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
200 lines
8.4 KiB
HTML
200 lines
8.4 KiB
HTML
<!DOCTYPE html>
|
||
<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
|
||
|
||
<!-- Mirrored from www.mathsisfun.com/builders-math.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:44:48 GMT -->
|
||
<head>
|
||
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
|
||
|
||
|
||
|
||
<!-- #BeginEditable "doctitle" -->
|
||
<title>Builder's Math</title>
|
||
<meta name="description" content="Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.">
|
||
<!-- #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">Builder's Mathematics</h1>
|
||
|
||
<p class="center">Here are some tips and tricks that may be useful when building.</p>
|
||
|
||
|
||
<h2>Need a Right Angle (90°) Fast ... ?</h2>
|
||
|
||
<table style="border: 0; margin:auto;">
|
||
<tbody>
|
||
<tr>
|
||
<td>
|
||
<p class="large">Make a 3,4,5 Triangle !</p>
|
||
<p>Connect three lines:</p>
|
||
<ul>
|
||
<li>3 long</li>
|
||
<li>4 long</li>
|
||
<li>5 long</li>
|
||
</ul>
|
||
<p>And we get a right angle (90°)</p></td>
|
||
<td><img src="geometry/images/triangle-3-4-5.svg" alt="3,4,5 Triangle" height="190" width="226"></td>
|
||
</tr>
|
||
</tbody></table>
|
||
|
||
<h3>Other Lengths</h3>
|
||
<p>You can use other lengths by multiplying each side by 2, or by 10, or any multiple:</p>
|
||
<p class="center"><img src="geometry/images/triangle-3-4-5-n.svg" alt="Multiples of 3,4,5" height="126" width="393"></p>
|
||
<p class="center">Learn more at <a href="geometry/triangle-3-4-5.html">3, 4, 5 Triangle</a></p>
|
||
|
||
|
||
<h2>Squaring and Diagonal</h2>
|
||
|
||
<p style="float:left; margin: 0 10px 5px 0;"><img src="geometry/images/triangle-build-diag-move.svg" alt="Diagonal fixes right angle" height="160" width="162"></p>
|
||
<p>How do we ensure two sides are at right angles?</p>
|
||
<p><br></p>
|
||
<p><b>Run a diagonal</b>.</p>
|
||
<p><br></p>
|
||
<p class="larger">But how long is the diagonal?</p>
|
||
<p style="float:right; margin: 0 0 5px 10px;"><img src="numbers/images/calculator-x2.svg" alt="calculator x^2"></p>
|
||
<p>The steps are:</p>
|
||
<ul>
|
||
<li>measure side <b>a</b> and square it (multiply it by itself)</li>
|
||
<li>measure side <b>b</b> and square it also</li>
|
||
<li>add those squares</li>
|
||
<li>finish with square root</li></ul>
|
||
<div class="example">
|
||
|
||
<h3>Example: A frame with sides of 2.4 and 5.365</h3>
|
||
<ul>
|
||
<li>2.4 squared is 2.4×2.4 = <b>5.76</b></li>
|
||
<li>5.365 squared is 5.365×5.365 = <b>28.783225</b></li>
|
||
<li>5.76 + 28.783225 = <b>34.543225</b></li>
|
||
<li>square root of 34.543225 is <b>5.877</b> (rounded to 3 decimal places)</li></ul>
|
||
<p>And we get this:</p>
|
||
<p class="center"><img src="geometry/images/triangle-build-diag1.svg" alt="Multiples of 3,4,5" height="141" width="307"></p>
|
||
<p>Perfection!</p>
|
||
</div>
|
||
<div class="example">
|
||
|
||
<h3>Example: Sides are 300 and 450.5</h3>
|
||
<ul>
|
||
<li>300 squared is 300×300 = <b>90000</b></li>
|
||
<li>450.5 squared is 450.5×450.5 = <b>202950.25</b></li>
|
||
<li>90000 + 202950.25 = <b>292950.25</b></li>
|
||
<li>square root of 292950.25 is <b>541.25</b> (rounded to 2 decimal places)</li></ul>
|
||
So the diagonal is <b>541.25</b>
|
||
<p>Notice how the squares can get very big, but come back to normal when we do the square root at the end</p></div>
|
||
<p>Try a few values here:</p>
|
||
<div class="script" style="height: 140px;">
|
||
geometry/images/pythagoras-diag.js
|
||
</div>
|
||
<p>Note: it is easy to slip a digit when doing these calcs, so double check!</p>
|
||
<p><br></p>
|
||
<div class="def">
|
||
<p>Why does it work? It is <a href="pythagoras.html">Pythagoras' Theorem</a> :</p>
|
||
<p style="float:left; margin: 0 10px 5px 0;"><img src="geometry/images/triangle-abc.svg" alt="triangle abc" height="109" width="189"></p>
|
||
<p>In a right-angled triangle, the square of a (a<sup>2</sup>) plus the square of b (b<sup>2</sup>) is equal to the square of c (c<sup>2</sup>):</p>
|
||
<p class="center large">a<sup>2</sup> + b<sup>2</sup> = c<sup>2</sup></p>
|
||
<p style="float:right; margin: 0 0 5px 10px;"><img src="geometry/images/pythagoras-square-root.svg" alt="triangle abc" height="141" width="286"><br>
|
||
Take the square root of c<sup>2</sup> to get <b>c</b></p>
|
||
<p><br></p>
|
||
<p>So we square a, square b, add those to get c<sup>2</sup>:</p>
|
||
</div>
|
||
|
||
|
||
|
||
<h2>Filling Round Holes</h2>
|
||
|
||
<p>A circle has <b>about 80%</b> of the area of a similar-width square:</p>
|
||
<p class="center"><img src="geometry/images/circle-area-vs-square.svg" alt="circle area is about 80% of square" height="129" width="264"><br>
|
||
see <a href="geometry/circle-area.html">circle area</a> for exact values</p>
|
||
<p>So a circular hole has <b>about 80%</b> of the volume of a squared-off hole!</p>
|
||
<p class="center"><img src="geometry/images/cylinder-vs-cuboid.svg" alt="circle area is about 80% of square" height="215" width="129"></p>
|
||
<div class="example">
|
||
|
||
<h3>Example: You want to drill foundation holes and fill them with concrete.</h3>
|
||
<p style="float:right; margin: 10px;"><img src="geometry/images/circle-area-ex2.svg" alt="circle area example" height="225" width="143"></p>
|
||
<p>The holes are <b>0.4 m wide</b> and <b>1 m deep</b>, how much concrete should you order for each hole?</p>
|
||
<p style="float:left; margin: 10px;"><img src="geometry/images/circle-auger.jpg" alt="circle auger" height="154" width="90"></p>
|
||
<p>They are circular (in <a href="geometry/cross-sections.html">cross section</a>) because they are drilled out using an auger.</p>
|
||
<div style="clear:both">
|
||
</div>
|
||
<p>You can make an <b>estimate</b> by:</p>
|
||
<ul>
|
||
<li>1. Calculating a square hole: 0.4<span class="center"> × 0.4 = <b>0.16 m<sup>2</sup></b></span></li>
|
||
<li>2. Taking 80% of that (estimates a circle): <span class="center"> 80% × 0.16 m<sup>2</sup></span> = <b>0.128 m<sup>2</sup></b></li>
|
||
<li>3. And the volume of a 1 m deep hole is: <span class="center"><b>0.128 m<sup>3</sup></b></span></li></ul>
|
||
<p class="larger">So you should order 0.128 cubic meters of concrete to fill each hole.</p>
|
||
|
||
<p>Note: a more accurate calculation using the circle's true area gives <b>0.126 m<sup>3</sup></b></p>
|
||
</div>
|
||
|
||
|
||
<h2>Estimating Piles</h2>
|
||
|
||
<p>A cone (such as a heaped pile of sand) <b>has exactly one third</b> of the volume of a surrounding cylinder</p>
|
||
<p class="center"><img src="geometry/images/cone-vs-cylinder-simple.svg" alt="cone vs cylinder" height="126" width="145"></p>
|
||
|
||
<p>A cone has <b>about one quarter</b> of the volume (closer to 26%) of a surrounding box with a square base:</p>
|
||
<p class="center"><img src="geometry/images/cone-vs-cuboid.svg" alt="cone vs cuboid" height="126" width="98"></p>But be careful: if the base of the heap is much wider in one direction, then this estimate won't work well.<br>
|
||
<p> </p>
|
||
|
||
<div class="related">
|
||
<a href="square-root.html">Squares and Square Roots</a>
|
||
<a href="index-3.html">Numbers Index</a>
|
||
</div>
|
||
<!-- #EndEditable -->
|
||
|
||
</article>
|
||
|
||
<div id="adend" class="centerfull noprint"></div>
|
||
<footer id="footer" class="centerfull noprint"></footer>
|
||
<div id="copyrt">Copyright © 2021 MathsIsFun.com</div>
|
||
|
||
</div>
|
||
</body><!-- #EndTemplate -->
|
||
<!-- Mirrored from www.mathsisfun.com/builders-math.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:44:51 GMT -->
|
||
</html> |