ar.wikipedia.org website review
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ar.wikipedia.org is 44% geoptimaliseerd!
SEO Keyword summary for ar.wikipedia.org/wiki/%d9%86%d8%b3%d8%a8%d8%a9_%d8%b0%d9%87%d8%a8%d9%8a%d8%a9
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 displaystyle frac |
long Tail Keywords (2 words) frac 1sqrt displaystyle varphi frac abafrac 11cfrac 11cfrac varphi frac |
long Tail Keywords (3 words) frac 1sqrt 52 varphi frac 1sqrt 19e3779b97f4a7c15f39 111111111displaystyle 1cfrac 16180339887498948482 19e3779b97f4a7c15f39 111111111displaystyle 11001111000110111011 16180339887498948482 19e3779b97f4a7c15f39 111111111displaystyle 1cfrac 11cfrac 11cfrac 11cfrac 11cfrac |
ar.wikipedia.org On-Page SEO Scan
Descriptive Elements
The <head> element of a ar.wikipedia.org/wiki/%d9%86%d8%b3%d8%a8%d8%a9_%d8%b0%d9%87%d8%a8%d9%8a%d8%a9 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
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
No headings were found !
Emphasis (bold and italic)
Emphasis SEO impact
Images
Number of images
Images dimensions
Image alt descriptions
Images SEO impact
wikidata displaystyle varphi frac sqrt abafrac abequiv stackrel textdef phi ldots cfrac ddots abvarphi aafrac dots nmfrac mnmqquad textstyle leftfrac right over cdots sum infty sinpi sin circ cscpi csc cospi cos tfrac abbctfrac acabphi fleftnrightvarphi nvarphi lim nto fnvarphi fnafnvarphi beginaligned approx endaligned kfkvarphi axb mathbb alpha xxx operatorname psl mathbf cdot noperatorname lfloor rfloor mvarphi nlnfnsqrt logvarphi rqcfrac quad left rightfrac abin abpi avarphi bvarphi xnxn times ntimes oeis fibonacci word detail artwork samuel monnier wikimedia foundation powered mediawiki
Mobile SEO ar.wikipedia.org/wiki/%d9%86%d8%b3%d8%a8%d8%a9_%d8%b0%d9%87%d8%a8%d9%8a%d8%a9
Mobile rendering
Mobile optimizations
Responsive design detected (mobile css)
No flash detected !
Mobile improvement
Marketing / lead generation for ar.wikipedia.org/wiki/%d9%86%d8%b3%d8%a8%d8%a9_%d8%b0%d9%87%d8%a8%d9%8a%d8%a9
Social Media
Facebook shares | Facebook likes | ||
Facebook comments | Tweets | ||
Google +1 |
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
No contextual keywords found in path
Structured data
Publisher Markup
Other Structured data
Website configuration
Correct processing of non-existing pages?
Favicon icon found?
Robots.txt found?
Sitemap found?
Navigation and internal links
Navigation
Url seperator
Human readable urls
Number of links
Link SEO Impact
ar.m.wikipedia.org |
ar.wikipedia.org |
creativecommons.org |
w jan tschichold
aeonium tabuliforme
parastichy
historia mathematica
posamentier alfred s
prometheus books
cook theodore andrea
gardner martin
nicolaas de bruijn
american scientist
jan tschichold
erica l flapan
ghyka matila
hogben lancelot
moscovich ivan
peterson ivars
roy batchelor
encyclopedia of mathematics
wolfram demonstrations
conways constant
hyperboloid structure
minimal surface
camera lucida
wallpaper group
algorithmic art
croatian interlace
vastu shastra
list of works designed with the golden ratio
pi in the sky
st marys cathedral
selfportrait in a convex mirror
the ancient of days
the swallows tail
circle limit iii
la condition humaine
jean metzinger
danseuse au caf
erik demaine
scott draves
helaman ferguson
peter forakis
susan goldstine
bathsheba grossman
desmond paul henry
garden of cosmic speculation
robert longhurst
jeanette mcleod
hamid naderi yeganeh
alba rojo cama
reza sarhangi
roman verostko
margaret wertheim
de prospectiva pingendi
de re aedificatoria
sebastiano serlio
i quattro libri dellarchitettura
jay hambidge
the grammar of ornament
ernest hanbury hankin
gdel escher bach
journal of mathematics and the arts
rhythm of structure
the bridges organization
european society for mathematics and the arts
goudreau museum of mathematics in art and science
institute for figuring
museum of mathematics
httpsarwikipediaorgwindexphptitleoldid66956784
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wiki boarisch
1914
1
strogatz steven
smith david eugene
hart george w
staatsgalerie stuttgart
|
Links to external pages
Outloing links
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he.wikipedia.org
hi.wikipedia.org
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hu.wikipedia.org
hy.wikipedia.org
id.wikipedia.org
is.wikipedia.org
it.wikipedia.org
ja.wikipedia.org
ka.wikipedia.org
kk.wikipedia.org
la.wikipedia.org
lb.wikipedia.org
li.wikipedia.org
lmo.wikipedia.org
lt.wikipedia.org
lv.wikipedia.org
mk.wikipedia.org
ms.wikipedia.org
nds-nl.wikipedia.org
nl.wikipedia.org
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no.wikipedia.org
oc.wikipedia.org
pa.wikipedia.org
pms.wikipedia.org
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ru.wikipedia.org
sh.wikipedia.org
si.wikipedia.org
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sl.wikipedia.org
sq.wikipedia.org
sr.wikipedia.org
ta.wikipedia.org
th.wikipedia.org
tr.wikipedia.org
tt.wikipedia.org
uz.wikipedia.org
vi.wikipedia.org
vls.wikipedia.org
wa.wikipedia.org
wuu.wikipedia.org
zh.wikipedia.org
zh-classical.wikipedia.org
zh-yue.wikipedia.org
www.wikidata.org
www.wikidata.org
commons.wikimedia.org
www.wikidata.org
www.wikidata.org
www.wikidata.org
www.wikidata.org
www.wikidata.org
www.wikidata.org
www.wikidata.org
www.wikidata.org
en.wikipedia.org
en.wikipedia.org
aleph0.clarku.edu
web.archive.org
www.real-sciences.com
www.real-sciences.com
web.archive.org
web.archive.org
web.archive.org
mathworld.wolfram.com
web.archive.org
www.archive.org
www.archive.org
www.doi.org
web.archive.org
mathworld.wolfram.com
web.archive.org
web.archive.org
web.archive.org
web.archive.org
mathworld.wolfram.com
web.archive.org
web.archive.org
www.emis.de
web.archive.org
web.archive.org
web.archive.org
web.archive.org
web.archive.org
web.archive.org
www.arxiv.org
www.archive.org
web.archive.org
books.google.com
web.archive.org
web.archive.org
www.huygens-fokker.org
web.archive.org
web.archive.org
web.archive.org
www.wikidata.org
mathworld.wolfram.com
web.archive.org
web.archive.org
web.archive.org
web.archive.org
www.arxiv.org
ui.adsabs.harvard.edu
www.doi.org
web.archive.org
www.maths.surrey.ac.uk
www.maths.surrey.ac.uk
www.numberworld.org
web.archive.org
www.wikidata.org
www.wikidata.org
web.archive.org
web.archive.org
web.archive.org
web.archive.org
www.jstor.org
www.umcs.maine.edu
web.archive.org
web.archive.org
www.archive.org
web.archive.org
web.archive.org
books.google.com
mediation.centrepompidou.fr
web.archive.org
www.encyclopediaofmath.org
www.wikidata.org
demonstrations.wolfram.com
commons.wikimedia.org
www.wikidata.org
catalogo.bne.es
www.d-nb.info
olduli.nli.org.il
id.ndl.go.jp
aleph.nkp.cz
www.idref.fr
foundation.wikimedia.org
foundation.wikimedia.org
foundation.wikimedia.org
SEO Advice for ar.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 | 0% | A title should reflect the contents of a site. This site has a 0 % match | |
Title Length | 100% | Limit your title to anywhere between 40 and 70 characters. Your title was 41 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 683 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 5 level 1 folders and 9 folders above or in the first level of navigation. | |
Headings | 0% | Headers should reflect the contents of a site. This site has a 0 % match | |
Links | 8% | Link anchors should to some degree reflect the contents of a site. This site has a 4 % match | |
Image alt tags | 45% | Image alt tags should to some degree reflect the contents of a site. This site has a 16 % match | |
Bold and italic | 24% | Bold and italic tags should reflect the contents of a site to some degree. This site has a 8 % match | |
Html ratio | 60% | 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 | 81% | 80.978260869565 % 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 3733 words | |
Server response time | 30% | A slow server slows down a website. This server responds 18.1% slower the 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 | 20% | There are no 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 459 inline style declarations ( <a style="color:green">) with a size of 14177 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 (3) 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!
ar.wikipedia.org images and descriptions
159 images found at ar.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://ar.wikipedia.org/static/images/icons/wikipedia.png height: 50 width: 50 description: no alt description found |
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http://ar.wikipedia.org/static/images/mobile/copyright/wikipedia-wordmark-ar.svg height: height attribute not set width: width attribute not set description: ويكيبيديا |
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http://ar.wikipedia.org/static/images/mobile/copyright/wikipedia-tagline-ar.svg height: 22 width: 105 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/6/63/arbcom_ru_editing.svg/10px-arbcom_ru_editing.svg.png height: 10 width: 10 description: عدل القيمة على wikidata |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0b498bd7bebdaa79ba86131a9f839f96a4e7628f height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ={\frac {1+{\sqrt {5}}}{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e height: height attribute not set width: width attribute not set description: {\displaystyle \varphi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2b78ccdb7e18e02d4fc567c66aac99bf524acb5f height: height attribute not set width: width attribute not set description: {\displaystyle {\sqrt {5}}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/4/43/test_template_info-icon_-_version_%282%29.svg/30px-test_template_info-icon_-_version_%282%29.svg.png height: 13 width: 30 description: حول القالب |
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https://upload.wikimedia.org/wikipedia/commons/thumb/4/44/golden_ratio_line.svg/220px-golden_ratio_line.svg.png height: 127 width: 220 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/8/8e/similargoldenrectangles.svg/220px-similargoldenrectangles.svg.png height: 202 width: 220 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/94b17cee919ba893572e106101885e9947e2d8c3 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {a+b}{a}}={\frac {a}{b}}\equiv \varphi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/19a92f2bf1181d6d7b4e8af138d01004fe7fe530 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {a+b}{a}}={\frac {a}{b}}\ {\stackrel {\text{def}}{=}}\ \varphi ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4 height: height attribute not set width: width attribute not set description: {\displaystyle \phi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e22ea5278827fbb7e09fb5fbeb5f50b234410f84 height: height attribute not set width: width attribute not set description: {\displaystyle x^{2}-x-1=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d4010f92e33cc559bc8d7f24b4ed017273a0628d height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ={\frac {1+{\sqrt {5}}}{2}}=1.6180339887\ldots .} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/3/32/golden_rectangle_construction.svg/220px-golden_rectangle_construction.svg.png height: 266 width: 220 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7fbad6d8c8d284ea5391a39db22c14858d696c1f height: height attribute not set width: width attribute not set description: {\displaystyle 1+{\cfrac {1}{1+{\cfrac {1}{1+{\cfrac {1}{1+{\cfrac {1}{1+\ddots }}}}}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2102ba6ed802cb9a98dc1a0fc1ac99b1a03b4047 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1+{\sqrt {5}}}{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cf7e51356f54a831db021e7e46922c778bbd91c0 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {a+b}{a}}={\frac {a}{b}}=\varphi .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5d253b8b63fe6f4a656787c015bec7e36645b04d height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {a+b}{a}}={\frac {a}{a}}+{\frac {b}{a}}=1+{\frac {b}{a}}=1+{\frac {1}{\varphi }}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/73516b60e9391da6113e1df0eab685d732451cc2 height: height attribute not set width: width attribute not set description: {\displaystyle 1+{\frac {1}{\varphi }}=\varphi .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7452e786dfd2a1a3e0cdc7cf38b508d0ccb43796 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi +1=\varphi ^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/909a0da5459476692cb089d9b951d4284387e927 height: height attribute not set width: width attribute not set description: {\displaystyle {\varphi }^{2}-\varphi -1=0.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/68dc7254348118480c0b51f9511f35f955ce86b1 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1+{\sqrt {5}}}{2}}=1.618\,033\,988\,7\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/60061ebfed9e4c449e7295a89dad486dd8381c61 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1-{\sqrt {5}}}{2}}=-0.618\,033\,988\,7\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1c9b7ed65783d1cdb2dfa7abd1361b1c1553bbe6 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ={\frac {1+{\sqrt {5}}}{2}}=1.61803\,39887\dots } |
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https://upload.wikimedia.org/wikipedia/commons/thumb/6/6a/michael_maestlin.jpg/220px-michael_maestlin.jpg height: 366 width: 220 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/fibonacci_spiral.svg/250px-fibonacci_spiral.svg.png height: 155 width: 250 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/lucas_number_spiral.svg/250px-lucas_number_spiral.svg.png height: 155 width: 250 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/d/d9/grande_mosqu%c3%a9e_de_kairouan%2c_vue_du_minaret_depuis_la_cour.jpg/220px-grande_mosqu%c3%a9e_de_kairouan%2c_vue_du_minaret_depuis_la_cour.jpg height: 322 width: 220 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/e/e8/divina_proportione_-_illustration_13%2c_crop_%26_monochrome.jpg/220px-divina_proportione_-_illustration_13%2c_crop_%26_monochrome.jpg height: 226 width: 220 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/f/f4/medieval_manuscript_framework.svg/220px-medieval_manuscript_framework.svg.png height: 167 width: 220 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/4/4f/aeonium_tabuliforme.jpg/220px-aeonium_tabuliforme.jpg height: 317 width: 220 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/2/22/whirling_squares.svg/220px-whirling_squares.svg.png height: 139 width: 220 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/38ac3e42a424c3c58fef739a80b3004cfe21acda height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {n}{m}}={\frac {m}{n-m}}.\qquad (*)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4ed2a354f87e571236b8835de41ea8bb1359641d height: height attribute not set width: width attribute not set description: {\displaystyle \textstyle {\frac {1+{\sqrt {5}}}{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1677e5a63a73c9344487b213cf0c9f1691fe3615 height: height attribute not set width: width attribute not set description: {\displaystyle \textstyle 2\left({\frac {1+{\sqrt {5}}}{2}}\right)-1={\sqrt {5}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/61c487350a9d43eeb4294c070e8ed6dea1e4a656 height: height attribute not set width: width attribute not set description: {\displaystyle x^{2}-x-1.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e2b4293e7a91fba2c422e7a44ea210b4be1c2a8c height: height attribute not set width: width attribute not set description: {\displaystyle -{\frac {1}{\varphi }}=1-\varphi ={\frac {1-{\sqrt {5}}}{2}}=-0.61803\,39887\dots .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/aed80a2011a3912b028ba32a52dfa57165455f24 height: height attribute not set width: width attribute not set description: {\displaystyle \phi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/54c6d840bc3bbdcf87cb1b9a54b7d2b1eb99b409 height: height attribute not set width: width attribute not set description: {\displaystyle \phi ={1 \over \varphi }=\varphi ^{-1}=0.61803\,39887\ldots .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/15e7744cc0e83cf255c0e90964562f1d4d537b89 height: height attribute not set width: width attribute not set description: {\displaystyle \phi =\varphi -1=1.61803\,39887\ldots -1=0.61803\,39887\ldots .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3209935abe1275f9e0a0ae29b2f4e43de66ac1bd height: height attribute not set width: width attribute not set description: {\displaystyle {1 \over \varphi }=\varphi -1,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/35dc2789d2f7187abd1769ce2ce91903593d5302 height: height attribute not set width: width attribute not set description: {\displaystyle {1 \over \phi }=\phi +1.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/95682588ffee3530627c3a7b00ff08bbba6e97d4 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi =[1;1,1,1,\dots ]=1+{\cfrac {1}{1+{\cfrac {1}{1+{\cfrac {1}{1+\ddots }}}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/165d255e32f4b9af1f9144f15302b147fc3fead2 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ^{-1}=[0;1,1,1,\dots ]=0+{\cfrac {1}{1+{\cfrac {1}{1+{\cfrac {1}{1+\ddots }}}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a9e0df6a1c52ae3dfe8a379e087e6214ca99487f height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ={\sqrt {1+{\sqrt {1+{\sqrt {1+{\sqrt {1+\cdots }}}}}}}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8c7c67264983f79987b79f9c79567fd728ca0a9f height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ={\frac {13}{8}}+\sum _{n=0}^{\infty }{\frac {(-1)^{n+1}(2n+1)!}{4^{2n+3}n!(n+2)!}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/48828f620b4e5dbbc76fce1ab2eb6d99849a2b77 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi =1+2\sin(\pi /10)=1+2\sin 18^{\circ }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/464a1c2f8a58ba12710fa27a90a5f50805480ef6 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ={1 \over 2}\csc(\pi /10)={1 \over 2}\csc 18^{\circ }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b8369c2099126532331f0dbd6367c24da123c39d height: height attribute not set width: width attribute not set description: {\displaystyle \varphi =2\cos(\pi /5)=2\cos 36^{\circ }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f7fbb3e64b7e6e6cbfaf06adbaf5fc4045c39b33 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi =2\sin(3\pi /10)=2\sin 54^{\circ }.} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/a/a5/fakereallogspiral.svg/350px-fakereallogspiral.svg.png height: 236 width: 350 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/1/1c/goldener_schnitt_konstr_beliebt.svg/250px-goldener_schnitt_konstr_beliebt.svg.png height: 157 width: 250 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/f/fe/goldener_schnitt_%28%c3%84u%c3%9fere_teilung%29.svg/250px-goldener_schnitt_%28%c3%84u%c3%9fere_teilung%29.svg.png height: 203 width: 250 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/a/a5/golden_triangle_%28math%29.svg/220px-golden_triangle_%28math%29.svg.png height: 147 width: 220 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0dd127eb29fc263536f158fc9dc08d5b6209e7d7 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {\pi }{5}}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/odom.svg/218px-odom.svg.png height: 220 width: 218 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/aa3e8e49aac073d18cc6f67a911461d1ad09b7c1 height: height attribute not set width: width attribute not set description: {\displaystyle {\tfrac {|ab|}{|bc|}}={\tfrac {|ac|}{|ab|}}=\phi } |
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https://upload.wikimedia.org/wikipedia/commons/thumb/3/30/pentagram-phi.svg/220px-pentagram-phi.svg.png height: 220 width: 220 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/5/52/ptolemy_pentagon.svg/220px-ptolemy_pentagon.svg.png height: 220 width: 220 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/70d522a6d2daf39488d82e9baff344b38870e514 height: height attribute not set width: width attribute not set description: {\displaystyle {b \over a}={{1+{\sqrt {5}}} \over 2}.} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/5/58/goldenrhombus.svg/220px-goldenrhombus.svg.png height: 153 width: 220 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/2/2c/rhombictriacontahedron.svg/220px-rhombictriacontahedron.svg.png height: 244 width: 220 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/06861150616f57b78785cbd98651586f2a83d5af height: height attribute not set width: width attribute not set description: {\displaystyle f\left(n\right)={{\varphi ^{n}-(1-\varphi )^{n}} \over {\sqrt {5}}}={{\varphi ^{n}-(-\varphi )^{-n}} \over {\sqrt {5}}}.} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/2/2a/golden_square_fractal_6.svg/220px-golden_square_fractal_6.svg.png height: 220 width: 220 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/9/93/fibonacci_spiral_34.svg/250px-fibonacci_spiral_34.svg.png height: 158 width: 250 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/6/6e/golden_square_fractal_with_t-branching_8.svg/220px-golden_square_fractal_with_t-branching_8.svg.png height: 136 width: 220 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c97c57b45024325087cc20cbfd9af27fc6c5a5bf height: height attribute not set width: width attribute not set description: {\displaystyle \lim _{n\to \infty }{\frac {f_{n+1}}{f_{n}}}=\varphi .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1bf71ffd589d154fe8b9918b087baac62555cc4f height: height attribute not set width: width attribute not set description: {\displaystyle \sum _{n=1}^{\infty }|f_{n}\varphi -f_{n+1}|=\varphi .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2ea79f64581cae9617519870d3e383e3b726f798 height: height attribute not set width: width attribute not set description: {\displaystyle \lim _{n\to \infty }{\frac {f_{n+a}}{f_{n}}}=\varphi ^{a},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c87aaf9fe1b82ddb0ba04b257c04f6d0eb4697a5 height: height attribute not set width: width attribute not set description: {\displaystyle a=1.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d559aa0bc0dc90ea05f9b8b49deb160c9e4f7528 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ^{n+1}=\varphi ^{n}+\varphi ^{n-1}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/49ad0d344bfe44a351629cea9fefc61e93c90d92 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}3\varphi ^{3}-5\varphi ^{2}+4&=3(\varphi ^{2}+\varphi )-5\varphi ^{2}+4\\&=3[(\varphi +1)+\varphi ]-5(\varphi +1)+4\\&=\varphi +2\approx 3.618.\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b30c0b41f39e61c572dcc2c2f25f9fae40a42b37 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ^{k}=f_{k}\varphi +f_{k-1},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e4eb94e88d1b1887f734606180a126abfdca3a17 height: height attribute not set width: width attribute not set description: {\displaystyle f_{k}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a351df10daaabd86035d4669870123424e6f76cc height: height attribute not set width: width attribute not set description: {\displaystyle x^{2}=ax+b} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bedf30cf0700ad5765c98e3eeccf3ec85a655d55 height: height attribute not set width: width attribute not set description: {\displaystyle \mathbb {q} (\alpha )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c5909f0b54e4718fa24d5fd34d54189d24a66e9a height: height attribute not set width: width attribute not set description: {\displaystyle \mathbb {q} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b26530cdb1605db6e613f1721ed6417709a536fb height: height attribute not set width: width attribute not set description: {\displaystyle \{1,\alpha ,\dots ,\alpha ^{n-1}\}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2ff134458d36ca22b52b4007b5ffd218e6caf23b height: height attribute not set width: width attribute not set description: {\displaystyle \varphi _{\pm }=(1\pm {\sqrt {5}})/2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/692425a9bd434e564bc18c122da805a0fdb05f32 height: height attribute not set width: width attribute not set description: {\displaystyle x,1/(1-x),(x-1)/x,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0d33921139c8b0582775ece0074e9eb9d0db3170 height: height attribute not set width: width attribute not set description: {\displaystyle 1/x,1-x,x/(x-1)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e308a3a46b7fdce07cc09dcab9e8d8f73e37d935 height: height attribute not set width: width attribute not set description: {\displaystyle 1/2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8d8cf29586d50af99da87b2157c1719ed7ceb25b height: height attribute not set width: width attribute not set description: {\displaystyle \operatorname {psl} (2,\mathbf {z} )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/791fcc238d3688eddfd96d84556ede2bc7b93a37 height: height attribute not set width: width attribute not set description: {\displaystyle s_{3},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0c484191f1f5e8c7dc986907b234d93e0a5a15ea height: height attribute not set width: width attribute not set description: {\displaystyle \{0,1,\infty \}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d17d5036ee74f59f934e410048da0d1463b46313 height: height attribute not set width: width attribute not set description: {\displaystyle s_{3}\to s_{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c15f0424ad3a5ee676daad77a672d35a28f5ff24 height: height attribute not set width: width attribute not set description: {\displaystyle c_{3} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9b7fe0994824cf3721fe3ab3a1fa47d8e25c2b4f height: height attribute not set width: width attribute not set description: {\displaystyle ()(01\infty )(0\infty 1)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2a1f5fdd09e2ec31e3d5847de0c7053ecbaad65e height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ^{2}=\varphi +1=2.618\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/76ece5a85917be2b24b8d0d764ad1b0321e5e484 height: height attribute not set width: width attribute not set description: {\displaystyle {1 \over \varphi }=\varphi -1=0.618\dots .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8ad08bb61358e218079041b641a5bed4105d4550 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ^{n}=\varphi ^{n-1}+\varphi ^{n-2}=\varphi \cdot \operatorname {f} _{n}+\operatorname {f} _{n-1}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2175cd9b8724605f94db196c7d0b092303a3e9d6 height: height attribute not set width: width attribute not set description: {\displaystyle \lfloor n/2-1\rfloor =m} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c953a5fb37135414903d386f87bd9229ff8d7874 height: height attribute not set width: width attribute not set description: {\displaystyle \!\ \varphi ^{n}=\varphi ^{n-1}+\varphi ^{n-3}+\cdots +\varphi ^{n-1-2m}+\varphi ^{n-2-2m}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/337773266871d316e1adac84cf26ff78d8e909df height: height attribute not set width: width attribute not set description: {\displaystyle \!\ \varphi ^{n}-\varphi ^{n-1}=\varphi ^{n-2}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/dbbbfb8837510c0185800997cbf555232ea6756a height: height attribute not set width: width attribute not set description: {\displaystyle \mathbb {q} ({\sqrt {5}})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/056d1a645e7bdc70ec2caec31d2255e1326714bc height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ^{n}={{l_{n}+f_{n}{\sqrt {5}}} \over 2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ebec334cb04f246db1139e2ca6be0b957d2ef520 height: height attribute not set width: width attribute not set description: {\displaystyle l_{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b height: height attribute not set width: width attribute not set description: {\displaystyle n} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/75c9600192a2ac99147f899abd2b0e62f57eb6c8 height: height attribute not set width: width attribute not set description: {\displaystyle 4\log(\varphi )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4bcc1cf91d1c94bd0f314916e8dace91d6ed8479 height: height attribute not set width: width attribute not set description: {\displaystyle r(q)={\cfrac {q^{1/5}}{1+{\cfrac {q}{1+{\cfrac {q^{2}}{1+{\cfrac {q^{3}}{1+\ddots }}}}}}}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/829abb4bcc61fd429b99feb63370e2559029bf7c height: height attribute not set width: width attribute not set description: {\displaystyle r(e^{-2\pi })={\sqrt {\varphi {\sqrt {5}}}}-\varphi ,\quad r(e^{-2\pi {\sqrt {5}}})={\frac {\sqrt {5}}{1+\left(5^{\frac {3}{4}}(\varphi -1)^{\frac {5}{2}}-1\right)^{\frac {1}{5}}}}-\varphi .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0476090cd325a435f3a6e22b9f8982bf3e7dca85 height: height attribute not set width: width attribute not set description: {\displaystyle a,b\in \mathbb {r} ^{+}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ef6c43965631891a09721cf944763491fb57b3f3 height: height attribute not set width: width attribute not set description: {\displaystyle ab=\pi ^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/60dbfab70752cb351ea5cf60c5be3f8239e267c9 height: height attribute not set width: width attribute not set description: {\displaystyle (r(e^{-2a})+\varphi )(r(e^{-2b})+\varphi )=\varphi {\sqrt {5}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/14aed20c75d73e2d417f7d982cb71ed6288357b1 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ={1+{\sqrt {5}} \over 2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9ea5d76ee9f12facc453871a87c6299a49b6e034 height: height attribute not set width: width attribute not set description: {\displaystyle x_{n+1}={\frac {(x_{n}+5/x_{n})}{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0d50cdef5820c3906f55c65e3d4a9f26f99cd7f9 height: height attribute not set width: width attribute not set description: {\displaystyle x_{n+1}={\frac {x_{n}^{2}+1}{2x_{n}-1}},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/435fb000c169c576a463944cba9f7651fb6a5c69 height: height attribute not set width: width attribute not set description: {\displaystyle x_{n+1}={\frac {x_{n}^{2}+2x_{n}}{x_{n}^{2}+1}}.} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/3/32/mathematical_pyramid.svg/250px-mathematical_pyramid.svg.png height: 164 width: 250 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d877fee12ff439aa86ab19fcd5744b8b630634bc height: height attribute not set width: width attribute not set description: {\displaystyle 1:{\sqrt {\varphi }}:\varphi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/812e4d28c06145195f958477efbda55d5c727c53 height: height attribute not set width: width attribute not set description: {\displaystyle 3:4:5} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6ceab422902a921f445eddfa71a010e964748fcf height: height attribute not set width: width attribute not set description: {\displaystyle 1:4/\pi :1.61899} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ae1094106c2237fda1e1d4f9e6e1bde3e464637b height: height attribute not set width: width attribute not set description: {\displaystyle {\sqrt {\varphi }}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/31d4b72968e12d115b2557d9f85386f03eeaa380 height: height attribute not set width: width attribute not set description: {\displaystyle {\sqrt {\varphi }}={\sqrt {\varphi ^{2}-1}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/43d8568148e4b709603889b3606b452b54e35c4e height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ={\sqrt {1+\varphi }}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b1636153aeebb9229fd9df7a8359db45ad8ab1ea height: height attribute not set width: width attribute not set description: {\displaystyle {\sqrt {\varphi }}\approx 4/\pi } |
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https://upload.wikimedia.org/wikipedia/commons/thumb/5/58/egypt._pyramids._pyramids_and_palm_grove_reflections_loc_matpc.23063.jpg/220px-egypt._pyramids._pyramids_and_palm_grove_reflections_loc_matpc.23063.jpg height: 156 width: 220 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/ar/0/0f/%d9%86%d8%b3%d8%a8%d8%a9_%d8%b0%d9%87%d8%a8%d9%8a%d8%a9.png height: 320 width: 172 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d350fd40f23f9456ab4e3765384f68820b755738 height: height attribute not set width: width attribute not set description: {\displaystyle 2\cos(36^{\circ })\,} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/0/01/pentagon_satellite_image.jpg/220px-pentagon_satellite_image.jpg height: 209 width: 220 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bbaeb69cac311256d0b6905114c20ea5784cd6b2 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi \times \varphi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/642e4bbe73e89ff3b93588bf2dbbee3ad852d3eb height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ^{2}=\varphi +1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/48660b3786169877654898d37329ff63c85a2b47 height: height attribute not set width: width attribute not set description: {\displaystyle 1 \over \varphi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0ed8a39ea5f856c9b1e1d5f037427b3e1add83f9 height: height attribute not set width: width attribute not set description: {\displaystyle {1 \over \varphi }=\varphi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1be2772b08bd52da854694ecb84693e003643402 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ^{n}=\varphi ^{n-1}+\varphi ^{n-2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/89151e6b7061a82c26d226c51a8cea9207d82a67 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {n}{\varphi }}=n\varphi -n} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bb8ef96cecf230f5978e1c177dbb642ae2c29ae3 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ={\frac {\varphi }{1}}={\frac {\varphi +1}{\varphi }}\;} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a3cffe085811769e6fbd9c45b4f803fa8142b5ea height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ^{2}=\varphi +1\!} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/64d4de3c03e69b3928aa49dad695c72bc0048079 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{\varphi }}=\varphi -1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fd13aabe3d1c522431b355af3c3a638020b9e739 height: height attribute not set width: width attribute not set description: {\displaystyle 1\times 1=\varphi \times (\varphi -1)\!} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/41dd744fc77e0c71cfb25944e2b9e12aacb0c748 height: height attribute not set width: width attribute not set description: {\displaystyle 1=\varphi ^{2}-\varphi \!} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b8f5f41a1eec7a8005629962b677991e15027ca5 height: height attribute not set width: width attribute not set description: {\displaystyle 1=\varphi +1-\varphi =1\!} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d4ca348311ee2996d122a5a8d556fdd53531c855 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ={\frac {\varphi ^{n-1}}{\varphi ^{n-2}}}\!} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8fbbfe528eea151558faa0080a63725af5efbea4 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {\varphi ^{n-1}}{\varphi ^{n-2}}}={\frac {\varphi ^{n-1}+\varphi ^{n-2}}{\varphi ^{n-1}}}\!} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/aab695fd3a110e6e45133e7a00f062b184ded1d3 height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ={\frac {\varphi ^{n-1}+\varphi ^{n-2}}{\varphi ^{n-1}}}={\frac {\varphi ^{n}}{\varphi ^{n-1}}}\!} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4d5feadcb2ac4fa0953cb4a1f916adb9765774cb height: height attribute not set width: width attribute not set description: {\displaystyle \varphi ^{n-1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/17810f3119b915573447f628b1a224c8ce822ae8 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {n}{\varphi }}=n\times ({\frac {1}{\varphi }})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0d76036c0575ad087c97c06a7e81309a6e34fc7c height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {n}{\varphi }}=n\times (\varphi -1)\!} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/43ac74b4eaa9a6535e8155b87f305017ae8dab26 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {n}{\varphi }}=n\varphi -n\!} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/c/cf/complete_graph_k5.svg/220px-complete_graph_k5.svg.png height: 196 width: 220 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/0/08/nautiluscutawaylogarithmicspiral.jpg/220px-nautiluscutawaylogarithmicspiral.jpg height: 166 width: 220 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/d/da/the_parthenon_in_athens.jpg/280px-the_parthenon_in_athens.jpg height: 197 width: 280 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/44dca93af8441b7e02c212f81854cb8a5861e8dd height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1-{\sqrt {5}}}{2}}} |
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