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< span class = "relative inline-block align-text-bottom icon" > < svg aria-hidden = "true" focusable = "false" data-prefix = "fas" data-icon = "search" class = "svg-inline--fa fa-search fa-w-16" role = "img" xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 512 512" > < path fill = "currentcolor" d = "M505 442.7 405.3 343c-4.5-4.5-10.6-7-17-7H372c27.6-35.3 44-79.7 44-128C416 93.1 322.9.0 208 0S0 93.1.0 208s93.1 208 208 208c48.3.0 92.7-16.4 128-44v16.3c0 6.4 2.5 12.5 7 17l99.7 99.7c9.4 9.4 24.6 9.4 33.9.0l28.3-28.3c9.4-9.4 9.4-24.6.1-34zM208 336c-70.7.0-128-57.2-128-128 0-70.7 57.2-128 128-128 70.7.0 128 57.2 128 128 0 70.7-57.2 128-128 128z" / > < / svg > < / span > < / button > < / li > < / ul > < / div > < div class = "relative flex flex-col grow" > < main id = main-content class = grow > < article > < header class = max-w-prose > < ol class = "text-sm text-neutral-500 dark:text-neutral-400 print:hidden" > < li class = "inline hidden" > < a class = "hover:underline decoration-neutral-300 dark:underline-neutral-600" href = /blowfish/ > Welcome to Blowfish! :tada:< / a > < span class = "px-1 text-primary-500" > /< / span > < / li > < li class = inline > < a class = "hover:underline decoration-neutral-300 dark:underline-neutral-600" href = /blowfish/samples/ > Content Samples< / a > < span class = "px-1 text-primary-500" > /< / span > < / li > < li class = "inline hidden" > < a class = "hover:underline decoration-neutral-300 dark:underline-neutral-600" href = /blowfish/samples/mathematical-notation/ > Mathematical notation< / a > < span class = "px-1 text-primary-500" > /< / span > < / li > < / ol > < h1 class = "mt-0 text-4xl font-extrabold text-neutral-900 dark:text-neutral" > Mathematical notation< / h1 > < div class = "mt-8 mb-12 text-base text-neutral-500 dark:text-neutral-400 print:hidden" > < div class = "flex flex-row flex-wrap items-center" > < time datetime = "2019-03-08 00:00:00 +0000 UTC" > 8 March 2019< / time > < span class = "px-2 text-primary-500" > · < / span > < span > 145 words< / span > < span class = "px-2 text-primary-500" > · < / span > < span title = "Reading time" > 1 min< / span > < span class = "px-2 text-primary-500" > · < / span > < span id = views_samples/mathematical-notation.md title = views > 0 views< / span > < / div > < / div > < / header > < section class = "flex flex-col max-w-full mt-0 prose dark:prose-invert lg:flex-row" > < div class = "order-first px-0 lg:order-last lg:max-w-xs ltr:lg:pl-8 rtl:lg:pr-8" > < div class = "toc ltr:pl-5 rtl:pr-5 print:hidden lg:sticky lg:top-10" > < details open class = "mt-0 overflow-hidden rounded-lg ltr:-ml-5 ltr:pl-5 rtl:-mr-5 rtl:pr-5" > < summary class = "block py-1 text-lg font-semibold cursor-pointer bg-neutral-100 text-neutral-800 ltr:-ml-5 ltr:pl-5 rtl:-mr-5 rtl:pr-5 dark:bg-neutral-700 dark:text-neutral-100 lg:hidden" > Table of Contents< / summary > < div class = "py-2 border-dotted border-neutral-300 ltr:-ml-5 ltr:border-l ltr:pl-5 rtl:-mr-5 rtl:border-r rtl:pr-5 dark:border-neutral-600" > < nav id = TableOfContents > < ul > < li > < a href = #inline-notation > Inline notation< / a > < / li > < li > < a href = #block-notation > Block notation< / a > < / li > < / ul > < / nav > < / div > < / details > < / div > < / div > < div class = "min-w-0 min-h-0 max-w-prose" > < p > KaTeX can be used to render mathematical notation within articles.< / p > < p > Blowfish will only bundle the KaTeX assets into your project if you make use of mathematical notation. In order for this to work, simply include the < a href = https://nunocoracao.github.io/blowfish/docs/shortcodes/#katex > < code > katex< / code > shortcode< / a > within the article. Any KaTeX syntax on that page will then be automatically rendered.< / p > < p > Use the online reference of < a href = https://katex.org/docs/supported.html > supported TeX functions< / a > for the available syntax.< / p > < h2 id = inline-notation class = "relative group" > Inline notation < span class = "absolute top-0 w-6 transition-opacity opacity-0 ltr:-left-6 rtl:-right-6 not-prose group-hover:opacity-100" > < a class = "group-hover:text-primary-300 dark:group-hover:text-neutral-700" style = text-decoration-line:none!important href = #inline-notation aria-label = Anchor > #< / a > < / span > < / h2 > < p > Inline notation can be generated by wrapping the expression in < code > \\(< / code > and < code > \\)< / code > delimiters.< / p > < p > < strong > Example:< / strong > < / p > < div class = highlight > < pre tabindex = 0 class = chroma > < code class = language-tex data-lang =
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< / span > < / span > < / span > < span class = line > < span class = cl > < span class = c > < / span > Inline notation: < span class = k > \\< / span > (< span class = k > \varphi< / span > = < span class = k > \dfrac< / span > < span class = nb > {< / span > 1+< span class = k > \sqrt< / span > 5< span class = nb > }{< / span > 2< span class = nb > }< / span > = 1.6180339887…< span class = k > \\< / span > )
< / span > < / span > < / code > < / pre > < / div > < p > Inline notation: \(\varphi = \dfrac{1+\sqrt5}{2}= 1.6180339887…\)< / p > < h2 id = block-notation class = "relative group" > Block notation < span class = "absolute top-0 w-6 transition-opacity opacity-0 ltr:-left-6 rtl:-right-6 not-prose group-hover:opacity-100" > < a class = "group-hover:text-primary-300 dark:group-hover:text-neutral-700" style = text-decoration-line:none!important href = #block-notation aria-label = Anchor > #< / a > < / span > < / h2 > < p > Alternatively, block notation can be generated using < code > $$< / code > delimiters. This will output the expression in its own HTML block.< / p > < p > < strong > Example:< / strong > < / p > < div class = highlight > < pre tabindex = 0 class = chroma > < code class = language-tex data-lang = tex > < span class = line > < span class = cl > < span class = c > % KaTeX block notation
< / span > < / span > < / span > < span class = line > < span class = cl > < span class = c > < / span > < span class = sb > $$< / span > < span class = nb >
< / span > < / span > < / span > < span class = line > < span class = cl > < span class = nb > < / span > < span class = nv > \varphi< / span > < span class = nb > < / span > < span class = o > =< / span > < span class = nb > < / span > < span class = m > 1< / span > < span class = o > +< / span > < span class = nv > \frac< / span > < span class = nb > {< / span > < span class = m > 1< / span > < span class = nb > } {< / span > < span class = m > 1< / span > < span class = o > +< / span > < span class = nv > \frac< / span > < span class = nb > {< / span > < span class = m > 1< / span > < span class = nb > } {< / span > < span class = m > 1< / span > < span class = o > +< / span > < span class = nv > \frac< / span > < span class = nb > {< / span > < span class = m > 1< / span > < span class = nb > } {< / span > < span class = m > 1< / span > < span class = o > +< / span > < span class = nv > \cdots< / span > < span class = nb > } } }
< / span > < / span > < / span > < span class = line > < span class = cl > < span class = nb > < / span > < span class = s > $$< / span >
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< / span > < / span > < / code > < / pre > < / div > < p > $$
\varphi = 1+\frac{1} {1+\frac{1} {1+\frac{1} {1+\cdots} } }
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$$< / p > < / div > < script > if ( typeof auth != 'undefined' ) { var oid = "views_samples/mathematical-notation.md" , id = oid && oid . replaceAll ( "/" , "-" ) , viewed = localStorage . getItem ( id ) ; viewed || auth . signInAnonymously ( ) . then ( ( ) => { var e = db . collection ( 'views' ) . doc ( id ) ; localStorage . setItem ( id , ! 0 ) , e . get ( ) . then ( e => { e . exists ? db . collection ( 'views' ) . doc ( id ) . update ( { views : firebase . firestore . FieldValue . increment ( 1 ) } ) : db . collection ( 'views' ) . doc ( id ) . set ( { views : 1 } ) } ) . catch ( e => { console . log ( "Error getting document:" , e ) } ) } ) . catch ( e => { var t = e . code , n = e . message ; console . error ( t , n ) } ) } < / script > < / section > < footer class = "pt-8 max-w-prose print:hidden" > < div class = flex > < img class = "!mt-0 !mb-0 h-24 w-24 rounded-full ltr:mr-4 rtl:ml-4" width = 96 height = 96 alt = Blowfish src = /blowfish/img/blowfish_logo_hu184ea2fa12490a2458ca388a16ab730e_227816_192x192_fill_box_smart1_3.png > < div class = place-self-center > < div class = "text-[0.6rem] uppercase leading-3 text-neutral-500 dark:text-neutral-400" > Author< / div > < div class = "font-semibold leading-6 text-neutral-800 dark:text-neutral-300" > Blowfish< / div > < div class = "text-sm text-neutral-700 dark:text-neutral-400" > A powerful, lightweight theme for Hugo built with Tailwind CSS.< / div > < div class = "text-2xl sm:text-lg" > < div class = "flex flex-wrap text-neutral-400 dark:text-neutral-500" > < a class = "px-1 hover:text-primary-700 dark:hover:text-primary-400" href = https://twitter.com/burufugu target = _blank aria-label = Twitter rel = "me noopener noreferrer" > < span class = "relative inline-block align-text-bottom icon" > < svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 512 512" > < path fill = "currentcolor" d = "M459.37 151.716c.325 4.548.325 9.097.325 13.645.0 138.72-105.583 298.558-298.558 298.558-59.452.0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055.0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421.0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391.0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04.0-57.828 46.782-104.934 104.934-104.934 30.213.0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z" / > < / svg > < / span > < / a > < a class = "px-1 hover:text-primary-700 dark:hover:text-primary-400" href = https://github.com/nunocoracao/blowfish target = _blank aria-label = Github rel = "me noopener noreferrer" > < span class = "relative inline-block align-text-bottom icon" > < svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 496 512" > < path fill = "currentcolor" d = "M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6.0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6.0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3.0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1.0-6.2-.3-40.4-.3-61.4.0.0-70 15-84.7-29.8.0.0-11.4-29.1-27.8-36.6.0.0-22.9-15.7 1.6-15.4.0.0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5.0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9.0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4.0 33.7-.3 75.4-.3 83.6.0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6.0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9.0-6.2-1.4-2.3-4-3.3-5.6-2z" / > < / svg > < / span > < / a > < / div > < / div > < / div > < / div > < section class = "flex flex-
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< span class = "ml-3 text-neutral-700 group-hover:text-primary-600 ltr:hidden rtl:inline dark:text-neutral dark:group-hover:text-primary-400" > → < / span >
< span class = "flex flex-col" > < span class = "mt-[0.1rem] leading-6 group-hover:underline group-hover:decoration-primary-500" > Charts< / span >
< span class = "mt-[0.1rem] text-xs text-neutral-500 dark:text-neutral-400" > < time datetime = "2019-03-06 00:00:00 +0000 UTC" > 6 March 2019< / time > < / span > < / span > < / a > < / span >
< span > < a class = "flex text-right group" href = /blowfish/samples/rich-content/ > < span class = "flex flex-col" > < span class = "mt-[0.1rem] leading-6 group-hover:underline group-hover:decoration-primary-500" > Rich Content< / span >
< span class = "mt-[0.1rem] text-xs text-neutral-500 dark:text-neutral-400" > < time datetime = "2019-03-10 00:00:00 +0000 UTC" > 10 March 2019< / time > < / span > < / span >
< span class = "ml-3 text-neutral-700 group-hover:text-primary-600 ltr:inline rtl:hidden dark:text-neutral dark:group-hover:text-primary-400" > → < / span >
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< span class = "mr-3 text-neutral-700 group-hover:text-primary-600 ltr:hidden rtl:inline dark:text-neutral dark:group-hover:text-primary-400" > ← < / span > < / a > < / span > < / div > < / div > < / footer > < / article > < / main > < footer class = "py-10 print:hidden" > < nav class = "pb-4 text-base font-medium text-neutral-500 dark:text-neutral-400" > < ul class = "flex flex-col list-none sm:flex-row" > < li class = "mb-1 ltr:text-right rtl:text-left sm:mb-0 ltr:sm:mr-7 ltr:sm:last:mr-0 rtl:sm:ml-7 rtl:sm:last:ml-0" > < a class = "decoration-primary-500 hover:underline hover:decoration-2 hover:underline-offset-2" href = /blowfish/tags/ title = Tags > Tags< / a > < / li > < / ul > < / nav > < div class = "flex items-center justify-between" > < p class = "text-sm text-neutral-500 dark:text-neutral-400" > ©
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2022
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Blowfish< / p > < p class = "text-xs text-neutral-500 dark:text-neutral-400" > Powered by < a class = "hover:underline hover:decoration-primary-400 hover:text-primary-500" href = https://gohugo.io/ target = _blank rel = "noopener noreferrer" > Hugo< / a > & < a class = "hover:underline hover:decoration-primary-400 hover:text-primary-500" href = https://nunocoracao.github.io/blowfish/ target = _blank rel = "noopener noreferrer" > Blowfish< / a > < / p > < / div > < script > mediumZoom ( document . querySelectorAll ( "img:not(.nozoom)" ) , { margin : 24 , background : 'rgba(0,0,0,0.5)' , scrollOffset : 0 } ) < / script > < script type = text/javascript src = /blowfish/js/process.min.9cb1881551ab5855d9cdee5d8dfb370e3f0242b9fc5ae05e57b3a881cb16ca53b312f879ab023e1b1f9cac2a318d2be1b20df5177878d1d93cb96ca11fe3bd97.js integrity = "sha512-nLGIFVGrWFXZze5djfs3Dj8CQrn8WuBeV7OogcsWylOzEvh5qwI+Gx+crCoxjSvhsg31F3h40dk8uWyhH+O9lw==" > < / script > < / footer > < div id = search-wrapper class = "invisible fixed inset-0 z-50 flex h-screen w-screen cursor-default flex-col bg-neutral-500/50 p-4 backdrop-blur-sm dark:bg-neutral-900/50 sm:p-6 md:p-[10vh] lg:p-[12vh]" data-url = https://nunocoracao.github.io/blowfish/ > < div id = search-modal class = "flex flex-col w-full max-w-3xl min-h-0 mx-auto border rounded-md shadow-lg top-20 border-neutral-200 bg-neutral dark:border-neutral-700 dark:bg-neutral-800" > < header class = "relative z-10 flex items-center justify-between flex-none px-2" > < form class = "flex items-center flex-auto min-w-0" > < div class = "flex items-center justify-center w-8 h-8 text-neutral-400" > < span class = "relative inline-block align-text-bottom icon" > < svg aria-hidden = "true" focusable = "false" data-prefix = "fas" data-icon = "search" class = "svg-inline--fa fa-search fa-w-16" role = "img" xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 512 512" > < path fill = "currentcolor" d = "M505 442.7 405.3 343c-4.5-4.5-10.6-7-17-7H372c27.6-35.3 44-79.7 44-128C416 93.1 322.9.0 208 0S0 93.1.0 208s93.1 208 208 208c48.3.0 92.7-16.4 128-44v16.3c0 6.4 2.5 12.5 7 17l99.7 99.7c9.4 9.4 24.6 9.4 33.9.0l28.3-28.3c9.4-9.4 9.4-24.6.1-34zM208 336c-70.7.0-128-57.2-128-128 0-70.7 57.2-128 128-128 70.7.0 128 57.2 128 128 0 70.7-57.2 128-128 128z" / > < / svg > < / span > < / div > < input type = search id = search-query class = "flex flex-auto h-12 mx-1 bg-transparent appearance-none focus:outline-dotted focus:outline-2 focus:outline-transparent" placeholder = Search tabindex = 0 > < / form > < button id = close-search-button class = "flex items-center justify-center w-8 h-8 text-neutral-700 hover:text-primary-600 dark:text-neutral dark:hover:text-primary-400" title = "Close (Esc)" >
2022-09-12 07:44:13 -05:00
< span class = "relative inline-block align-text-bottom icon" > < svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 320 512" > < path fill = "currentcolor" d = "M310.6 361.4c12.5 12.5 12.5 32.75.0 45.25C304.4 412.9 296.2 416 288 416s-16.38-3.125-22.62-9.375L160 301.3 54.63 406.6C48.38 412.9 40.19 416 32 416S15.63 412.9 9.375 406.6c-12.5-12.5-12.5-32.75.0-45.25l105.4-105.4L9.375 150.6c-12.5-12.5-12.5-32.75.0-45.25s32.75-12.5 45.25.0L160 210.8l105.4-105.4c12.5-12.5 32.75-12.5 45.25.0s12.5 32.75.0 45.25l-105.4 105.4L310.6 361.4z" / > < / svg > < / span > < / button > < / header > < section class = "flex-auto px-2 overflow-auto" > < ul id = search-results > < / ul > < / section > < / div > < / div > < / div > < / body > < / html >
