1 #LyX 1.6.5svn created this file. For more info see http://www.lyx.org/
7 \use_default_options true
12 \font_typewriter default
13 \font_default_family default
20 \paperfontsize default
29 \paperorientation portrait
32 \paragraph_separation indent
34 \quotes_language english
37 \paperpagestyle default
38 \tracking_changes false
54 \begin_layout Standard
55 \begin_inset CommandInset toc
56 LatexCommand tableofcontents
64 The Features of the Tufte-book Class
67 \begin_layout Standard
68 In this document, I endeavor to show some of the features of the Tufte-book
70 In the first chapter, I outline their use.
71 In the second chapter, I demonstrate their use through a handout I created
73 For those who are viewing the .lyx file, I had to remove the figures and
74 replace them by boxes so that the download would not become overwhelming.
75 \begin_inset Flex Sidenote
78 \begin_layout Plain Layout
79 I created the figures with a combination of RLPlot and Inkscape.
91 \begin_layout Standard
92 The Tufte-book class is based on the work of Edward Tufte.
93 His documents consist of a column of text beside a wide column of margin
94 notes and margin figures.
95 This is to improve readability.
98 \begin_layout Standard
99 Features included in this format include:
102 \begin_layout Itemize
106 \begin_layout Itemize
107 Ordinary figures in text with captions in margins
110 \begin_layout Itemize
111 Full width figures and text when needed
114 \begin_layout Itemize
115 \begin_inset Quotes eld
119 \begin_inset Quotes erd
125 \begin_layout Itemize
126 Limited layers of sections and subsections
129 \begin_layout Standard
130 In this sample document, I will demonstrate some of these features.
131 For a full demonstration, visit the webpage.
134 \begin_layout Section
138 \begin_layout Standard
140 \begin_inset Quotes eld
144 \begin_inset Quotes erd
147 rather than justified.
148 \begin_inset Flex Sidenote
151 \begin_layout Plain Layout
152 This document is justified.
153 Add the option "justified" to the Custom line of the Document Class part
154 of the Document Settings.
159 The ragged right is used in most of his works, but the option exists for
163 \begin_layout Standard
164 Tufte also formats his pages so that they are not symmetric.
165 Instead, each page is the same and all the marginalia appear on the right
167 After experimentation, I agree that this option is best.
168 A symmetric layout appeared strange, to say the least.
169 \begin_inset Flex Sidenote
172 \begin_layout Plain Layout
173 To create a symmetric layout, add the option "symmetric" to the Custom line
174 of the Document Class part of the Document Settings.
182 \begin_layout Standard
183 Finally, by default, Tufte does not number his chapters or his sections.
184 Since I like to refer to sections by number, I changed this section in
185 the Document Settings by moving the slider under the Numbering and TOC
189 \begin_layout Section
193 \begin_layout Standard
194 Tufte uses ordinary figure floats like this:
197 \begin_layout Standard
198 \begin_inset Float figure
203 \begin_layout Plain Layout
204 \begin_inset Box Boxed
213 height_special "totalheight"
216 \begin_layout Plain Layout
217 Imagine your favorite figure inside this box instead of this boring text.
225 \begin_layout Plain Layout
226 An ordinary figure float.
239 \begin_layout Standard
240 Tufte also uses margin figures, a feature I wish I could apply to the Memoir
244 \begin_layout Standard
245 \begin_inset Float marginfigure
250 \begin_layout Plain Layout
251 \begin_inset Box Boxed
260 height_special "totalheight"
263 \begin_layout Plain Layout
264 Imagine your favorite photograph of a squirrel inside this box instead of
273 \begin_layout Plain Layout
287 \begin_layout Standard
288 Naturally, the Tufte-book class also allows the use of tables in the margins
289 and in the text in the same way that the figures are used.
290 I would use the margin tables for a small set of data to illustrate a concept
292 \begin_inset Quotes eld
295 Look, distance-time data is quadratic when the object is falling.
296 \begin_inset Quotes erd
299 I might put flame test results and comments in a full-width table.
302 \begin_layout Standard
303 I did attempt to use the figure-wrap float with Tufte.
304 LyX interpreted it as a figure float and sometimes didn't show it at all.
305 With only the narrow column of text available, I think that it should probably
306 be suppressed when someone edits the layout file!
309 \begin_layout Standard
310 A final type of figure is a full-width figure.
311 This is one which takes up the entire width of the page: text and margin
313 I'm proud of this because this was my one original contribution as it does
314 not seem to be in the Tufte-handout.layout file.
317 \begin_layout Standard
318 \begin_inset Float figure
323 \begin_layout Plain Layout
324 \begin_inset Box Boxed
333 height_special "totalheight"
336 \begin_layout Plain Layout
337 Imagine a photograph of a squirrel stretched out on its side in this box.
338 One of the bugs in my layout is that this only works with pictures, not
339 with frames around minipages, the way it's set up here.
347 \begin_layout Plain Layout
350 \begin_layout Plain Layout
364 \begin_layout Section
368 \begin_layout Standard
369 Tufte provides a number of innovations for use with his text.
370 The first is the extensive use of margin notes.
371 \begin_inset Flex Sidenote
374 \begin_layout Plain Layout
375 This is an example of a Tufte style margin note.
380 Tufte's margin notes use a slightly smaller font and they have the added
381 benefit of reference by a superscript.
382 Ordinary margin notes do not have this.
383 Both types are shown.
384 \begin_inset Marginal
387 \begin_layout Plain Layout
388 This is an ordinary margin note.
396 \begin_layout Standard
397 \begin_inset Flex Newthought
400 \begin_layout Plain Layout
406 innovation is Tufte's
411 It introduces new thoughts, such as this paragraph, with small capitals.
414 \begin_layout Standard
415 Finally, Tufte has a setting to print full-width text.
416 This spreads it from margin to margin.
417 I believe this might be useful for quoting a text.
420 \begin_layout Standard
421 Another available style is
422 \begin_inset Flex Allcaps
425 \begin_layout Plain Layout
434 \begin_layout Full Width
435 This is full width text.
436 I'm not going to quote a text because I don't want to mess with citations
437 and I haven't yet figured out how to use BiBTeX.
438 I thought about quoting from some of my own materials, but then I decided
440 Instead, I decided to just type for a while and fill up 3 lines on my screen
441 with whatever nonsense came into my head.
445 \begin_layout Standard
446 I've honestly not found a use for the fullwidth setting in my own materials.
449 \begin_layout Section
453 \begin_layout Standard
454 I like a lot of what Tufte has done.
455 At the moment, however, I only use his style in my Calculus class.
456 I have a good Calculus book, but it requires extensive notes to adapt it
457 for the high school level.
458 For my Physics, Chemistry, and Biology courses, the Memoir class seems
460 I wish it were possible to take the idea of margin figures from Tufte and
462 I also prefer Tufte's method of dealing with margin notes.
465 \begin_layout Chapter
466 Calculation of Volume: Sections 2.12-2.13
469 \begin_layout Abstract
470 Imagine taking a function like
471 \begin_inset Formula $y=\sqrt{x}$
474 and rotating it in 3 dimensions around the x-axis.
475 The resulting shape would look somewhat like a cup (on its side).
476 Interestingly, integration empowers us to do exactly this and to find out
477 how much water that cup could hold.
480 \begin_layout Section
484 \begin_layout Standard
485 \begin_inset Float marginfigure
490 \begin_layout Plain Layout
491 \begin_inset Box Boxed
500 height_special "totalheight"
503 \begin_layout Plain Layout
504 I had a graph of the square root function here.
512 \begin_layout Plain Layout
513 \begin_inset CommandInset label
515 name "mar:A-graph-of"
520 \begin_inset Formula $f(x)=\sqrt{x}$
536 \begin_layout Standard
537 \begin_inset Float marginfigure
542 \begin_layout Plain Layout
543 \begin_inset Box Boxed
552 height_special "totalheight"
555 \begin_layout Plain Layout
556 Here I rotated the square root function and then drew a disk on the figure
557 to illustrate how I would calculate the volume of the figure.
565 \begin_layout Plain Layout
566 \begin_inset CommandInset label
573 \begin_inset Formula $f(x)=\sqrt{x}$
576 rotated about the x-axis and with additional remarks for integration.
589 \begin_layout Standard
591 \begin_inset CommandInset ref
593 reference "mar:A-graph-of"
597 shows the plot of the function
598 \begin_inset Formula $f(x)=\sqrt{x}.$
601 Now, imagine that we rotate that function about the x-axis.
602 The resulting figure would be somewhat like figure
603 \begin_inset CommandInset ref
605 reference "mar:rotated"
610 This is akin to a cup lying on its side.
611 For the sake of clarity, the artist (me) drew a circle on the end of the
612 figure to show that it is indeed rotated.
615 \begin_layout Standard
616 Now, suppose we wished to find the volume of the figure.
617 When we integrated the original square root function to find its area,
618 we imagined a series of rectangles inside the figure.
620 \begin_inset Formula $h=f(x)$
624 \begin_inset Formula $dx$
628 Since height multiplied by width was the area of each rectangle, we summed
629 these areas and rewrote this as
630 \begin_inset Formula $\int\, f(x)\, dx$
633 , or, in this specific case,
634 \begin_inset Formula $\int\,\sqrt{x}\, dx$
640 \begin_layout Standard
641 To find the volume of our rotated figure the prodecure is quite similar.
642 Begin by rotating each rectangle about the x-axis.
643 This creates a series of cylinders.
644 \begin_inset Flex Sidenote
647 \begin_layout Plain Layout
648 The text refers to these cylinders as "disks".
649 This is standard practice in all the Calculus books I checked.
654 Then, we can find the volume of each cylinder/disk.
655 The basic formula is:
658 \begin_layout Standard
659 \begin_inset Formula \[
667 \begin_layout Standard
670 \begin_inset Formula $h$
673 is the height of the cylinder (width of the rectangle)
674 \begin_inset Formula $dx$
678 The area of each figure is a circle where
679 \begin_inset Formula $A=\pi r^{2}$
683 The radius in this case is the function
684 \begin_inset Formula $f(x)$
691 \begin_layout Standard
692 \begin_inset Formula \[
700 \begin_layout Standard
702 In our specific case,
705 \begin_layout Standard
706 \begin_inset Formula \begin{eqnarray*}
707 A & = & \pi\left(\sqrt{x}\right)^{2}\\
708 & = & \pi x\end{eqnarray*}
715 \begin_layout Standard
716 To calculate the volume of one disk, we have
719 \begin_layout Standard
720 \begin_inset Formula \[
728 \begin_layout Standard
730 or, in the general case
733 \begin_layout Standard
734 \begin_inset Formula \[
735 V=\pi f^{2}(x)\, dx\]
742 \begin_layout Standard
743 To find the volume of the figure between points
744 \begin_inset Formula $a$
748 \begin_inset Formula $b$
751 we sum the volumes by means of integration:
754 \begin_layout Standard
755 \begin_inset Formula \begin{equation}
756 \int_{a}^{b}\,\pi f^{2}(x)\, dx\end{equation}
763 \begin_layout Standard
765 In the specific example, over the interval
766 \begin_inset Formula $[0,4]$
772 \begin_layout Standard
773 \begin_inset Formula \begin{eqnarray*}
774 \int_{0}^{4}\,\pi x\, dx & = & \pi\int_{0}^{4}\, x\, dx\\
775 & = & \pi\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}\\
776 & = & \pi\left(\frac{4^{2}}{2}-0\right)\\
777 & = & 8\pi\end{eqnarray*}
784 \begin_layout Standard
785 \begin_inset Flex Newthought
788 \begin_layout Plain Layout
794 a special hole down the length of the cup we just worked with.
795 It is made with a quadratic shaped bit.
796 \begin_inset Flex Sidenote
799 \begin_layout Plain Layout
800 I have no idea how I'd do this in real life, but I'm making a point.
805 I find that the hole the bit makes can be modeled with the function
806 \begin_inset Formula $g(x)=\frac{x^{2}}{16}$
810 I would need to subtract the volume of the material removed from the volume
812 \begin_inset Quotes eld
816 \begin_inset Quotes erd
820 Each individual cylinder would become like a
821 \begin_inset Quotes eld
825 \begin_inset Quotes erd
829 To get the area of one washer, I would use the formula
832 \begin_layout Standard
833 \begin_inset Float marginfigure
838 \begin_layout Plain Layout
839 \begin_inset Box Boxed
848 height_special "totalheight"
851 \begin_layout Plain Layout
852 Here I used RLPlot to draw the square root function and the quadratic function.
853 Then I used Inkscape to shade the area between them.
861 \begin_layout Plain Layout
863 \begin_inset Formula $f(x)$
867 \begin_inset Formula $g(x)$
871 \begin_inset Formula $f(x)-g(x)$
887 \begin_layout Standard
888 \begin_inset Formula \begin{eqnarray*}
889 A_{washer} & = & A_{cup}-A_{drill}\\
890 & = & \pi f^{2}(x)-\pi g^{2}(x)\\
891 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\end{eqnarray*}
898 \begin_layout Standard
899 The volume of each washer would be
902 \begin_layout Standard
903 \begin_inset Formula \begin{eqnarray*}
904 V_{washer} & = & A_{washer}\, dx\\
905 & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\, dx\end{eqnarray*}
912 \begin_layout Standard
914 Then, by summing the volumes of all the washers between points
915 \begin_inset Formula $a$
919 \begin_inset Formula $b$
922 , the integral is derived:
925 \begin_layout Standard
926 \begin_inset Formula \begin{equation}
927 \int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\, dx\end{equation}
934 \begin_layout Standard
935 In the case of our quadratic drill bit::
936 \begin_inset Float marginfigure
941 \begin_layout Plain Layout
942 \begin_inset Box Boxed
951 height_special "totalheight"
954 \begin_layout Plain Layout
955 This was the rotated set of 2 functions.
963 \begin_layout Plain Layout
964 The cup with a quadratic hole drilled down its length
977 \begin_layout Standard
978 \begin_inset Formula \begin{eqnarray*}
979 \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\\
980 & = & \pi\left(\int_{0}^{4}\, x\, dx-\int_{0}^{4}\,\frac{x^{4}}{256}\, dx\right)\\
981 & = & \pi\left(\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}-\left.\left(\frac{x^{5}}{1280}\right)\right|_{0}^{4}\right)\\
982 & = & \pi\left(\left(\frac{4^{2}}{2}-0\right)-\left(\frac{4^{5}}{1280}-0\right)\right)\\
983 & = & \pi\left(8-0.8\right)\\
984 & = & 7.2\pi\end{eqnarray*}
991 \begin_layout Standard
995 \begin_layout Section
999 \begin_layout Itemize
1000 p114: 1, 4, 5, 6, 8, 10, 12, 15