WinTriangle Intro
1. Introduction
You should read this document before using Triangle. Instructions for installing and starting Triangle are given in the help file.
1.1 Purpose
Triangle allows users to create documents with many special math and science characters, and in particular, to write compact linear math equations. Before beginning, you should review the math and science symbols available in the readable fonts files. You can do this by typing ALT-i, Enter, the hot key combination for entering the character insert menu item in Triangle. The insert character box consists of the Readable Fonts and Characters list, a lookup search tool and a preview window to display the character currently selected.
The first font in the list is Times New Roman. If you highlight it and arrow down, the names of the available fonts will be spoken aloud, followed by the hot key combinations for each font.
Scroll down and select the Symbol font from the list. As in the Readable Fonts box, highlighting characters in the list and pressing arrow down will step through the available options, speaking them aloud in turn.
Arrow down to select the absolute symbol (or type "abs" in the lookup box). You will hear "absolute" followed by "ALT vertical bar". If you press enter while this item is highlighted, an absolute value bar will be inserted into your document. You can also insert an absolute value bar by using the hot key combination ALT-g followed by the vertical bar (SHIFT Backslash). You can select other characters in the same way. All characters in the symbol font can be called with hot keys using either ALT-g or ALT-a. I recommend you browse through the entire list to become familiar with the characters available. You may also wish to explore the list of characters in the markup font, MT Extra. Though the math symbols in this font are highly specialized, the markup symbols are necessary for many basic applications.
The rest of this tutorial is devoted to learning the most Triangle features that will be commonly used in simple algebra.
1.2 Getting Started
If you know how to use Notepad, Wordpad or MS Word, you already know the basic way that Windows word processors work and should have no trouble reading text in Triangle up to this point. Up, down, left and right arrows, as well as Ctrl-left and Ctrl-right move the cursor as in any other word processor or screen reader. When the cursor reaches a new line in Triangle, the line is spoken aloud.
The File menu contains the same items as standard word processors, and these items (such as Open, Save and Save As) operate in the usual way.
There are relatively few specific speech commands in Triangle. The most important is the read-line function, Ctrl-r. Hold down the Control key and press r now to hear the current line spoken aloud. Another specific Triangle function is ALT-right or left arrows. Use these to hear each letter pronounced in the international phonetic alphabet. You may silence speech at any time by pressing the SHIFT key.
2. Superscripts and Subscripts
Most people first encounter superscripts in exponential math. The simple algebraic expression x squared is written by placing a superscript 2 to the right of the x, or x2. A superscript can be created in several ways. The easiest way is to type CTRL-Shift-+ followed by the character(s) to be superscripted. Windows is unpredictable about exiting superscript and subscript mode, however, so it is good practice to type the character following the superscript before creating the superscript itself. Practice now by typing x followed by a SPACE, cursor back and type CTRL-Shift-+, 2.
Most people first encounter subscripts in introductory chemistry where subscripts are used to show the number of atoms of the same type in a molecule. For example, the molecular formula for water is H2O. The easiest way to subscript character(s) is to type CTRL-+ followed by the character(s) to be subscripted. To write H2O, type HO, cursor back and type CTRL-+, 2.
Note that CTRL-Shift-+ and CTRL-+ toggle between super/subscript mode and normal mode.
Subscripts and superscripts can appear on the left side of symbols. For example, radicals in algebra often have a superscripted number to the left of the radical symbol to indicate nth root. The cube root of 7 is written 37 while the twelfth root of 2 is written 122. In Triangle, these superscripts can be expressed with the left superscript indicator as 37 and (12)2. There are also indicators for regular superscripts and subscripts. x2 can be correctly written x2, but it is generally preferable to use real subscripts and superscripts. When writing complex expressions containing sub/superscripts within a sub/superscript one must use indicator symbols.
3. Fractions
Simple fractions containing one character only in both the numerator and the denominator are expressed in Triangle using the "over" (/) symbol. The hot key for this common symbol is ALT-/. To write 1/2, for example, type 1 ALT-/ 2.
More complicated fractions with multiple terms are more difficult to express. For example, 1/2 is clearly one half, but the term 1/2x is less clear. Does it mean 1 divided by 2x or 1/2 times x? And does 11/2 represent 11 divided by 2, or 1 times 1/2? In practice, parentheses are used to establish certainty with fractions. 1 over 2x becomes 1/(2x) and 11 over 2 becomes (11)/2. In Triangle, however, complex fractions are represented using fraction enclosures. For example, The expression (11)/2 is written 112. There are a number of ways to obtain these enclosures in Triangle. The easiest way is to use hot keys. CTRL-T,, is the hot key for , CTRL-T, is for , and CTRL-T,F. is for . The hot key CTRL-T,N, produces all three enclosures at once. The cursor is placed in the numerator position (between the and ). You can cursor between the enclosures using the arrow keys. To write (11)/2, then, type CTRL-T,N, 11, arrow right once then type 2.
4. Greek Letters
Greek letters are ubiquitous in almost all levels of math and science. For example, the symbol Pi () is used in basic geometry to find the area of a circle in the equation a=r2. In Triangle, many of the Greek letters can be obtained through intuitive hot keys. Pi () is the Greek equivalent of the letter p, so it is inserted with the hot key combination ALT-g, p. Many other Greek letters can be inserted by the same logic: for alpha (), type ALT-g, a; for beta (), type ALT-g, b. Some hot key combinations are less intuitive. Theta (), for example, is inserted by typing ALT-g, q. You can lookup the hot key combinations for every letter in the insert character list.
5. Creating Equations
5.1 Creating Notes
Entering mathematical equations in any editor can be time consuming and laborious. To make this process easier, Triangle is equipped with feature called notes that allows the user to save complicated equations for easy recall at a later date. For example, if a chemist is writing a paper on sucrose, molecular formula C12H22O11, they can type the formula once, save it as a note, and recall it for every subsequent use. Notes can be saved either permanently and temporarily. Permanent notes are remembered by Triangle even after the program has been closed and reloaded. Temporary notes are abandoned every time Triangle is closed.
To create a note, highlight the text you wish to save. In the Edit menu, select "copy notes" (or type ALT-c). A box will open. In the name field, type a name for your note. For example, if you are saving the molecular formula for sucrose C12H22O11 you could type "sucrose" in this field. You can also choose to make the note temporary or permanent, the default being temporary.
To recall notes at a later date, select "paste notes" from the Edit menu (or type ALT-p). Select the note you wish to insert from the list of available notes and click OK.
5.2 Using Macros
Several macros for math tools, functions and symbols are included in Triangle, and allow the user to type some special math and Triangle functions with a simple hotkey combination. To view the list of available macros, select "Macros" from the Tools menu. A box will open with the complete macro list with relevant hotkeys, organized by type.
For example, the entry for the plus minus sign is listed under the "Triangle Math Function Toolbar Controls" heading. The hotkey is shown to be ALT-M,L.
6. Conclusion
Readers with applications not covered in this tutorial are encouraged to read the full description of markup characters in Markup.rtf (see below).
Triangle Markup and Symbols
April 25, 2003
Triangle.ttf Version 02, November 11, 2001
I Introduction
Triangle permits use of all characters in regular fonts as well as the Windows Symbol
and MT Extra fonts. However these are inadequate for representing everything one needs to write in math and science. The Triangle.ttf font provides the flexibility needed to reproduce essentially anything. The Triangle markup symbols are listed below in groups having similar function.
II Markup symbols
1 Typeface indicators and other single symbol modifiers
Markup symbols are given, and examples shown illustrating use for single symbols and extension to multiple symbols by use of various enclosures, including the Triangle "invisible parentheses" open and close indicators.
1(a) Typeface indicators
(Note that WinTriangle can read bold and italic fonts, so the bold and italic indicators need not be used. WinTriangle cannot distinguish gothic or other less common typefaces, so these markup indicators are needed.)
Bold - A is a A. right now is right now.
Italic - x is x. never again is never again.
Script - S is a script capital S ,and Name is the word "name" expressed in script font.
Gothic - G is a Gothic capital G, and Antique Shoppe is the name "Antique Shoppe" expressed in Gothic font.
Roman font - C is a capital C in roman font, and Cu is the chemical symbol Cu in roman font. These are sometimes used in scientific expressions to distinguish from variables - which are typically written in an italic typeface.
Transcriber definable font - P is a capital P in some previously-defined typeface, and AB is the term "AB" in that thypeface.
1(b) Other single symbol modifiers
Underline - x is x with a line under it. This is important! is the term "This is important!" with a line under the entire term.
Overbar - x is x with a bar over it. AB is "AB" with bar over the two letters. (a+b) is (A+B) with a bar over the entire term including the parentheses.
Inverted - A is
Large - A, B are large capital A and large script capital B, typical of some symbols in advanced math.
Stroke - h is the used in quantum physics. The modifier means that a stroke is added across the symbol.
Variant - is a variant of the Greek letter .
Vector - r is vector r, an r with a right arrow above it.
Hat above - i is i with a hat (caret) above it.
Tilde above - x is x with a tilde above it.
1(c) Positional modifiers
Subscript - x1 is x1. xij is xij.
Superscript - x2 is x2. x12 is x12.
Underscript - limx is x written beneath the term "Lim". It means the limit as x approaches infinity, a common notation in calculus.
Overscript - 0 is the integral from zero to infinity, i=1N is the sum over i from i=0 to i=N.
Left subscript - iN is iN. I know of no use of left subscripts without other sub and superscripts, but that doesn't mean it cannot happen.
Left superscript - 32 is 32, the radical symbol with a raised 3 on its left. This is the common notation for cube root of 2. 24He is the way physicists show that the atomic mass of the most common helium isotope is four and its atomic number is 2. One could write this symbol 24He provided there is a space in front. The former notation is alwys unambiguous.
2 Double symbol indicators
Horizontal - < combines the two < horizontally into the single symbol .
Stack + stacks the + onto the sign to create the symbol .
Superposition - superimposes the first symbol on the second to create the symbol .
3 Enclosures
Fractions may be written linearly by enclosing numerator and denominator in parentheses, brackets, or braces, and separating by a slash. This will always work, but big complicated fractions can often have a large number of parentheses, and it is difficult to avoid parenthesis mistakes in authoring or reading. The Triangle fraction enclosures can reduce mistakes and mental effort considerably. The fraction a+b over c+d can be written using the fraction indicators fraction open , denominator , and fraction close as:
a+bc+d.
The invisible parentheses and have been introduced already. They and any other set of enclosures around an expression creates what is in effect one big single symbol that can be modified by any symbol operator of part 1 and 2.
The math enclosures exist primarily in order for Triangle eventually to become an authoring tool for regular print documents. Transcribers and users can use them to distinguish some math symbols in the text that might be confused with text. For example a is the acceleration, which might be a confusing phrase without the math indicators.
Displayed equation indicators may help users distinguish equations from text. I recommend them when equations are numbered. Example:
The solution to the binary equation
ax2 + bx +c =0 Eq. 1
is
x = b b2 4ac2a Eq. 2
Array markup is used for two dimensional arrays and tables. Arrays start with and end with . Lines are enclosed by and , and cells within a line are enclosed by and . The first line is opened by the symbol, and the final line is closed by the symbol, so one doesn't need a in the first line or a in the final line. The 3x3 identity matrix is most compactly represed as:
100
010
001
The fully-marked up matrix is
100
010
001
and is considerably harder to read.
Tables may use the same markup and may have a title. I recommend putting the title just before the table and marking the title with the notation Table.
Described symbol indicators and are used for graphic symbols whose name is good enough. For example, clown face might be found in a child's math book. In chemistry, I would recommend using benzene ring and phenol ring when these symbols appear in text.
4 Multiple symbol modifiers
Macro is a tag used in two ways. It is used to indicate that the letters following it are a function. Example sin, Lim, ln. sum is the same as .
The second use of the macro is to identify some structural element such as Table: Author:
The quantity indicator is a tag useful for defining parts of equations and other large structures in order to break them up into more manageable pieces. For example the expression
a+b+cd+ef +g+hi+j
might be easier to comprehend if written
a+1f+2
1=b+cd+e
2=g+hi+j
5 Miscellaneous other symbols
The over indicator is used for simple fractions like 12, ab, i4 consisting of a single character in both numerator and denominator. These are very common in science, and the three-symbol fraction enclosures are tedious for such simple fractions. Simple fractions such as 1/2, 7/8 written with a regular slash is acceptable but can be ambiguous in some contexts.
Braille prefix cells 1-8, a, c, e and a braille mode symbol are included for special braille translation purposes.
6 Full character list in ASCII order
First column is ASCII position.
Second column is standard keyboard character at that position
Third column is Triangle character
Fourth column is name of Triangle character
33 ! Start cell of an array
34 " End described symbol
37 % Macro
38 & Left superscript
39 ' End cell of an array
40 ( Overscript
41 ) Underscript
42 * Superposition combination
43 + Left subscript
44 , Start array
45 - Horizontal combination
46 . End array
47 / Over
48 0 End in-line math expression
49 1 Prefix 1 braille symbol
50 2 Prefix 2 braille symbol
51 3 Prefix 3 braille symbol
52 4 Prefix 4 braille symbol
53 5 Prefix 5 braille symbol
54 6 Prefix 6 braille symbol
55 7 Prefix 7 braille symbol
56 8 Prefix 8 braille symbol
57 9 Start in-line math expression
58 : Start described symbol
59 ; End line of an array
60 < Start fraction
61 = Stack combination
62 > End fraction
63 ? Denominator (middle of fraction)
64 @ Start line of an array
67 C End caps mode braille symbol
73 I Inverted
76 L Large
83 S Stroke (bar through symbol)
86 V Variant
91 [ Start displayed equation
93 ] End displayed equation
94 ^ Superscript
95 _ Subscript
98 b Bold
102 f Font defined by author or transcriber
103 g Gothic
104 h Hat above
105 i Italic
111 o Overbar
113 q Quantity tag
114 r Roman
115 s Script
116 t Tilde above
117 u Underline
118 v Vector, arrow above
123 { Opening invisible parenthesis
125 } Closing invisible parenthesis
WinTriangle Intro1