#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 Standard \begin_inset Note Note status open \begin_layout Plain Layout \series bold Important note: \series default The menu \family sans Insert\SpecialChar \menuseparator Hyperlinks \family default and the \family sans PDF properties \family default in the \family sans Document\SpecialChar \menuseparator Settings \family default menu cannot be used for tufte document classes! \end_layout \end_inset \end_layout \begin_layout Title Random Tufte Examples \end_layout \begin_layout Author Fake Author \begin_inset Note Note status open \begin_layout Plain Layout author of this example file: Jason Waskiewicz \end_layout \end_inset \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, it was endeavored to show some of the features of the Tufte-book class. In the first chapter, their use is outlined. In the second chapter, their use through a handout thjat was created in a calculus class is demonstrated. \end_layout \begin_layout Section Features \end_layout \begin_layout Standard The Tufte-book class is based on the work of Edward Tufte. It provides the same functionality as the Tufte-handout class with book-specifi c additions. Tufte's 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, some of these features are demonstrated. For a full demonstration, visit the tufte-latex webpage: \begin_inset Flex URL status collapsed \begin_layout Plain Layout http://code.google.com/p/tufte-latex \end_layout \end_inset . \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. \begin_inset Flex Marginnote status collapsed \begin_layout Plain Layout marginnote \end_layout \end_inset \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 One of the most prominent and distinctive features of this style is the extensive use of sidenotes. There is a wide margin to provide ample room for sidenotes and small figures. Any footnotes will automatically be converted to sidenotes. \begin_inset Foot status open \begin_layout Plain Layout This is a sidenote that was entered using a \family typewriter footnote \family default . \end_layout \end_inset Alternatively, you can also use directly the sidenote inset. \begin_inset Flex Sidenote status open \begin_layout Plain Layout This is a sidenote that was entered using a \family typewriter sidenote \family default . \end_layout \end_inset \end_layout \begin_layout Standard If you like to place ancillary information in the margin without the sidenote mark (the superscript number), you can use the \family typewriter Marginnote \family default inset. \begin_inset Flex Marginnote status open \begin_layout Plain Layout This is Tufte's margin note. Notice that there isn't a number preceding the note, and there is no number in the main text where this note was written. \end_layout \end_inset The normal margin note will work as well, but it will look rather odd. \begin_inset Marginal status open \begin_layout Plain Layout This is a normal margin note. Don't use it. \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. To accomplish this, use the \family typewriter NewThought \family default character style ( \family sans Edit\SpecialChar \menuseparator TextStyle\SpecialChar \menuseparator NewThought \family default ). \end_layout \begin_layout Standard The Tufte document classes includes two new character styles and some improvemen ts on existing commands for letterspacing. \end_layout \begin_layout Standard When setting strings of \begin_inset Flex AllCaps status open \begin_layout Plain Layout ALL CAPS \end_layout \end_inset or \begin_inset Flex SmallCaps status open \begin_layout Plain Layout Small Caps \end_layout \end_inset , the letterspacing---that is, the spacing between the letters---should be increased slightly. \begin_inset CommandInset citation LatexCommand cite key "Bringhurst2005" \end_inset The \emph on AllCaps \emph default character style ( \family sans Edit\SpecialChar \menuseparator TextStyle\SpecialChar \menuseparator AllCaps \family default ) has proper letterspacing for strings of \begin_inset Flex AllCaps status open \begin_layout Plain Layout FULL CAPITAL LETTERS \end_layout \end_inset , and the \emph on SmallCaps \emph default character style ( \family sans Edit\SpecialChar \menuseparator TextStyle\SpecialChar \menuseparator SmallCaps \family default ) has letterspacing for \begin_inset Flex SmallCaps status open \begin_layout Plain Layout small capital letters \end_layout \end_inset . These commands will also automatically convert the case of the text to upper- or lowercase, respectively. \end_layout \begin_layout Standard The normal \emph on Small Caps \emph default shape has also been redefined to include letterspacing. Its case is left as is, however. This allows one to use both uppercase and lowercase letters: \shape smallcaps The Initial Letters Of The Words In This Sentence Are Capitalized. \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 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 \begin_layout Standard \begin_inset CommandInset bibtex LatexCommand bibtex bibfiles "biblioExample" options "plainnat" \end_inset \end_layout \end_body \end_document