[lyx.git] / lib / examples / tufte-book.lyx

#LyX 1.6.5svn created this file. For more info see http://www.lyx.org/
\lyxformat 345
\begin_document
\begin_header
\textclass tufte-book
\options justified
\use_default_options true
\language english
\inputencoding auto
\font_roman default
\font_sans default
\font_typewriter default
\font_default_family default
\font_sc false
\font_osf false
\font_sf_scale 100
\font_tt_scale 100

\graphics default
\paperfontsize default
\spacing single
\use_hyperref false
\papersize default
\use_geometry true
\use_amsmath 1
\use_esint 1
\cite_engine basic
\use_bibtopic false
\paperorientation portrait
\secnumdepth 2
\tocdepth 2
\paragraph_separation indent
\defskip medskip
\quotes_language english
\papercolumns 1
\papersides 1
\paperpagestyle default
\tracking_changes false
\output_changes false
\author "" 
\author "" 
\end_header

\begin_body

\begin_layout Title
Random Tufte Examples
\end_layout

\begin_layout Author
Fake Author
\end_layout

\begin_layout Standard
\begin_inset CommandInset toc
LatexCommand tableofcontents

\end_inset


\end_layout

\begin_layout Chapter
The Features of the Tufte-book Class
\end_layout

\begin_layout Standard
In this document, I endeavor to show some of the features of the Tufte-book
 class.
 In the first chapter, I outline their use.
 In the second chapter, I demonstrate their use through a handout I created
 in my Calculus class.
 For those who are viewing the .lyx file, I had to remove the figures and
 replace them by boxes so that the download would not become overwhelming.
\begin_inset Flex Sidenote
status collapsed

\begin_layout Plain Layout
I created the figures with a combination of RLPlot and Inkscape.
\end_layout

\end_inset


\end_layout

\begin_layout Section
Features
\end_layout

\begin_layout Standard
The Tufte-book class is based on the work of Edward Tufte.
 His documents consist of a column of text beside a wide column of margin
 notes and margin figures.
 This is to improve readability.
\end_layout

\begin_layout Standard
Features included in this format include:
\end_layout

\begin_layout Itemize
Margin figures
\end_layout

\begin_layout Itemize
Ordinary figures in text with captions in margins
\end_layout

\begin_layout Itemize
Full width figures and text when needed
\end_layout

\begin_layout Itemize
\begin_inset Quotes eld
\end_inset

Footnotes
\begin_inset Quotes erd
\end_inset

 in margins
\end_layout

\begin_layout Itemize
Limited layers of sections and subsections
\end_layout

\begin_layout Standard
In this sample document, I will demonstrate some of these features.
 For a full demonstration, visit the webpage.
\end_layout

\begin_layout Section
Page Layout
\end_layout

\begin_layout Standard
Tufte's margins are 
\begin_inset Quotes eld
\end_inset

ragged right
\begin_inset Quotes erd
\end_inset

 rather than justified.
\begin_inset Flex Sidenote
status collapsed

\begin_layout Plain Layout
This document is justified.
 Add the option "justified" to the Custom line of the Document Class part
 of the Document Settings.
\end_layout

\end_inset

 The ragged right is used in most of his works, but the option exists for
 justified text.
\end_layout

\begin_layout Standard
Tufte also formats his pages so that they are not symmetric.
 Instead, each page is the same and all the marginalia appear on the right
 side of each page.
 After experimentation, I agree that this option is best.
 A symmetric layout appeared strange, to say the least.
\begin_inset Flex Sidenote
status collapsed

\begin_layout Plain Layout
To create a symmetric layout, add the option "symmetric" to the Custom line
 of the Document Class part of the Document Settings.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Finally, by default, Tufte does not number his chapters or his sections.
 Since I like to refer to sections by number, I changed this section in
 the Document Settings by moving the slider under the Numbering and TOC
 section.
\end_layout

\begin_layout Section
Figures
\end_layout

\begin_layout Standard
Tufte uses ordinary figure floats like this:
\end_layout

\begin_layout Standard
\begin_inset Float figure
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
Imagine your favorite figure inside this box instead of this boring text.
\end_layout

\end_inset


\begin_inset Caption

\begin_layout Plain Layout
An ordinary figure float.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Tufte also uses margin figures, a feature I wish I could apply to the Memoir
 class.
\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
Imagine your favorite photograph of a squirrel inside this box instead of
 this boring text.
\end_layout

\end_inset


\begin_inset Caption

\begin_layout Plain Layout
A margin figure
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Naturally, the Tufte-book class also allows the use of tables in the margins
 and in the text in the same way that the figures are used.
 I would use the margin tables for a small set of data to illustrate a concept
 such as 
\begin_inset Quotes eld
\end_inset

Look, distance-time data is quadratic when the object is falling.
\begin_inset Quotes erd
\end_inset

 I might put flame test results and comments in a full-width table.
\end_layout

\begin_layout Standard
I did attempt to use the figure-wrap float with Tufte.
 LyX interpreted it as a figure float and sometimes didn't show it at all.
 With only the narrow column of text available, I think that it should probably
 be suppressed when someone edits the layout file!
\end_layout

\begin_layout Standard
A final type of figure is a full-width figure.
 This is one which takes up the entire width of the page: text and margin
 alike.
 I'm proud of this because this was my one original contribution as it does
 not seem to be in the Tufte-handout.layout file.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide true
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
Imagine a photograph of a squirrel stretched out on its side in this box.
 One of the bugs in my layout is that this only works with pictures, not
 with frames around minipages, the way it's set up here.
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
A full-width figure.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Section
Working with Text
\end_layout

\begin_layout Standard
Tufte provides a number of innovations for use with his text.
 The first is the extensive use of margin notes.
\begin_inset Flex Sidenote
status open

\begin_layout Plain Layout
This is an example of a Tufte style margin note.
\end_layout

\end_inset

 Tufte's margin notes use a slightly smaller font and they have the added
 benefit of reference by a superscript.
 Ordinary margin notes do not have this.
 Both types are shown.
\begin_inset Marginal
status open

\begin_layout Plain Layout
This is an ordinary margin note.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Flex Newthought
status open

\begin_layout Plain Layout
Another useful
\end_layout

\end_inset

 innovation is Tufte's 
\series bold
new thought
\series default
 command.
 It introduces new thoughts, such as this paragraph, with small capitals.
\end_layout

\begin_layout Standard
Finally, Tufte has a setting to print full-width text.
 This spreads it from margin to margin.
 I believe this might be useful for quoting a text.
\end_layout

\begin_layout Standard
Another available style is 
\begin_inset Flex Allcaps
status open

\begin_layout Plain Layout
allcaps
\end_layout

\end_inset

.
\end_layout

\begin_layout Full Width
This is full width text.
 I'm not going to quote a text because I don't want to mess with citations
 and I haven't yet figured out how to use BiBTeX.
 I thought about quoting from some of my own materials, but then I decided
 not to.
 Instead, I decided to just type for a while and fill up 3 lines on my screen
 with whatever nonsense came into my head.
 
\end_layout

\begin_layout Standard
I've honestly not found a use for the fullwidth setting in my own materials.
\end_layout

\begin_layout Section
Conclusions
\end_layout

\begin_layout Standard
I like a lot of what Tufte has done.
 At the moment, however, I only use his style in my Calculus class.
 I have a good Calculus book, but it requires extensive notes to adapt it
 for the high school level.
 For my Physics, Chemistry, and Biology courses, the Memoir class seems
 more suited.
 I wish it were possible to take the idea of margin figures from Tufte and
 put it into Memoir.
 I also prefer Tufte's method of dealing with margin notes.
\end_layout

\begin_layout Chapter
Calculation of Volume: Sections 2.12-2.13
\end_layout

\begin_layout Abstract
Imagine taking a function like 
\begin_inset Formula $y=\sqrt{x}$
\end_inset

 and rotating it in 3 dimensions around the x-axis.
 The resulting shape would look somewhat like a cup (on its side).
 Interestingly, integration empowers us to do exactly this and to find out
 how much water that cup could hold.
\end_layout

\begin_layout Section
Visualizing Rotation
\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
I had a graph of the square root function here.
\end_layout

\end_inset


\begin_inset Caption

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "mar:A-graph-of"

\end_inset

A graph of 
\begin_inset Formula $f(x)=\sqrt{x}$
\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\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 rotated the square root function and then drew a disk on the figure
 to illustrate how I would calculate the volume of the figure.
\end_layout

\end_inset


\begin_inset Caption

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "mar:rotated"

\end_inset

A graph of 
\begin_inset Formula $f(x)=\sqrt{x}$
\end_inset

 rotated about the x-axis and with additional remarks for integration.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "mar:A-graph-of"

\end_inset

 shows the plot of the function 
\begin_inset Formula $f(x)=\sqrt{x}.$
\end_inset

 Now, imagine that we rotate that function about the x-axis.
 The resulting figure would be somewhat like figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "mar:rotated"

\end_inset

.
 This is akin to a cup lying on its side.
 For the sake of clarity, the artist (me) drew a circle on the end of the
 figure to show that it is indeed rotated.
\end_layout

\begin_layout Standard
Now, suppose we wished to find the volume of the figure.
 When we integrated the original square root function to find its area,
 we imagined a series of rectangles inside the figure.
 Their height was 
\begin_inset Formula $h=f(x)$
\end_inset

 and their width was 
\begin_inset Formula $dx$
\end_inset

.
 Since height multiplied by width was the area of each rectangle, we summed
 these areas and rewrote this as 
\begin_inset Formula $\int\, f(x)\, dx$
\end_inset

, or, in this specific case, 
\begin_inset Formula $\int\,\sqrt{x}\, dx$
\end_inset

.
\end_layout

\begin_layout Standard
To find the volume of our rotated figure the prodecure is quite similar.
 Begin by rotating each rectangle about the x-axis.
 This creates a series of cylinders.
\begin_inset Flex Sidenote
status collapsed

\begin_layout Plain Layout
The text refers to these cylinders as "disks".
 This is standard practice in all the Calculus books I checked.
\end_layout

\end_inset

 Then, we can find the volume of each cylinder/disk.
 The basic formula is:
\end_layout

\begin_layout Standard
\begin_inset Formula \[
V=hA\]

\end_inset


\end_layout

\begin_layout Standard
\noindent
where 
\begin_inset Formula $h$
\end_inset

 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 
\begin_inset Formula $A=\pi r^{2}$
\end_inset

.
 The radius in this case is the function 
\begin_inset Formula $f(x)$
\end_inset

.
 By substitution
\end_layout

\begin_layout Standard
\begin_inset Formula \[
A=\pi f^{2}(x)\]

\end_inset


\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


\end_layout

\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

\end_body
\end_document