e39465ad2f
new file: Files/flashplayer_32_sa.exe
new file: favicon.ico
new file: globe.gif
new file: imgs/download.png
new file: imgs/zuck.jpg
new file: index.html
new file: other.ico
new file: script.js
new file: site.webmanifest
new file: sitemap.html
new file: styles/backround.css
new file: styles/border.css
new file: styles/fonts/Titillium_Web/OFL.txt
new file: styles/fonts/Titillium_Web/TitilliumWeb-Black.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Bold.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-BoldItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-ExtraLight.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-ExtraLightItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Italic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Light.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-LightItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Regular.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-SemiBold.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-SemiBoldItalic.ttf
new file: styles/fonts/webfontkit-20221027-163353/generator_config.txt
new file: styles/fonts/webfontkit-20221027-163353/specimen_files/grid_12-825-55-15.css
new file: styles/fonts/webfontkit-20221027-163353/specimen_files/specimen_stylesheet.css
new file: styles/fonts/webfontkit-20221027-163353/stylesheet.css
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-demo.html
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-webfont.woff
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-webfont.woff2
new file: styles/fonts/webfontkit-20221027-165950/generator_config.txt
new file: styles/fonts/webfontkit-20221027-165950/specimen_files/grid_12-825-55-15.css
new file: styles/fonts/webfontkit-20221027-165950/specimen_files/specimen_stylesheet.css
new file: styles/fonts/webfontkit-20221027-165950/stylesheet.css
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-demo.html
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-webfont.woff
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-webfont.woff2
new file: styles/style.css
new file: tools/2048/.gitignore
new file: tools/2048/.jshintrc
new file: tools/2048/CONTRIBUTING.md
new file: tools/2048/LICENSE.txt
new file: tools/2048/README.md
new file: tools/2048/Rakefile
new file: tools/2048/favicon.ico
new file: tools/2048/index.html
new file: tools/2048/js/animframe_polyfill.js
new file: tools/2048/js/application.js
new file: tools/2048/js/bind_polyfill.js
new file: tools/2048/js/classlist_polyfill.js
new file: tools/2048/js/game_manager.js
new file: tools/2048/js/grid.js
new file: tools/2048/js/html_actuator.js
new file: tools/2048/js/keyboard_input_manager.js
new file: tools/2048/js/local_storage_manager.js
new file: tools/2048/js/tile.js
new file: tools/2048/meta/apple-touch-icon.png
new file: tools/webretro/cores/neocd_libretro.js
new file: tools/webretro/cores/neocd_libretro.wasm
new file: tools/webretro/cores/nestopia_libretro.js
new file: tools/webretro/cores/nestopia_libretro.wasm
new file: tools/webretro/cores/o2em_libretro.js
new file: tools/webretro/cores/o2em_libretro.wasm
new file: tools/webretro/cores/opera_libretro.js
new file: tools/webretro/cores/opera_libretro.wasm
290 lines
12 KiB
HTML
290 lines
12 KiB
HTML
<!DOCTYPE html>
|
||
<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
|
||
|
||
<!-- Mirrored from www.mathsisfun.com/numbers/pi.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:35:52 GMT -->
|
||
<head>
|
||
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
|
||
|
||
<!-- #BeginEditable "doctitle" -->
|
||
<title>Pi</title>
|
||
|
||
<style>
|
||
.pi {
|
||
font: bold 150% "Times New Roman", serif;
|
||
}
|
||
</style>
|
||
<!-- #EndEditable -->
|
||
<meta name="keywords" content="math, maths, mathematics, school, homework, education">
|
||
<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
|
||
<meta name="HandheldFriendly" content="true">
|
||
<meta name="referrer" content="always">
|
||
<link rel="preload" href="../images/style/font-champ-bold.ttf" as="font" type="font/ttf" crossorigin="">
|
||
<link rel="preload" href="../style4.css" as="style">
|
||
<link rel="preload" href="../main4.js" as="script">
|
||
<link rel="stylesheet" href="../style4.css">
|
||
<script src="../main4.js" defer="defer"></script>
|
||
<!-- Global site tag (gtag.js) - Google Analytics -->
|
||
<script async="" src="https://www.googletagmanager.com/gtag/js?id=UA-29771508-1"></script>
|
||
<script>
|
||
window.dataLayer = window.dataLayer || [];
|
||
function gtag(){dataLayer.push(arguments);}
|
||
gtag('js', new Date());
|
||
gtag('config', 'UA-29771508-1');
|
||
</script>
|
||
</head>
|
||
|
||
<body id="bodybg">
|
||
|
||
<div id="stt"></div>
|
||
<div id="adTop"></div>
|
||
<header>
|
||
<div id="hdr"></div>
|
||
<div id="tran"></div>
|
||
<div id="adHide"></div>
|
||
<div id="cookOK"></div>
|
||
</header>
|
||
|
||
<div class="mid">
|
||
|
||
<nav>
|
||
<div id="menuWide" class="menu"></div>
|
||
<div id="logo"><a href="../index.html"><img src="../images/style/logo.svg" alt="Math is Fun"></a></div>
|
||
|
||
<div id="search" role="search"></div>
|
||
<div id="linkto"></div>
|
||
|
||
<div id="menuSlim" class="menu"></div>
|
||
<div id="menuTiny" class="menu"></div>
|
||
</nav>
|
||
|
||
<div id="extra"></div>
|
||
|
||
<article id="content" role="main">
|
||
|
||
<!-- #BeginEditable "Body" -->
|
||
|
||
|
||
<h1 class="center">Pi (<span class="times">π</span>)</h1>
|
||
|
||
<p style="float:left; margin: 0 10px 5px 0;"><img src="images/pi-dia.svg" alt="pi circle diameter" height="202" width="179"></p>
|
||
<p> </p>
|
||
<p>Draw a circle with a <b>diameter</b> (all the way across the circle) of <b>1</b></p>
|
||
<p>Then the <b style="color:#cb0">circumference</b> (all the way around the circle) is <b style="color:#cb0">3.14159265...</b> a number known as <b style="color:#cb0">Pi</b></p>
|
||
<p> </p>
|
||
<p><b style="color:#cb0">Pi</b> (pronounced like "pie") is often written using the greek symbol <span class="pi" style="color:#cb0">π</span></p>
|
||
<div style="clear:both"></div>
|
||
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/pi.svg" alt="circumference, diameter, radius" height="248" width="293"></p>
|
||
<p>The definition of <span class="pi" style="color:#cb0">π</span> is:</p>
|
||
<p class="center"><i class="larger">The <b>Circumference</b><br>
|
||
divided by the <b>Diameter</b><br>
|
||
of a Circle.</i></p>
|
||
<div style="clear:both"></div>
|
||
<p>The circumference divided by the diameter of a circle is always <span class="pi" style="color:#cb0">π</span>, no matter how large or small the circle is!</p>
|
||
<p style="float:left; margin: 0 10px 5px 0;"><img src="images/pi-dia-simple.svg" alt="pi circle diameter" height="174" width="142"></p>
|
||
<p> </p>
|
||
<p>To help you remember what <span class="pi">π</span> is ... just draw this diagram.</p>
|
||
<div style="clear:both"></div>
|
||
|
||
|
||
<h2>Finding Pi Yourself</h2>
|
||
|
||
<p>Draw a circle, or use something circular like a plate.</p>
|
||
<p>Measure around the edge (the <b>circumference</b>):</p>
|
||
<p class="center"><img src="images/pi-plate-circumference.jpg" alt="plate circumference 82" height="156" width="250"><br>
|
||
I got <b>82 cm</b></p>
|
||
<p>Measure across the circle (the <b>diameter</b>):</p>
|
||
<p class="center"><img src="images/pi-plate-diameter.jpg" alt="plate diameter" height="194" width="250"><br>
|
||
I got <b>26 cm</b></p>
|
||
<p>Divide:</p>
|
||
<p class="center large">82 cm / 26 cm = 3.1538...</p>
|
||
<p>That is pretty close to <span class="pi">π</span>. Maybe if I measured more accurately?</p>
|
||
|
||
|
||
<h2>Using Pi</h2>
|
||
|
||
<p>We can use <span class="pi">π</span> to find a Circumference when we know the Diameter</p>
|
||
<p class="center larger">Circumference = <span class="pi">π</span> × Diameter</p>
|
||
|
||
<div class="example">
|
||
|
||
<h3>Example: You walk around a circle which has a diameter of 100 m, how far have you walked?</h3>
|
||
<p class="center"><img src="../geometry/images/pi-circle-ex1.svg" alt="pi circle 100m diameter" height="" width=""></p>
|
||
<div class="tbl">
|
||
<div class="row"><span class="left"><span class="center">Distance walked</span></span><span class="right"> = Circumference </span></div>
|
||
<div class="row"><span class="left"> </span><span class="right">= <span class="pi">π</span> × 100 m</span></div>
|
||
<div class="row"><span class="left"> </span><span class="right"> = 314.159... m </span></div>
|
||
<div class="row"><span class="left"> </span><span class="right"><span class="center">= <b>314 m</b> (to the nearest m) </span></span></div>
|
||
</div>
|
||
</div>
|
||
<p>Also we can use <span class="pi">π</span> to find a Diameter when we know the Circumference</p>
|
||
<p class="center larger">Diameter = Circumference / <span class="pi">π</span></p>
|
||
|
||
<div class="example">
|
||
<img src="../geometry/images/annulus-pipe.jpg" alt="annulus pipe" style="float:right; margin: 10px;" height="184" width="118">
|
||
|
||
<h3>Example: Sam measured 94 mm around the outside of a pipe ... what is its Diameter?</h3>
|
||
<div class="tbl">
|
||
<div class="row"><span class="left">Diameter</span><span class="right"> = Circumference / <span class="pi">π</span></span></div>
|
||
<div class="row"><span class="left"> </span><span class="right">= 94 mm / <span class="pi">π</span></span></div>
|
||
<div class="row"><span class="left"> </span><span class="right"> = 29.92... mm </span></div>
|
||
<div class="row"><span class="left"> </span><span class="right"><span class="center">= <b>30 mm</b> (to the nearest mm) </span></span></div>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
<h2>Radius</h2>
|
||
|
||
<p>The radius is half of the diameter, so we can also say:</p>
|
||
<p style="float:left; margin: 0 20px 5px 0;"><img src="images/pi-circle.gif" alt="circle radius=1, half circumference=pi" height="188" width="172"></p>
|
||
<p> </p>
|
||
<p>For a circle with a <b>radius</b> of <b>1</b></p>
|
||
<p>The distance <i>half way around</i> the circle is <b><span class="pi">π</span> = 3.14159265...</b></p>
|
||
<div style="clear:both"></div>
|
||
|
||
|
||
<h2>Digits</h2>
|
||
|
||
<p><span class="pi">π</span> is approximately equal to:</p>
|
||
<p class="center larger"><b>3.14159265358979323846…</b></p>
|
||
<p>The digits go on and on with no pattern.</p>
|
||
<p><span class="pi">π</span> has been calculated to over 100 trillion decimal places and still there is <b>no pattern</b> to the digits, see <a href="pi-normal.html">Pi Normal</a>.</p>
|
||
<div style="clear:both"></div>
|
||
|
||
|
||
<h2>Approximation</h2>
|
||
|
||
<p>A quick and easy approximation for <span class="pi">π</span> is 22/7</p>
|
||
<p class="center larger">22/7 = <b>3.1428571...</b></p>
|
||
<p>But as you can see, 22/7 is <b>not exactly right</b>. In fact <span class="pi">π</span> is not equal to the ratio of any two numbers, which makes it an <a href="../irrational-numbers.html">irrational number</a>.</p>
|
||
<p> </p>
|
||
<p>A really good approximation, better than 1 part in 10 million, is:</p>
|
||
<p class="center"><span class="larger">355/113 = <b>3.1415929...</b></span><br>
|
||
<i>(think "113355", slash the middle "113/355", then flip "355/113")</i></p>
|
||
<p>Summary:</p>
|
||
|
||
<table style="border: 0; margin:auto;">
|
||
<tbody>
|
||
<tr>
|
||
<td style="text-align:right;">22/7</td>
|
||
<td style="text-align:center; width:20px;">=</td>
|
||
<td><b>3.14</b>28571...</td>
|
||
</tr>
|
||
<tr>
|
||
<td style="text-align:right;">355/113</td>
|
||
<td style="text-align:center;">=</td>
|
||
<td><b>3.141592</b>9...</td>
|
||
</tr>
|
||
<tr>
|
||
<td style="text-align:right;"><span class="pi">π</span></td>
|
||
<td style="text-align:center;">=</td>
|
||
<td><b>3.14159265</b>...</td>
|
||
</tr>
|
||
</tbody></table>
|
||
|
||
|
||
<h2>Remembering The Digits</h2>
|
||
|
||
<p>I usually just remember "3.14159", but you can also count the letters of:</p>
|
||
<p class="larger center"><i>"May I have a large container of butter today"<br>
|
||
3 1 4 1 5 9 2 6 5</i></p>
|
||
|
||
|
||
<h2>To 100 Decimal Places</h2>
|
||
|
||
<p>Here is <span class="pi">π</span> with the first 100 decimal places:</p>
|
||
|
||
<table style="border: 0; margin:auto;">
|
||
<tbody>
|
||
<tr>
|
||
<td class="large" align="center">3.14159265358979323846264338327950288<br>
|
||
4197169399375105820974944592307816<br>
|
||
4062862089986280348253421170679...</td>
|
||
</tr>
|
||
</tbody></table>
|
||
<p> </p>
|
||
<div class="fun">
|
||
|
||
<h3>Calculating Pi Yourself</h3>
|
||
<p>There are many special methods used to calculate <span class="pi">π</span> and here is one you can try yourself: it is called the <b>Nilakantha series</b> (after an Indian mathematician who lived in the years 1444–1544).</p>
|
||
<p>It goes on for ever and has this pattern:</p>
|
||
<p class="center larger">3 + <span class="intbl">
|
||
<em>4</em>
|
||
<strong>2×3×4</strong>
|
||
</span> − <span class="intbl">
|
||
<em>4</em>
|
||
<strong>4×5×6</strong>
|
||
</span> + <span class="intbl">
|
||
<em>4</em>
|
||
<strong>6×7×8</strong>
|
||
</span> − <span class="intbl">
|
||
<em>4</em>
|
||
<strong>8×9×10</strong>
|
||
</span> + ...</p>
|
||
<p>(Notice the <span class="center larger">+</span> and <span class="center larger">−</span> pattern, and also the pattern of numbers below the lines.)</p>
|
||
<p>It gives these results:</p>
|
||
<div class="simple">
|
||
|
||
<table style="border: 0; margin:auto;">
|
||
<tbody>
|
||
<tr>
|
||
<th>Term</th>
|
||
<th>Result (to 12 decimals)</th>
|
||
</tr>
|
||
<tr>
|
||
<td>1</td>
|
||
<td>3</td>
|
||
</tr>
|
||
<tr>
|
||
<td>2</td>
|
||
<td>3.166666666667</td>
|
||
</tr>
|
||
<tr>
|
||
<td>3</td>
|
||
<td>3.133333333333</td>
|
||
</tr>
|
||
<tr>
|
||
<td>4</td>
|
||
<td>3.145238095238</td>
|
||
</tr>
|
||
<tr>
|
||
<td>...</td>
|
||
<td>... etc! ...</td>
|
||
</tr>
|
||
</tbody></table>
|
||
</div>
|
||
<p>Get a calculator (or use a spreadsheet) and see if you can get better results.</p>
|
||
</div>
|
||
<p> </p>
|
||
<div class="fun">
|
||
<img src="../images/style/balloons.svg" alt="ballons" style="float:right; margin: 0 0 5px 10px;" height="140" width="103">
|
||
|
||
<h3>Pi Day</h3>
|
||
<p>Pi Day is celebrated on March 14. March is the 3rd month, so it looks like 3/14</p>
|
||
</div>
|
||
<p> </p>
|
||
<div class="questions">5839,5050,5052,1745,2106,5473,5477,1744,3236,3237</div>
|
||
<div class="activity"> <a href="../activity/pi-approximation.html">Activity: Find an Approximate Value For Pi</a></div>
|
||
|
||
<div class="related">
|
||
<a href="../geometry/circle.html">Circle</a>
|
||
<a href="../geometry/radians.html">Radians</a>
|
||
<a href="pi-digits.html">1 Hundred to 1 Million Digits of Pi</a>
|
||
<a href="pi-normal.html">Is Pi Normal?</a>
|
||
<a href="../geometry/annulus.html">Annulus</a>
|
||
<a href="../irrational-numbers.html">Irrational Number</a>
|
||
</div>
|
||
<!-- #EndEditable -->
|
||
|
||
</article>
|
||
|
||
<div id="adend" class="centerfull noprint"></div>
|
||
<footer id="footer" class="centerfull noprint"></footer>
|
||
<div id="copyrt">Copyright © 2022 Rod Pierce</div>
|
||
|
||
</div>
|
||
|
||
|
||
|
||
</body><!-- #EndTemplate -->
|
||
<!-- Mirrored from www.mathsisfun.com/numbers/pi.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:35:54 GMT -->
|
||
</html> |