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1762b5cb9d
- tufte-book.layout; synchronize with the tufte-handout.layout - tufte-book.lyx: add important note and improve the documentation according the example file for the similar tufte-handout class - biblioExample.bib: new entry used by the tufte example files git-svn-id: svn://svn.lyx.org/lyx/lyx-devel/trunk@31760 a592a061-630c-0410-9148-cb99ea01b6c8
1186 lines
21 KiB
Plaintext
1186 lines
21 KiB
Plaintext
#LyX 1.6.5svn created this file. For more info see http://www.lyx.org/
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\lyxformat 345
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\begin_document
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\begin_header
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\textclass tufte-book
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\options justified
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\use_default_options true
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\language english
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\inputencoding auto
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\font_roman default
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\font_sans default
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\font_typewriter default
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\font_default_family default
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\font_sc false
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\font_osf false
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\font_sf_scale 100
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\font_tt_scale 100
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\graphics default
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\paperfontsize default
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\spacing single
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\use_hyperref false
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\papersize default
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\use_geometry true
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\use_amsmath 1
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\use_esint 1
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\cite_engine basic
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\use_bibtopic false
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\paperorientation portrait
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\secnumdepth 2
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\tocdepth 2
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\paragraph_separation indent
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\defskip medskip
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\quotes_language english
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\papercolumns 1
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\papersides 1
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\paperpagestyle default
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\tracking_changes false
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\output_changes false
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\author ""
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\author ""
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\end_header
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\begin_body
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\begin_layout Standard
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\begin_inset Note Note
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status open
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\begin_layout Plain Layout
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\series bold
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Important note:
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\series default
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The menu
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\family sans
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Insert\SpecialChar \menuseparator
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Hyperlinks
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\family default
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and the
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\family sans
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PDF properties
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\family default
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in the
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\family sans
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Document\SpecialChar \menuseparator
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Settings
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\family default
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menu cannot be used for tufte document classes!
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Title
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Random Tufte Examples
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\end_layout
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\begin_layout Author
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Fake Author
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\begin_inset Note Note
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status open
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\begin_layout Plain Layout
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author of this example file: Jason Waskiewicz
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset CommandInset toc
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LatexCommand tableofcontents
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\end_inset
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\end_layout
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\begin_layout Chapter
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The Features of the Tufte-book Class
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\end_layout
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\begin_layout Standard
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In this document, it was endeavored to show some of the features of the
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Tufte-book class.
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In the first chapter, their use is outlined.
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In the second chapter, their use through a handout thjat was created in
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a calculus class is demonstrated.
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\end_layout
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\begin_layout Section
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Features
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\end_layout
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\begin_layout Standard
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The Tufte-book class is based on the work of Edward Tufte.
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It provides the same functionality as the Tufte-handout class with book-specifi
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c additions.
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Tufte's documents consist of a column of text beside a wide column of margin
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notes and margin figures.
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This is to improve readability.
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\end_layout
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\begin_layout Standard
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Features included in this format include:
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\end_layout
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\begin_layout Itemize
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Margin figures
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\end_layout
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\begin_layout Itemize
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Ordinary figures in text with captions in margins
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\end_layout
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\begin_layout Itemize
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Full width figures and text when needed
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\end_layout
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\begin_layout Itemize
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\begin_inset Quotes eld
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\end_inset
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Footnotes
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\begin_inset Quotes erd
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\end_inset
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in margins
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\end_layout
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\begin_layout Itemize
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Limited layers of sections and subsections
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\end_layout
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\begin_layout Standard
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In this sample document, some of these features are demonstrated.
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For a full demonstration, visit the tufte-latex webpage:
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\begin_inset Flex URL
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status collapsed
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\begin_layout Plain Layout
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http://code.google.com/p/tufte-latex
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\end_layout
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\end_inset
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.
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\end_layout
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\begin_layout Section
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Page Layout
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\end_layout
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\begin_layout Standard
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Tufte's margins are
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\begin_inset Quotes eld
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\end_inset
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ragged right
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\begin_inset Quotes erd
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\end_inset
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rather than justified.
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\begin_inset Flex Sidenote
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status collapsed
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\begin_layout Plain Layout
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This document is justified.
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Add the option "justified" to the Custom line of the Document Class part
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of the Document Settings.
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\end_layout
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\end_inset
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The ragged right is used in most of his works, but the option exists for
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justified text.
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\end_layout
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\begin_layout Standard
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Tufte also formats his pages so that they are not symmetric.
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Instead, each page is the same and all the marginalia appear on the right
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side of each page.
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After experimentation, I agree that this option is best.
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A symmetric layout appeared strange, to say the least.
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\begin_inset Flex Sidenote
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status collapsed
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\begin_layout Plain Layout
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To create a symmetric layout, add the option "symmetric" to the Custom line
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of the Document Class part of the Document Settings.
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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Finally, by default, Tufte does not number his chapters or his sections.
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Since I like to refer to sections by number, I changed this section in
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the Document Settings by moving the slider under the Numbering and TOC
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section.
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\begin_inset Flex Marginnote
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status collapsed
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\begin_layout Plain Layout
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marginnote
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Section
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Figures
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\end_layout
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\begin_layout Standard
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Tufte uses ordinary figure floats like this:
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\end_layout
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\begin_layout Standard
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\begin_inset Float figure
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\begin_inset Box Boxed
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position "t"
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hor_pos "c"
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has_inner_box 1
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inner_pos "t"
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use_parbox 0
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width "100col%"
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special "none"
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height "1in"
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height_special "totalheight"
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status open
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\begin_layout Plain Layout
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Imagine your favorite figure inside this box instead of this boring text.
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\end_layout
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\end_inset
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\begin_inset Caption
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\begin_layout Plain Layout
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An ordinary figure float.
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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Tufte also uses margin figures, a feature I wish I could apply to the Memoir
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class.
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\end_layout
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\begin_layout Standard
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\begin_inset Float marginfigure
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\begin_inset Box Boxed
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position "t"
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hor_pos "c"
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has_inner_box 1
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inner_pos "t"
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use_parbox 0
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width "100col%"
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special "none"
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height "1in"
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height_special "totalheight"
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status open
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\begin_layout Plain Layout
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Imagine your favorite photograph of a squirrel inside this box instead of
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this boring text.
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\end_layout
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\end_inset
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\begin_inset Caption
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\begin_layout Plain Layout
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A margin figure
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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Naturally, the Tufte-book class also allows the use of tables in the margins
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and in the text in the same way that the figures are used.
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I would use the margin tables for a small set of data to illustrate a concept
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such as
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\begin_inset Quotes eld
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\end_inset
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Look, distance-time data is quadratic when the object is falling.
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\begin_inset Quotes erd
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\end_inset
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I might put flame test results and comments in a full-width table.
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\end_layout
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\begin_layout Standard
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I did attempt to use the figure-wrap float with Tufte.
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LyX interpreted it as a figure float and sometimes didn't show it at all.
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With only the narrow column of text available, I think that it should probably
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be suppressed when someone edits the layout file!
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\end_layout
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\begin_layout Standard
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A final type of figure is a full-width figure.
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This is one which takes up the entire width of the page: text and margin
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alike.
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I'm proud of this because this was my one original contribution as it does
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not seem to be in the Tufte-handout.layout file.
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\end_layout
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\begin_layout Standard
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\begin_inset Float figure
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wide true
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sideways false
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status open
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\begin_layout Plain Layout
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\begin_inset Box Boxed
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position "t"
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hor_pos "c"
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has_inner_box 1
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inner_pos "t"
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use_parbox 0
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width "100col%"
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special "none"
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height "1in"
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height_special "totalheight"
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status open
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\begin_layout Plain Layout
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Imagine a photograph of a squirrel stretched out on its side in this box.
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One of the bugs in my layout is that this only works with pictures, not
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with frames around minipages, the way it's set up here.
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\begin_inset Caption
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\begin_layout Plain Layout
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A full-width figure.
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Section
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Working with Text
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\end_layout
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\begin_layout Standard
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One of the most prominent and distinctive features of this style is the
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extensive use of sidenotes.
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There is a wide margin to provide ample room for sidenotes and small figures.
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Any footnotes will automatically be converted to sidenotes.
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\begin_inset Foot
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status open
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\begin_layout Plain Layout
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This is a sidenote that was entered using a
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\family typewriter
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footnote
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\family default
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.
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\end_layout
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\end_inset
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Alternatively, you can also use directly the sidenote inset.
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\begin_inset Flex Sidenote
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status open
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\begin_layout Plain Layout
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This is a sidenote that was entered using a
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\family typewriter
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sidenote
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\family default
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.
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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If you like to place ancillary information in the margin without the sidenote
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mark (the superscript number), you can use the
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\family typewriter
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Marginnote
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\family default
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inset.
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\begin_inset Flex Marginnote
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status open
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\begin_layout Plain Layout
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This is Tufte's margin note.
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Notice that there isn't a number preceding the note, and there is no number
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in the main text where this note was written.
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\end_layout
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\end_inset
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The normal margin note will work as well, but it will look rather odd.
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\begin_inset Marginal
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status open
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\begin_layout Plain Layout
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This is a normal margin note.
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Don't use it.
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Flex NewThought
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status open
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\begin_layout Plain Layout
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Another useful
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\end_layout
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\end_inset
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innovation is Tufte's
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\series bold
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new thought
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\series default
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command.
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It introduces new thoughts, such as this paragraph, with small capitals.
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To accomplish this, use the
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\family typewriter
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NewThought
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\family default
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character style (
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\family sans
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Edit\SpecialChar \menuseparator
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TextStyle\SpecialChar \menuseparator
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NewThought
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\family default
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).
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\end_layout
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\begin_layout Standard
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The Tufte document classes includes two new character styles and some improvemen
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ts on existing commands for letterspacing.
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\end_layout
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\begin_layout Standard
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When setting strings of
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\begin_inset Flex AllCaps
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status open
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\begin_layout Plain Layout
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ALL CAPS
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\end_layout
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\end_inset
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or
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\begin_inset Flex SmallCaps
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status open
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\begin_layout Plain Layout
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Small Caps
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\end_layout
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\end_inset
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, the letterspacing---that is, the spacing between the letters---should
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be increased slightly.
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\begin_inset CommandInset citation
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LatexCommand cite
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key "Bringhurst2005"
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\end_inset
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|
The
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\emph on
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AllCaps
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\emph default
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character style (
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\family sans
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Edit\SpecialChar \menuseparator
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TextStyle\SpecialChar \menuseparator
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AllCaps
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\family default
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) has proper letterspacing for strings of
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\begin_inset Flex AllCaps
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status open
|
|
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|
\begin_layout Plain Layout
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FULL CAPITAL LETTERS
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\end_layout
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\end_inset
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, and the
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\emph on
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SmallCaps
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\emph default
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character style (
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\family sans
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Edit\SpecialChar \menuseparator
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TextStyle\SpecialChar \menuseparator
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SmallCaps
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\family default
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) has letterspacing for
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\begin_inset Flex SmallCaps
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|
status open
|
|
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|
\begin_layout Plain Layout
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small capital letters
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\end_layout
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\end_inset
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.
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These commands will also automatically convert the case of the text to
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upper- or lowercase, respectively.
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\end_layout
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|
|
|
\begin_layout Standard
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The normal
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\emph on
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Small Caps
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\emph default
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shape has also been redefined to include letterspacing.
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Its case is left as is, however.
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This allows one to use both uppercase and lowercase letters:
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\shape smallcaps
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The Initial Letters Of The Words In This Sentence Are Capitalized.
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\end_layout
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|
\begin_layout Full Width
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This is full width text.
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I'm not going to quote a text because I don't want to mess with citations
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and I haven't yet figured out how to use BiBTeX.
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I thought about quoting from some of my own materials, but then I decided
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not to.
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Instead, I decided to just type for a while and fill up 3 lines on my screen
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with whatever nonsense came into my head.
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\end_layout
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|
|
|
\begin_layout Section
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|
Conclusions
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\end_layout
|
|
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|
\begin_layout Standard
|
|
I like a lot of what Tufte has done.
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|
At the moment, however, I only use his style in my Calculus class.
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|
I have a good Calculus book, but it requires extensive notes to adapt it
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for the high school level.
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|
For my Physics, Chemistry, and Biology courses, the Memoir class seems
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more suited.
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|
I wish it were possible to take the idea of margin figures from Tufte and
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put it into Memoir.
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|
I also prefer Tufte's method of dealing with margin notes.
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\end_layout
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|
|
\begin_layout Chapter
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|
Calculation of Volume: Sections 2.12-2.13
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|
\end_layout
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|
|
|
\begin_layout Abstract
|
|
Imagine taking a function like
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\begin_inset Formula $y=\sqrt{x}$
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\end_inset
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|
|
|
and rotating it in 3 dimensions around the x-axis.
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|
The resulting shape would look somewhat like a cup (on its side).
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|
Interestingly, integration empowers us to do exactly this and to find out
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how much water that cup could hold.
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\end_layout
|
|
|
|
\begin_layout Section
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|
Visualizing Rotation
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\end_layout
|
|
|
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\begin_layout Standard
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\begin_inset Float marginfigure
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\begin_inset Box Boxed
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position "t"
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hor_pos "c"
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has_inner_box 1
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inner_pos "t"
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use_parbox 0
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width "100col%"
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special "none"
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height "1in"
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height_special "totalheight"
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status open
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\begin_layout Plain Layout
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I had a graph of the square root function here.
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\end_layout
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\end_inset
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\begin_inset Caption
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\begin_layout Plain Layout
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\begin_inset CommandInset label
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LatexCommand label
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name "mar:A-graph-of"
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\end_inset
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A graph of
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\begin_inset Formula $f(x)=\sqrt{x}$
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset Float marginfigure
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\begin_inset Box Boxed
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position "t"
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hor_pos "c"
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has_inner_box 1
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inner_pos "t"
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use_parbox 0
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width "100col%"
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special "none"
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height "1in"
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height_special "totalheight"
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status open
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\begin_layout Plain Layout
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Here I rotated the square root function and then drew a disk on the figure
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to illustrate how I would calculate the volume of the figure.
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\end_layout
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\end_inset
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\begin_inset Caption
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\begin_layout Plain Layout
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\begin_inset CommandInset label
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LatexCommand label
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name "mar:rotated"
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\end_inset
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A graph of
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\begin_inset Formula $f(x)=\sqrt{x}$
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\end_inset
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rotated about the x-axis and with additional remarks for integration.
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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Figure
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "mar:A-graph-of"
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\end_inset
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shows the plot of the function
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\begin_inset Formula $f(x)=\sqrt{x}.$
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\end_inset
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Now, imagine that we rotate that function about the x-axis.
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The resulting figure would be somewhat like figure
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "mar:rotated"
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\end_inset
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.
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This is akin to a cup lying on its side.
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For the sake of clarity, the artist (me) drew a circle on the end of the
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figure to show that it is indeed rotated.
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\end_layout
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\begin_layout Standard
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Now, suppose we wished to find the volume of the figure.
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When we integrated the original square root function to find its area,
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we imagined a series of rectangles inside the figure.
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Their height was
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\begin_inset Formula $h=f(x)$
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\end_inset
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and their width was
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\begin_inset Formula $dx$
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\end_inset
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.
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Since height multiplied by width was the area of each rectangle, we summed
|
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these areas and rewrote this as
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\begin_inset Formula $\int\, f(x)\, dx$
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\end_inset
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, or, in this specific case,
|
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\begin_inset Formula $\int\,\sqrt{x}\, dx$
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\end_inset
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.
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\end_layout
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\begin_layout Standard
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To find the volume of our rotated figure the prodecure is quite similar.
|
|
Begin by rotating each rectangle about the x-axis.
|
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This creates a series of cylinders.
|
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\begin_inset Flex Sidenote
|
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status collapsed
|
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|
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\begin_layout Plain Layout
|
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The text refers to these cylinders as "disks".
|
|
This is standard practice in all the Calculus books I checked.
|
|
\end_layout
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\end_inset
|
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|
|
Then, we can find the volume of each cylinder/disk.
|
|
The basic formula is:
|
|
\end_layout
|
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\begin_layout Standard
|
|
\begin_inset Formula \[
|
|
V=hA\]
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|
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\end_inset
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\end_layout
|
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|
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\begin_layout Standard
|
|
\noindent
|
|
where
|
|
\begin_inset Formula $h$
|
|
\end_inset
|
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|
|
is the height of the cylinder (width of the rectangle)
|
|
\begin_inset Formula $dx$
|
|
\end_inset
|
|
|
|
.
|
|
The area of each figure is a circle where
|
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\begin_inset Formula $A=\pi r^{2}$
|
|
\end_inset
|
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.
|
|
The radius in this case is the function
|
|
\begin_inset Formula $f(x)$
|
|
\end_inset
|
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|
|
.
|
|
By substitution
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Formula \[
|
|
A=\pi f^{2}(x)\]
|
|
|
|
\end_inset
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\end_layout
|
|
|
|
\begin_layout Standard
|
|
\noindent
|
|
In our specific case,
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Formula \begin{eqnarray*}
|
|
A & = & \pi\left(\sqrt{x}\right)^{2}\\
|
|
& = & \pi x\end{eqnarray*}
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
To calculate the volume of one disk, we have
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Formula \[
|
|
V=\pi x\, dx\]
|
|
|
|
\end_inset
|
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\end_layout
|
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|
|
\begin_layout Standard
|
|
\noindent
|
|
or, in the general case
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Formula \[
|
|
V=\pi f^{2}(x)\, dx\]
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
To find the volume of the figure between points
|
|
\begin_inset Formula $a$
|
|
\end_inset
|
|
|
|
and
|
|
\begin_inset Formula $b$
|
|
\end_inset
|
|
|
|
we sum the volumes by means of integration:
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Formula \begin{equation}
|
|
\int_{a}^{b}\,\pi f^{2}(x)\, dx\end{equation}
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\noindent
|
|
In the specific example, over the interval
|
|
\begin_inset Formula $[0,4]$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Formula \begin{eqnarray*}
|
|
\int_{0}^{4}\,\pi x\, dx & = & \pi\int_{0}^{4}\, x\, dx\\
|
|
& = & \pi\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}\\
|
|
& = & \pi\left(\frac{4^{2}}{2}-0\right)\\
|
|
& = & 8\pi\end{eqnarray*}
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Flex NewThought
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
Suppose I drill
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
a special hole down the length of the cup we just worked with.
|
|
It is made with a quadratic shaped bit.
|
|
\begin_inset Flex Sidenote
|
|
status collapsed
|
|
|
|
\begin_layout Plain Layout
|
|
I have no idea how I'd do this in real life, but I'm making a point.
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
I find that the hole the bit makes can be modeled with the function
|
|
\begin_inset Formula $g(x)=\frac{x^{2}}{16}$
|
|
\end_inset
|
|
|
|
.
|
|
I would need to subtract the volume of the material removed from the volume
|
|
of the entire
|
|
\begin_inset Quotes eld
|
|
\end_inset
|
|
|
|
cup
|
|
\begin_inset Quotes erd
|
|
\end_inset
|
|
|
|
.
|
|
Each individual cylinder would become like a
|
|
\begin_inset Quotes eld
|
|
\end_inset
|
|
|
|
washer
|
|
\begin_inset Quotes erd
|
|
\end_inset
|
|
|
|
.
|
|
To get the area of one washer, I would use the formula
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float marginfigure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Box Boxed
|
|
position "t"
|
|
hor_pos "c"
|
|
has_inner_box 1
|
|
inner_pos "t"
|
|
use_parbox 0
|
|
width "100col%"
|
|
special "none"
|
|
height "1in"
|
|
height_special "totalheight"
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
Here I used RLPlot to draw the square root function and the quadratic function.
|
|
Then I used Inkscape to shade the area between them.
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Caption
|
|
|
|
\begin_layout Plain Layout
|
|
The functions
|
|
\begin_inset Formula $f(x)$
|
|
\end_inset
|
|
|
|
and
|
|
\begin_inset Formula $g(x)$
|
|
\end_inset
|
|
|
|
and the area left by
|
|
\begin_inset Formula $f(x)-g(x)$
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Formula \begin{eqnarray*}
|
|
A_{washer} & = & A_{cup}-A_{drill}\\
|
|
& = & \pi f^{2}(x)-\pi g^{2}(x)\\
|
|
& = & \pi\left(f^{2}(x)-g^{2}(x)\right)\end{eqnarray*}
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The volume of each washer would be
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Formula \begin{eqnarray*}
|
|
V_{washer} & = & A_{washer}\, dx\\
|
|
& = & \pi\left(f^{2}(x)-g^{2}(x)\right)\, dx\end{eqnarray*}
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\noindent
|
|
Then, by summing the volumes of all the washers between points
|
|
\begin_inset Formula $a$
|
|
\end_inset
|
|
|
|
and
|
|
\begin_inset Formula $b$
|
|
\end_inset
|
|
|
|
, the integral is derived:
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Formula \begin{equation}
|
|
\int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\, dx\end{equation}
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
In the case of our quadratic drill bit::
|
|
\begin_inset Float marginfigure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Box Boxed
|
|
position "t"
|
|
hor_pos "c"
|
|
has_inner_box 1
|
|
inner_pos "t"
|
|
use_parbox 0
|
|
width "100col%"
|
|
special "none"
|
|
height "1in"
|
|
height_special "totalheight"
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
This was the rotated set of 2 functions.
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Caption
|
|
|
|
\begin_layout Plain Layout
|
|
The cup with a quadratic hole drilled down its length
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Formula \begin{eqnarray*}
|
|
\int_{0}^{4}\,\pi\left(\left(\sqrt{x}\right)^{2}-\left(\frac{x^{2}}{16}\right)\right)\, dx & = & \pi\int_{0}^{4}\,\left(x-\frac{x^{4}}{256}\right)\, dx\\
|
|
& = & \pi\left(\int_{0}^{4}\, x\, dx-\int_{0}^{4}\,\frac{x^{4}}{256}\, dx\right)\\
|
|
& = & \pi\left(\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}-\left.\left(\frac{x^{5}}{1280}\right)\right|_{0}^{4}\right)\\
|
|
& = & \pi\left(\left(\frac{4^{2}}{2}-0\right)-\left(\frac{4^{5}}{1280}-0\right)\right)\\
|
|
& = & \pi\left(8-0.8\right)\\
|
|
& = & 7.2\pi\end{eqnarray*}
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Homework
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
p114: 1, 4, 5, 6, 8, 10, 12, 15
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset CommandInset bibtex
|
|
LatexCommand bibtex
|
|
bibfiles "biblioExample"
|
|
options "plainnat"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_body
|
|
\end_document
|