en.wikipedia.org website review
![](/include/images/menno/screenl1.png)
![](/include/images/loader.gif)
![](/include/images/pixel.png)
![](/include/images/menno/screenl2.png)
![](/include/images/loader.gif)
![](/include/images/pixel.png)
![](/include/images/loader.gif)
![](/include/images/pixel.png)
![](/include/images/menno/highlight.png)
Improve your SEO :: free trial!
en.wikipedia.org is 56% geoptimaliseerd!
SEO Keyword summary for en.wikipedia.org/wiki/polar_coordinate_system
Keywords are extracted from the main content of your website and are the primary indicator of the words this page could rank for. By frequenty count we expect your focus keyword to be varphi
Focus keyword
Short and long tail
Short Tail Keywords varphi polar displaystyle |
long Tail Keywords (2 words) polar coordinates coordinate system polar coordinate between polar angular coordinate |
long Tail Keywords (3 words) polar coordinate system polar and cartesian move to sidebar converting between polar polar coordinates r cavalieri independently introduced bonaventura cavalieri independently |
en.wikipedia.org On-Page SEO Scan
Descriptive Elements
The <head> element of a en.wikipedia.org/wiki/polar_coordinate_system page is used to inform the browser and visitors of the page about the general meta information. The head section of the page is where we place the page title, the definition of the HTML version used, the language of in which the page is written. In the head section we can also include JavaScript and CSS (markup) files for the page.
Page title
Title length
polar coordinate system wikipedia
Meta description
Meta description legth
Meta description SEO
No meta relevance in the description detected !
Content SEO
Number of Words
Spam detected?
Headings
Heading distribution
Heading normalisation
Heading SEO impact
Emphasis (bold and italic)
Emphasis SEO impact
Images
Number of images
Images dimensions
Image alt descriptions
Images SEO impact
wikipedia free encyclopedia displaystyle beginalignedxrcos varphi yrsin endaligned beginalignedrsqrt operatorname hypot xyvarphi atan yxendaligned yxbegincasesarctan leftfrac yxrightmboxif arctan yxrightpi mboxif mbox ygeq frac textundefinedmboxif endcases begincasesarccos xrrightmboxif rneq arccos zxiy zrcos isin zreivarphi rexp ivarphi zroperatorname mathrm cis rangle eivarphi eileftvarphi right leftreivarphi rightnrneinvarphi sqrtnreivarphi over ysin cdot rsin theta gamma cosvarphi rvarphi acosvarphi sqrt sin secvarphi acos leftkvarphi abvarphi rell ecos ell rftheta rgtheta ftheta gtheta itheta kpi beginalignedrfrac dudrrfrac partial upartial xcos rfrac xfrac xyfrac ptfrac dudvarphi xrsin yrcos yfrac xxfrac yendaligned ddrxfrac ddvarphi beginalignedfrac dudxfrac rpartial dudyfrac xsqrt ptcos ysqrt ptsin rcos ddxcos ddysin beginalignedxrvarphi cos yrvarphi dxdvarphi dydvarphi dydxfrac lint absqrt leftrvarphi lefttfrac drvarphi dvarphi int ableftrvarphi iright delta sum ntfrac jdet xypartial beginvmatrixfrac xpartial ypartial endvmatrixbeginvmatrixcos endvmatrixrcos dadxdy jdrdvarphi rdrdvarphi iint rfxydaint abint frvarphi fxex infty dxsqrt mathbf hat sinvarphi times boldsymbol beginalignedmathbf rhat dot leftdot yrightdot rdot ddot leftddot yrightddot rddot rrdot righthat leftrddot ddtleftr beginalignedvec rrtheta erfrac dvec rdtheta drdtheta errhat etheta vec rrighthat fboldsymbol ftextcfboldsymbol ftextcormddot beginalignedfrmromega mddot rfvarphi mdot romega mrddot beginalignedfrmddot rmrdot fvarphi dtheta costheta approx rquad erdrquad omega ijbeginpmatrix endpmatrix icon edit wikidata wikimedia foundation powered mediawiki
Mobile SEO en.wikipedia.org/wiki/polar_coordinate_system
Mobile rendering
![](/include/images/menno/screenl1.png)
![](/include/images/menno/screenl2.png)
![](/include/images/menno/highlight.png)
Mobile optimizations
Responsive design detected (mobile css)
No flash detected !
Mobile improvement
![](/include/images/icons/loader.gif)
![](/include/images/icons/loader.gif)
Marketing / lead generation for en.wikipedia.org/wiki/polar_coordinate_system
Social Media
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
Conversion form
Search form
Analytics
Online presence
SERP Preview
SERP Title
SERP Link
SERP Description
Domain Level SEO
Domain name
16 characters long
Domain name SEO Impact
Path name
coordinate found in path !
polar found in path !
system found in path !
Structured data
Publisher Markup
Other Structured data
Website configuration
Correct processing of non-existing pages?
![](http://www.webcijfers.nl/include/images/icons/loader.gif)
Favicon icon found?
![](http://www.webcijfers.nl/include/images/icons/loader.gif)
Robots.txt found?
![](http://www.webcijfers.nl/include/images/icons/loader.gif)
Sitemap found?
![](http://www.webcijfers.nl/include/images/icons/loader.gif)
Navigation and internal links
Navigation
Url seperator
Human readable urls
Number of links
Link SEO Impact
statistics
|
en.m.wikipedia.org |
en.wikipedia.org wikimedia foundation inc
|
w httpsenwikipediaorgwindexphptitlepolarcoordinatesystemoldid1230535529
page information
printable version
|
wiki mathematics
twodimensional
coordinate system
point
plane
distance
angle
cartesian
ray
azimuth
degrees
radians
1
grgoire de saintvincent
bonaventura cavalieri
gregorio fontana
circular
orbital motion
spirals
cylindrical
spherical
history of trigonometry
greek astronomer
astrologer
hipparchus
chord
on spirals
archimedes
archimedean spiral
mecca
qibla
spherical trigonometry
map projection
equatorial polar coordinates
longitude
latitude
great circle
antipodal point
harvard
coolidge julian
blaise pascal
parabola
method of fluxions
isaac newton
acta eruditorum
jacob bernoulli
radius of curvature
english
george peacock
lacroix
alexis clairaut
leonhard euler
1
1
1
3111
navigation
surveying
physics
clockwise cw
bearing
heading
turns
integer
interval
codomain
arctan function
trigonometric functions
pythagorean sum
atan2
arctangent
arccosine
eulers formula
complex number
complex plane
imaginary unit
eulers number
principal value
angle notations
multiplication
division
exponentiation
root extraction
de moivres formula
plane curve
function
graph
symmetry
rotationally symmetric
polar rose
lemniscate
limaon
cardioid
slope
perpendicularly
variable
conic section
major axis
eccentricity
semilatus rectum
hyperbola
ellipse
calculus
total derivatives
parametric equations
differentiating
curvilinear coordinates
planimeter
sector
riemann sum
linkage
greens theorem
cartesian coordinates
substitution rule for multiple integrals
jacobian
gaussian integral
vector calculus
orthonormal basis
mechanics of planar particle motion
centrifugal force
second law of motion
fictitious forces
osculating circle
centripetal force
differential geometry
coordinate charts
differentiable manifold
metric tensor
differential forms
exterior derivative
orthonormal
dual coframe
connection form
levicivita connection
curvature form
flat manifold
aircraft
magnetic north
zeroninerzero
air traffic control
radial symmetry
groundwater flow equation
radial force
gravitational fields
inversesquare law
point sources
radio antennas
microphone
pickup pattern
list of common coordinate transformations
logpolar
polar decomposition
unit circle
isbn
jstor
eve torrence
eargle john
encyclopedia of mathematics
ems press
curlie
orthogonal coordinate systems
parabolic
bipolar
elliptic
parabolic
paraboloidal
oblate spheroidal
prolate spheroidal
ellipsoidal
elliptic cylindrical
toroidal
bispherical
bipolar cylindrical
conical
6sphere
|
Links to external pages
Outloing links
ar.wikipedia.org
az.wikipedia.org
bn.wikipedia.org
ba.wikipedia.org
be.wikipedia.org
bs.wikipedia.org
ca.wikipedia.org
cv.wikipedia.org
cs.wikipedia.org
cy.wikipedia.org
da.wikipedia.org
de.wikipedia.org
et.wikipedia.org
el.wikipedia.org
es.wikipedia.org
eo.wikipedia.org
eu.wikipedia.org
fa.wikipedia.org
ga.wikipedia.org
gl.wikipedia.org
ko.wikipedia.org
hi.wikipedia.org
hr.wikipedia.org
io.wikipedia.org
id.wikipedia.org
is.wikipedia.org
it.wikipedia.org
he.wikipedia.org
lv.wikipedia.org
lt.wikipedia.org
hu.wikipedia.org
mk.wikipedia.org
nl.wikipedia.org
ja.wikipedia.org
frr.wikipedia.org
no.wikipedia.org
nn.wikipedia.org
pa.wikipedia.org
pl.wikipedia.org
pt.wikipedia.org
ro.wikipedia.org
ru.wikipedia.org
sco.wikipedia.org
sq.wikipedia.org
simple.wikipedia.org
sk.wikipedia.org
sl.wikipedia.org
ckb.wikipedia.org
sr.wikipedia.org
fi.wikipedia.org
sv.wikipedia.org
ta.wikipedia.org
th.wikipedia.org
tr.wikipedia.org
uk.wikipedia.org
wuu.wikipedia.org
zh-yue.wikipedia.org
zh.wikipedia.org
www.wikidata.org
www.wikidata.org
commons.wikimedia.org
www.archive.org
books.google.com
books.google.com
www-history.mcs.st-and.ac.uk
www.doi.org
www.jstor.org
www.doi.org
www.jstor.org
jeff560.tripod.com
web.archive.org
web.archive.org
www.ping.be
web.archive.org
web.archive.org
books.google.com
web.archive.org
en.wikibooks.org
en.wikibooks.org
www.encyclopediaofmath.org
www.curlie.org
www.random-science-tools.com
www.wikidata.org
www.d-nb.info
foundation.wikimedia.org
foundation.wikimedia.org
foundation.wikimedia.org
www.wikimediafoundation.org
SEO Advice for en.wikipedia.org
In this section we provide pointers on how you can to optimize your web page so it can be found more easily by search engines and how to make it rank higher by optimizing the content of the page itself. For each of the individual criteria the maximum score is 100%. A score below 70% is considered to be indication that the page is not complying with general SEO standards and should be evaluated and/or fixed. Not every factor is weighted the same and some are not as important as others. Relatively unimportant factors like meta keywords are not included in the overall score.
Item | Factor | Pointers | |
---|---|---|---|
PageTitle | 100% | Far too many sites lack a page title. A page title is the first thing that shows in the search results so always use the title element. | |
Title relevance | 98% | A title should reflect the contents of a site. This site has a 75 % match | |
Title Length | 80% | Limit your title to anywhere between 40 and 70 characters. Your title was 36 characters long | |
Meta Description | 0% | A meta description is the second element that shows in the search results so always use the meta description. | |
Meta description length | 0% | The meta description should be between 145 and 160 characters. This meta description is 1 characters long. | |
Meta description relevance | 0% | Meta Description should reflect the contents of a site. This site has a 0 % match | |
Number of internal links | 30% | Linking to internal pages makes pages easier to find for search engines. Try to keep the number of links on your page roughly below 100. There are 267 internal links on this page. | |
Folder structure | 100% | We found a folder structure in the links on your page. A good folder structure makes a site easier to navigate. We found 3 level 1 folders and 6 folders above or in the first level of navigation. | |
Headings | 30% | Headers should reflect the contents of a site. This site has a 13 % match | |
Links | 8% | Link anchors should to some degree reflect the contents of a site. This site has a 4 % match | |
Image alt tags | 20% | Image alt tags should to some degree reflect the contents of a site. This site has a 7 % match | |
Bold and italic | 42% | Bold and italic tags should reflect the contents of a site to some degree. This site has a 14 % match | |
Html ratio | 30% | Try to keep the html / text ratio as low as possible. More html means longer loading times. Layout should be handled in a serpate css file | |
Image descriptions | 83% | 82.945736434109 % of all images have been described via the "alt" attribute. Describing images with relevant text may lead to better results in the search engines. | |
Page errors | 100% | Pages with no errors display significantly faster on most browsers. We detected 0 errors and warnings | |
WordCount | 20% | An ideal page contains between 400 and 600 words.This page contains 7047 words | |
Server response time | 100% | A fast server speeds up a website. This server responds 75.22% faster then average | |
Gzip compression | 30% | This site does not use Gzip compression. Pages may not display as fast as they could | |
Keywords in Domainname | 30% | There are no important keywords in your domain name | |
Keywords in domain path | 100% | There are important keywords in the domain path | |
Structured Data | 100% | Structured data makes it easier for search engines to index your website | |
Inline css | 0% | Do not use inline css declarations. Inline css will slow down the rendering of the website. We detected 243 inline style declarations ( <a style="color:green">) with a size of 8315 bytes | |
Excessive use of the same words | 100% | There is no indication that there are one or more keywords that are used excessively. | |
Frames or iframes | 100% | Perfect, detected not (i)frames on your webpagina | |
Flash | 100% | Perfect, we detected no flash objects on your page | |
Css | 30% | We detected too much (2) CSS files on your page. Css files block the loading of a webpage. | |
Javascript | 100% | Perfect, we did not detect too many blocking JavaScript files | |
Mobile Website | 100% | Perfect, we found a responsive design for mobile users | |
Most important heading | 100% | Perfect, we detected a correct use of the most important (h1) heading! | |
Normalized headings | 40% | We dit not font a normalized heading structure. A heading 2 (h2) for example should be followed by a heading of an equal level (h2), a child heading (h3) or even a aprent heading (h1). |
How would you like to have SEO advice for all your pages ?? Start your SEO Dashboard and optimize your website!
en.wikipedia.org images and descriptions
121 images found at en.wikipedia.org Images can improve the user experience for a website by making a pag visually appealing Images can also add extra keyword relevance to a webpage by using alt tags. Images can also slow down a website. If the width and height for a picture is not specified for a browser know in advance how large the image is. A browser must first load the picture and see before it knows how much space should be on the page. Upon reservation In the meantime, the browser can do little but wait. When the height and width for the plate are given in the HTML code, a browser just continues to build for a page while the images load in the background.
http://en.wikipedia.org/static/images/icons/wikipedia.png height: 50 width: 50 description: no alt description found |
|
http://en.wikipedia.org/static/images/mobile/copyright/wikipedia-wordmark-en.svg height: height attribute not set width: width attribute not set description: wikipedia |
|
http://en.wikipedia.org/static/images/mobile/copyright/wikipedia-tagline-en.svg height: 13 width: 117 description: the free encyclopedia |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/d/d3/examples_of_polar_coordinates.svg/250px-examples_of_polar_coordinates.svg.png height: 206 width: 250 description: no alt description found |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/c/c6/head_of_hipparchus_%28cropped%29.jpg/180px-head_of_hipparchus_%28cropped%29.jpg height: 224 width: 180 description: no alt description found |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/1/13/polar_graph_paper.svg/300px-polar_graph_paper.svg.png height: 300 width: 300 description: no alt description found |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/7/78/polar_to_cartesian.svg/250px-polar_to_cartesian.svg.png height: 248 width: 250 description: no alt description found |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/32c7f6c81b7b59f338ab20da873bdd8e714f347b height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}x&=r\cos \varphi ,\\y&=r\sin \varphi .\end{aligned}}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/1e3a8927c8a4129125bc15d5b0c62d3f4056aae2 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}r&={\sqrt {x^{2}+y^{2}}}=\operatorname {hypot} (x,y)\\\varphi &=\operatorname {atan2} (y,x),\end{aligned}}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/020a176bd95008f91e938bb68e78eb0f3b4be9c4 height: height attribute not set width: width attribute not set description: {\displaystyle \operatorname {atan2} (y,x)={\begin{cases}\arctan \left({\frac {y}{x}}\right)&{\mbox{if }}x>0\\\arctan \left({\frac {y}{x}}\right)+\pi &{\mbox{if }}x<0{\mbox{ and }}y\geq 0\\\arctan \left({\frac {y}{x}}\right)-\pi &{\mbox{if }}x<0{\mbox{ and }}y<0\\{\frac {\pi }{2}}&{\mbox{if }}x=0{\mbox{ and }}y>0\\-{\frac {\pi }{2}}&{\mbox{if }}x=0{\mbox{ and }}y<0\\{\text{undefined}}&{\mbox{if }}x=0{\mbox{ and }}y=0.\end{cases}}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/3f358ec57db4fdf72027c6003fe741c65ae335a9 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ={\begin{cases}\arccos \left({\frac {x}{r}}\right)&{\mbox{if }}y\geq 0{\mbox{ and }}r\neq 0\\-\arccos \left({\frac {x}{r}}\right)&{\mbox{if }}y<0\\{\text{undefined}}&{\mbox{if }}r=0.\end{cases}}} |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/7/71/imaginarynumber2.svg/265px-imaginarynumber2.svg.png height: 220 width: 265 description: no alt description found |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/7/71/euler%27s_formula.svg/265px-euler%27s_formula.svg.png height: 265 width: 265 description: no alt description found |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/08e90bb6b36fef59c6113eed2a08f10d77240741 height: height attribute not set width: width attribute not set description: {\displaystyle z=x+iy} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/9fe097f200e7ea38fe974bf69e6af9a50711f431 height: height attribute not set width: width attribute not set description: {\displaystyle z=r(\cos \varphi +i\sin \varphi )} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/fa4851a3817d44e19d4432ddd1d920a750cf299d height: height attribute not set width: width attribute not set description: {\displaystyle z=re^{i\varphi }=r\exp i\varphi .} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/ac4c954a9291a076a06678cb802ce1f2c091ee0a height: height attribute not set width: width attribute not set description: {\displaystyle z=r\operatorname {\mathrm {cis} } \varphi =r\angle \varphi .} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/bb0ab9451e932e31b25551bb0fac473da6f91ef6 height: height attribute not set width: width attribute not set description: {\displaystyle r_{0}e^{i\varphi _{0}}\,r_{1}e^{i\varphi _{1}}=r_{0}r_{1}e^{i\left(\varphi _{0}+\varphi _{1}\right)}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/a6feef865ff906bab2170b9d6a0bc02a4ef12cbe height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {r_{0}e^{i\varphi _{0}}}{r_{1}e^{i\varphi _{1}}}}={\frac {r_{0}}{r_{1}}}e^{i(\varphi _{0}-\varphi _{1})}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/7bf55ee93e12eb2ac00715c6ea258ea537c19ac0 height: height attribute not set width: width attribute not set description: {\displaystyle \left(re^{i\varphi }\right)^{n}=r^{n}e^{in\varphi }} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/9702297c60884f24c748553ecc7246eccf95a448 height: height attribute not set width: width attribute not set description: {\displaystyle {\sqrt[{n}]{re^{i\varphi }}}={\sqrt[{n}]{r}}e^{i\varphi \over n}} |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/5/53/cartesian_to_polar.gif/251px-cartesian_to_polar.gif height: 251 width: 251 description: no alt description found |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/bf591d693bd935388272e00709852d7bf7546464 height: height attribute not set width: width attribute not set description: {\displaystyle y=\sin(6\!\cdot \!x)+2} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/ce36e6b7aff8172fdcfd13cba463edd2841036e7 height: height attribute not set width: width attribute not set description: {\displaystyle r=\sin(6\!\cdot \!\theta )+2} |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/3/33/circle_r%3d1.svg/220px-circle_r%3d1.svg.png height: 220 width: 220 description: no alt description found |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/d5ba4978ce2510f55703b6912c4eac28c7b259f5 height: height attribute not set width: width attribute not set description: {\displaystyle (r_{0},\gamma )} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/a5b2133629adf698f1cbbfb515b96bbf4b98854a height: height attribute not set width: width attribute not set description: {\displaystyle r^{2}-2rr_{0}\cos(\varphi -\gamma )+r_{0}^{2}=a^{2}.} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/e1bd9d6b55e284e3e39e44b031bab3545e094b8d height: height attribute not set width: width attribute not set description: {\displaystyle r(\varphi )=a} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/afe766975258871bd446ee93b07c2e95cc7b4543 height: height attribute not set width: width attribute not set description: {\displaystyle r=2a\cos(\varphi -\gamma ).} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/d994793bd0b5f0b27d5f44c0ee5c358eea0dcf0e height: height attribute not set width: width attribute not set description: {\displaystyle r=r_{0}\cos(\varphi -\gamma )+{\sqrt {a^{2}-r_{0}^{2}\sin ^{2}(\varphi -\gamma )}}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/69719ee225311b045858df8195025e200e1cd201 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi =\gamma ,} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a height: height attribute not set width: width attribute not set description: {\displaystyle \gamma } |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/6e619df44e8373642f59fbbd6624b14b2f8a2b92 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi =\arctan m} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc height: height attribute not set width: width attribute not set description: {\displaystyle m} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/d92fa30c8d0384ef454ffd19bdd96deb59227d03 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi =\gamma } |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/ef6da7aade8923fd88ff2e33b0770bacd37e37fc height: height attribute not set width: width attribute not set description: {\displaystyle r(\varphi )=r_{0}\sec(\varphi -\gamma ).} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/fb12fcfddb65e3d1e6a044215f6e833f0cd4337b height: height attribute not set width: width attribute not set description: {\displaystyle r_{0}} |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/d/dd/rose_2sin%284theta%29.svg/220px-rose_2sin%284theta%29.svg.png height: 220 width: 220 description: no alt description found |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/a1253e5cbb9692700eebdb3f01dca8bd42d35744 height: height attribute not set width: width attribute not set description: {\displaystyle r(\varphi )=a\cos \left(k\varphi +\gamma _{0}\right)} |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/f/fd/spiral_of_archimedes.svg/220px-spiral_of_archimedes.svg.png height: 220 width: 220 description: no alt description found |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/b6bc07b3412232dc537a723cc05e6cb670c6bb08 height: height attribute not set width: width attribute not set description: {\displaystyle r(\varphi )=a+b\varphi .} |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/3/35/elps-slr.svg/250px-elps-slr.svg.png height: 139 width: 250 description: no alt description found |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/6e9ca91efb44ae1c78c1a9344ec9d9c209cdc98a height: height attribute not set width: width attribute not set description: {\displaystyle r={\ell \over {1-e\cos \varphi }}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/f066e981e530bacc07efc6a10fa82deee985929e height: height attribute not set width: width attribute not set description: {\displaystyle \ell } |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/74b1c1243470e52a5b3e0dded9ce187554c998f6 height: height attribute not set width: width attribute not set description: {\displaystyle r=f(\theta )} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/5b91bd02a323fda2f673914202c9e392ba3de6f5 height: height attribute not set width: width attribute not set description: {\displaystyle r=g(\theta )} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/cd8517172980db67ff4d64f1861d97dea3038be9 height: height attribute not set width: width attribute not set description: {\displaystyle f(\theta )=0} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/7fee61e9df244268896c1f8197e0fb8e578a51ff height: height attribute not set width: width attribute not set description: {\displaystyle g(\theta )=0} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/8c3942e962cea54fd104a33ebac17dde8bffa819 height: height attribute not set width: width attribute not set description: {\displaystyle [g(\theta _{i}),\theta _{i}]} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/302b19204ed378e99ff4575341a67eebdbe5a555 height: height attribute not set width: width attribute not set description: {\displaystyle \theta _{i}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/0a2f15bfe8b3ae192a02890befba28345dc3051a height: height attribute not set width: width attribute not set description: {\displaystyle f(\theta +2k\pi )=g(\theta )} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40 height: height attribute not set width: width attribute not set description: {\displaystyle k} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/4421b2abe8af4eea8f0e49401d48228f35651887 height: height attribute not set width: width attribute not set description: {\displaystyle f(\theta +(2k+1)\pi )=-g(\theta )} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/01d876b55918333fa5b3792a72f5254b82b86c63 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}r{\frac {du}{dr}}&=r{\frac {\partial u}{\partial x}}\cos \varphi +r{\frac {\partial u}{\partial y}}\sin \varphi =x{\frac {\partial u}{\partial x}}+y{\frac {\partial u}{\partial y}},\\[2pt]{\frac {du}{d\varphi }}&=-{\frac {\partial u}{\partial x}}r\sin \varphi +{\frac {\partial u}{\partial y}}r\cos \varphi =-y{\frac {\partial u}{\partial x}}+x{\frac {\partial u}{\partial y}}.\end{aligned}}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/9f6d6d1a9e05c093275ecaf66033a4298e41fe1d height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}r{\frac {d}{dr}}&=x{\frac {\partial }{\partial x}}+y{\frac {\partial }{\partial y}}\\[2pt]{\frac {d}{d\varphi }}&=-y{\frac {\partial }{\partial x}}+x{\frac {\partial }{\partial y}}.\end{aligned}}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/f446e4f0df07ead889d7039cec3301472fc1f9ea height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}{\frac {du}{dx}}&={\frac {\partial u}{\partial r}}{\frac {\partial r}{\partial x}}+{\frac {\partial u}{\partial \varphi }}{\frac {\partial \varphi }{\partial x}},\\[2pt]{\frac {du}{dy}}&={\frac {\partial u}{\partial r}}{\frac {\partial r}{\partial y}}+{\frac {\partial u}{\partial \varphi }}{\frac {\partial \varphi }{\partial y}},\end{aligned}}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/8dcc66ee6a6250cc206f488bb56f976a9a8bd2e8 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}{\frac {du}{dx}}&={\frac {\partial u}{\partial r}}{\frac {x}{\sqrt {x^{2}+y^{2}}}}-{\frac {\partial u}{\partial \varphi }}{\frac {y}{x^{2}+y^{2}}}\\[2pt]&=\cos \varphi {\frac {\partial u}{\partial r}}-{\frac {1}{r}}\sin \varphi {\frac {\partial u}{\partial \varphi }},\\[2pt]{\frac {du}{dy}}&={\frac {\partial u}{\partial r}}{\frac {y}{\sqrt {x^{2}+y^{2}}}}+{\frac {\partial u}{\partial \varphi }}{\frac {x}{x^{2}+y^{2}}}\\[2pt]&=\sin \varphi {\frac {\partial u}{\partial r}}+{\frac {1}{r}}\cos \varphi {\frac {\partial u}{\partial \varphi }}.\end{aligned}}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/0a08bfe016a4d8e15a933032d077bcdf8c49d41e height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}{\frac {d}{dx}}&=\cos \varphi {\frac {\partial }{\partial r}}-{\frac {1}{r}}\sin \varphi {\frac {\partial }{\partial \varphi }}\\[2pt]{\frac {d}{dy}}&=\sin \varphi {\frac {\partial }{\partial r}}+{\frac {1}{r}}\cos \varphi {\frac {\partial }{\partial \varphi }}.\end{aligned}}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/d57e14dd98cc1b390d69a4f11c9b4086542b45f7 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}x&=r(\varphi )\cos \varphi \\y&=r(\varphi )\sin \varphi \end{aligned}}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/341713e0b0d484e169fb6cc867ab6a6e31b7ca65 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}{\frac {dx}{d\varphi }}&=r'(\varphi )\cos \varphi -r(\varphi )\sin \varphi \\[2pt]{\frac {dy}{d\varphi }}&=r'(\varphi )\sin \varphi +r(\varphi )\cos \varphi .\end{aligned}}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/ff730497ec3671286d63415d676817f8f14299e1 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {dy}{dx}}={\frac {r'(\varphi )\sin \varphi +r(\varphi )\cos \varphi }{r'(\varphi )\cos \varphi -r(\varphi )\sin \varphi }}.} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/34f62c06ac2868b9ac160abe1e75a075cad9e261 height: height attribute not set width: width attribute not set description: {\displaystyle l=\int _{a}^{b}{\sqrt {\left[r(\varphi )\right]^{2}+\left[{\tfrac {dr(\varphi )}{d\varphi }}\right]^{2}}}d\varphi } |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/polar_coordinates_integration_region.svg/220px-polar_coordinates_integration_region.svg.png height: 128 width: 220 description: no alt description found |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/9fc7958a00360514f36fabcac7cab0361c2ae068 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{2}}\int _{a}^{b}\left[r(\varphi )\right]^{2}\,d\varphi .} |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/polar_coordinates_integration_riemann_sum.svg/220px-polar_coordinates_integration_riemann_sum.svg.png height: 128 width: 220 description: no alt description found |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/5/54/planimeter.jpg/220px-planimeter.jpg height: 168 width: 220 description: no alt description found |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/ec0cb32735f6a73076e1db62726c0eace3f000f6 height: height attribute not set width: width attribute not set description: {\displaystyle \left[r(\varphi _{i})\right]^{2}\pi \cdot {\frac {\delta \varphi }{2\pi }}={\frac {1}{2}}\left[r(\varphi _{i})\right]^{2}\delta \varphi .} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/3102375792a188288a60e6138e3eb3497d54eed4 height: height attribute not set width: width attribute not set description: {\displaystyle \sum _{i=1}^{n}{\tfrac {1}{2}}r(\varphi _{i})^{2}\,\delta \varphi .} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/52a1293fcb0e90b77017c0d9176c62aa06615b9b height: height attribute not set width: width attribute not set description: {\displaystyle j=\det {\frac {\partial (x,y)}{\partial (r,\varphi )}}={\begin{vmatrix}{\frac {\partial x}{\partial r}}&{\frac {\partial x}{\partial \varphi }}\\[2pt]{\frac {\partial y}{\partial r}}&{\frac {\partial y}{\partial \varphi }}\end{vmatrix}}={\begin{vmatrix}\cos \varphi &-r\sin \varphi \\\sin \varphi &r\cos \varphi \end{vmatrix}}=r\cos ^{2}\varphi +r\sin ^{2}\varphi =r.} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/204ed02c6ad48093830a86a8f76829a384e16bac height: height attribute not set width: width attribute not set description: {\displaystyle da=dx\,dy\ =j\,dr\,d\varphi =r\,dr\,d\varphi .} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/91b80d79c6bc8a4a265145bedfd8cdbc864eba37 height: height attribute not set width: width attribute not set description: {\displaystyle \iint _{r}f(x,y)\,da=\int _{a}^{b}\int _{0}^{r(\varphi )}f(r,\varphi )\,r\,dr\,d\varphi .} |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/2/2f/e%5e%28-x%5e2%29.svg/220px-e%5e%28-x%5e2%29.svg.png height: 176 width: 220 description: no alt description found |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/1bed0b77b34cab03996deb42d464becab2f05636 height: height attribute not set width: width attribute not set description: {\displaystyle f(x)=e^{-x^{2}}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4 height: height attribute not set width: width attribute not set description: {\displaystyle x} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/7ae18ec124928c74818b516e6350ca9610966c6e height: height attribute not set width: width attribute not set description: {\displaystyle {\sqrt {\pi }}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/b06d446e3c625f48f318811eabdfe5902b11508a height: height attribute not set width: width attribute not set description: {\displaystyle \int _{-\infty }^{\infty }e^{-x^{2}}\,dx={\sqrt {\pi }}.} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/eca0f46511c4c986c48b254073732c0bd98ae0c1 height: height attribute not set width: width attribute not set description: {\displaystyle \mathbf {r} } |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/dea4252337486f32086a8eca580118da61998da8 height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {\mathbf {r} }}=(\cos(\varphi ),\sin(\varphi ))} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/45c643fb60ea71542145705fe801c7ab8c769507 height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {\mathbf {k} }}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/bb0b0fd52a60edf991ec517a0079d1404c159f84 height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {\mathbf {k} }}={\hat {\mathbf {v} }}\times {\hat {\mathbf {r} }}.} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/38836592838cbd2616f64f824d7f20f76c6a1e28 height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {\boldsymbol {\varphi }}}=(-\sin(\varphi ),\cos(\varphi ))={\hat {\mathbf {k} }}\times {\hat {\mathbf {r} }}\ ,} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/12bf589db793cfbbd8b200aea175a99a74991455 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}\mathbf {r} &=(x,\ y)=r(\cos \varphi ,\ \sin \varphi )=r{\hat {\mathbf {r} }}\ ,\\{\dot {\mathbf {r} }}&=\left({\dot {x}},\ {\dot {y}}\right)={\dot {r}}(\cos \varphi ,\ \sin \varphi )+r{\dot {\varphi }}(-\sin \varphi ,\ \cos \varphi )={\dot {r}}{\hat {\mathbf {r} }}+r{\dot {\varphi }}{\hat {\boldsymbol {\varphi }}}\ ,\\{\ddot {\mathbf {r} }}&=\left({\ddot {x}},\ {\ddot {y}}\right)\\&={\ddot {r}}(\cos \varphi ,\ \sin \varphi )+2{\dot {r}}{\dot {\varphi }}(-\sin \varphi ,\ \cos \varphi )+r{\ddot {\varphi }}(-\sin \varphi ,\ \cos \varphi )-r{\dot {\varphi }}^{2}(\cos \varphi ,\ \sin \varphi )\\&=\left({\ddot {r}}-r{\dot {\varphi }}^{2}\right){\hat {\mathbf {r} }}+\left(r{\ddot {\varphi }}+2{\dot {r}}{\dot {\varphi }}\right){\hat {\boldsymbol {\varphi }}}\\&=\left({\ddot {r}}-r{\dot {\varphi }}^{2}\right){\hat {\mathbf {r} }}+{\frac {1}{r}}\;{\frac {d}{dt}}\left(r^{2}{\dot {\varphi }}\right){\hat {\boldsymbol {\varphi }}}.\end{aligned}}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af height: height attribute not set width: width attribute not set description: {\displaystyle \theta } |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/dd7a4bee07779272933ffaf63d8ad0c091143e83 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}{\vec {r}}&=r(\theta ){\hat {e}}_{r}\\{\frac {d{\vec {r}}}{d\theta }}&={\frac {dr}{d\theta }}{\hat {e}}_{r}+r{\hat {e}}_{\theta }\\{\frac {d^{2}{\vec {r}}}{d\theta ^{2}}}&=\left({\frac {d^{2}r}{d\theta ^{2}}}-r\right){\hat {e}}_{r}+{\frac {dr}{d\theta }}{\hat {e}}_{\theta }\end{aligned}}} |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/f/fe/position_vector_plane_polar_coords.svg/100px-position_vector_plane_polar_coords.svg.png height: 137 width: 100 description: no alt description found |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/d/d6/velocity_vector_plane_polar_coords.svg/150px-velocity_vector_plane_polar_coords.svg.png height: 125 width: 150 description: no alt description found |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/5/58/acceleration_vector_plane_polar_coords.svg/200px-acceleration_vector_plane_polar_coords.svg.png height: 123 width: 200 description: no alt description found |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/4a43d54e4ab6b4e75edf3915099451d1d87ce4cd height: height attribute not set width: width attribute not set description: {\displaystyle r{\dot {\varphi }}^{2}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/31062c81fca84b3560ed160d47ae3b0850001845 height: height attribute not set width: width attribute not set description: {\displaystyle 2{\dot {r}}{\dot {\varphi }}} |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/0/0c/co-rotating_frame_vector.svg/220px-co-rotating_frame_vector.svg.png height: 157 width: 220 description: no alt description found |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/4f1007aa373f62ce606c7390e6a20218b3183ea4 height: height attribute not set width: width attribute not set description: {\displaystyle {\boldsymbol {f}}+{\boldsymbol {f}}_{\text{cf}}+{\boldsymbol {f}}_{\text{cor}}=m{\ddot {\boldsymbol {r}}}\ ,} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/c3a86cde193c5bce5cdbac8827bf824f44a6a188 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}f_{r}+mr\omega ^{2}&=m{\ddot {r}}\\f_{\varphi }-2m{\dot {r}}\omega &=mr{\ddot {\varphi }}\ ,\end{aligned}}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/c4a698bd84bbff8bdf676c2a723b63abad1a7f78 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}f_{r}&=m{\ddot {r}}-mr{\dot {\varphi }}^{2}\\f_{\varphi }&=mr{\ddot {\varphi }}+2m{\dot {r}}{\dot {\varphi }}\ .\end{aligned}}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/45e4367248c8cd078f74f838c99b8b2e0766e4bc height: height attribute not set width: width attribute not set description: {\displaystyle ds^{2}=dr^{2}+r^{2}d\theta ^{2}.} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/24a89bb206b44f2fedf322ef8adb6bed3f36587d height: height attribute not set width: width attribute not set description: {\displaystyle p_{1}=(x_{1},y_{1})=(r_{1},\theta _{1})} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/3bea2a177c765b80efe065428bd5eec3f1144983 height: height attribute not set width: width attribute not set description: {\displaystyle p_{2}=(x_{2},y_{2})=(r_{2},\theta _{2})} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/e269a03041ad37930bf2a7d4d9c3002868812e61 height: height attribute not set width: width attribute not set description: {\displaystyle ds^{2}=dx^{2}+dy^{2}=(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}.} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/46d4f7c2c0934aa842ce3473cfb3603ba037c381 height: height attribute not set width: width attribute not set description: {\displaystyle dx^{2}=(r_{2}\cos \theta _{2}-r_{1}\cos \theta _{1})^{2}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/af09247c26fde2acecc1cbd248f89bc27dce4216 height: height attribute not set width: width attribute not set description: {\displaystyle dy^{2}=(r_{2}\sin \theta _{2}-r_{1}\sin \theta _{1})^{2}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/ec2e9e5df0fa75543fc012e6e5f5fcf580420f89 height: height attribute not set width: width attribute not set description: {\displaystyle ds^{2}=r_{2}^{2}\cos ^{2}\theta _{2}-2r_{1}r_{2}\cos \theta _{1}\cos \theta _{2}+r_{1}^{2}\cos ^{2}\theta _{1}+r_{2}^{2}\sin ^{2}\theta _{2}-2r_{1}r_{2}\sin \theta _{1}\sin \theta _{2}+r_{1}^{2}\sin ^{2}\theta _{1}=} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/5fb5c48631364b2ca69314016015e23c740b7488 height: height attribute not set width: width attribute not set description: {\displaystyle r_{2}^{2}(\cos ^{2}\theta _{2}+\sin ^{2}\theta _{2})+r_{1}^{2}(\cos ^{2}\theta _{1}+\sin ^{2}\theta _{1})-2r_{1}r_{2}(\cos \theta _{1}\cos \theta _{2}+\sin \theta _{1}\sin \theta _{2})=} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/b1eb646f79e055ea55e2a85b79860587bf03654f height: height attribute not set width: width attribute not set description: {\displaystyle r_{1}^{2}+r_{2}^{2}-2r_{1}r_{2}(1-1+\cos \theta _{1}\cos \theta _{2}+\sin \theta _{1}\sin \theta _{2})=} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/b696d30f4211f7466c2a68885dbe3bb265fe8fae height: height attribute not set width: width attribute not set description: {\displaystyle (r_{2}-r_{1})^{2}+2r_{1}r_{2}(1-\cos \theta _{1}\cos \theta _{2}-\sin \theta _{1}\sin \theta _{2}).} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/75fd64c78f2fbc630ce57e4d0fa622314d1705ab height: height attribute not set width: width attribute not set description: {\displaystyle \cos(\theta _{2}-\theta _{1})=\cos \theta _{1}\cos \theta _{2}+\sin \theta _{1}\sin \theta _{2}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/5ed38cc678a1fcd4997dd251f8020d56e674c165 height: height attribute not set width: width attribute not set description: {\displaystyle ds^{2}=dr^{2}+2r_{1}r_{2}(1-\cos d\theta ).} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538 height: height attribute not set width: width attribute not set description: {\displaystyle r} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/f3bc8304486a0d1e230104dde407e2a499885344 height: height attribute not set width: width attribute not set description: {\displaystyle r_{1}r_{2}\approx r^{2}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/75ae6ca1248d081ef3fcfdd3e17ba0e3f6c02ee9 height: height attribute not set width: width attribute not set description: {\displaystyle d\theta } |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/ea3229e6fb55e20caea0b9ed2ba2821a77dc01f9 height: height attribute not set width: width attribute not set description: {\displaystyle \cos d\theta \approx 1-{\frac {d\theta ^{2}}{2}},} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/084a928582c1b0231ac8429d76176edacc13e4d8 height: height attribute not set width: width attribute not set description: {\displaystyle 1-\cos d\theta \approx {\frac {d\theta ^{2}}{2}}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/b4525d31de3a3237144c515f309d3684a25f9925 height: height attribute not set width: width attribute not set description: {\displaystyle 2r_{1}r_{2}(1-\cos d\theta )\approx 2r^{2}{\frac {d\theta ^{2}}{2}}=r^{2}d\theta ^{2}} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/94033f289cb986e49f994aacfec12bd61fec03b7 height: height attribute not set width: width attribute not set description: {\displaystyle ds^{2}=dr^{2}+r^{2}d\theta ^{2},} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/f6758e0f65d688a8afc9ece6d3c3d516f42e6e9e height: height attribute not set width: width attribute not set description: {\displaystyle e_{r}={\frac {\partial }{\partial r}},\quad e_{\theta }={\frac {1}{r}}{\frac {\partial }{\partial \theta }},} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/cd1c06d78c84de73182642ed63b3a4f89015c669 height: height attribute not set width: width attribute not set description: {\displaystyle e^{r}=dr,\quad e^{\theta }=rd\theta .} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/9f7ae10ad77fd9535b2536bcb66e9bcc013a0fb1 height: height attribute not set width: width attribute not set description: {\displaystyle {\omega ^{i}}_{j}={\begin{pmatrix}0&-d\theta \\d\theta &0\end{pmatrix}}} |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/3/3e/nuvola_apps_edu_mathematics_blue-p.svg/28px-nuvola_apps_edu_mathematics_blue-p.svg.png height: 28 width: 28 description: icon |
|
https://upload.wikimedia.org/wikipedia/commons/thumb/d/df/wikibooks-logo-en-noslogan.svg/40px-wikibooks-logo-en-noslogan.svg.png height: 40 width: 40 description: no alt description found |
|
https://upload.wikimedia.org/wikipedia/en/thumb/8/8a/oojs_ui_icon_edit-ltr-progressive.svg/10px-oojs_ui_icon_edit-ltr-progressive.svg.png height: 10 width: 10 description: edit this at wikidata |
|
https://login.wikimedia.org/wiki/special:centralautologin/start?type=1x1 height: 1 width: 1 description: no alt description found |
|
http://en.wikipedia.org/static/images/footer/wikimedia-button.svg height: 29 width: 84 description: wikimedia foundation |
|
http://en.wikipedia.org/static/images/footer/poweredby_mediawiki.svg height: 29 width: 84 description: powered by mediawiki |
How are images contributing to your SEO site-wise ? Your leading content tool has the awnsers!