler's line (red) is a straight line through the centroid (orange), orthocenter (blue), circumcenter (green) and center of the nine-point circle (red).

In geometry, the Euler line, named after Leonhard Euler, is a line determined from any triangle that is not equilateral; it passes through several important points determined from the triangle. It passes through the orthocenter, the circumcenter, the centroid, the Exeter point and the center of the nine-point circle of the triangle.

Euler showed in 1765 that in any triangle, the orthocenter, circumcenter and centroid are collinear. This property is also true for the nine-point center, although it had not been defined in Euler's time. In equilateral triangles, these four points coincide, but in any other triangle they do not, and the Euler line is determined by any two of them. The center of the nine-point circle lies midway along the Euler line between the orthocenter and the circumcenter, and the distance from the centroid to the circumcenter is half that from the centroid to the orthocenter.

Other notable points that lie on the Euler line are the de Longchamps point, the Schiffler point, the Exeter point and the far-out point. However, the incenter lies on the Euler line only for isosceles triangles.

Let A, B, C denote the vertex angles of the reference triangle, and let x : y : z be a variable point in trilinear coordinates; then an equation for the Euler line is

Another particularly useful way to represent the Euler line is in terms of a parameter t. Starting with the circumcenter (with trilinears ) and the orthocenter (with trilinears , every point on the Euler line, except the orthocenter, is given as

for some t.

Examples:

See also

References

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External links

ar:مستقيم أويلر bg:Ойлерова права ca:Recta d'Euler cs:Eulerova přímka de:Eulersche Gerade es:Recta de Euler fr:Droite d'Euler ko:오일러선 it:Retta di Eulero he:ישר אוילר hu:Euler-egyenes nl:Rechte van Euler ja:オイラー線 km:បន្ទាត់អយល័រ pms:Reta d'Euler pl:Prosta Eulera pt:Reta de Euler ro:Dreapta lui Euler ru:Прямая Эйлера sq:Drejtëza e Eulerit sl:Eulerjeva premica sr:Ојлерова права fi:Eulerin suora ta:ஆய்லர் கோடு uk:Лінія Ейлера vi:Đường thẳng Euler zh:歐拉線

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