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# Lesson 4.5: Basic Geometric Symbols

## Symbols

$\text{△ triangle}$
⠫⠞

$\text{∠ angle}$
⠫⠪

$\text{punctuation indicator}$

## Basic Geometry Symbols

### Explanation

#### Uses of shapes

Mathematicians have developed a type of shorthand including symbols, signs, and abbreviations that are used internationally. This usage allows mathematicians, scientists, engineers, researchers, and others in many other fields to have the ability to communicate across different languages and cultures by using certain agreed upon symbols. The symbols used in mathematics are, therefore, concise and have specific applications.

Shapes are used to indicate special meanings. Most often, a shape is used to represent just that: a miniature shape or picture, such as a geometric form. These miniature shapes are not used in place of labeled diagrams. The shape symbol should be used only when a corresponding miniature shape symbol is used in printed matter. Another use is to apply shape symbols in a manner similar to that of other mathematical symbols, such as using them as signs of operation or signs of comparison. Often, a shape symbol is combined with another symbol, such as a minus, plus, or multiplication sign. Shape symbols can also be used to represent omitted items or as place-value holders in much the same manner as the general omission symbol represents an omitted item.

The shape indicator is unique to braille and is made using dots one-two-four-six.

#### Application of the shape indicator

Braille incorporates the use of a shape indicator, dots one two four six, to indicate that the character or characters following it represent a shape. The shape indicator has no corresponding symbol in print; it is used to indicate that a shape appears in print. The shape indicator is the first symbol in a series of braille characters, except when the print symbol is shown canceled by a sign of negation such as a slash or vertical bar. A letter or letters, a numeral, or characters suggestive of the shape are placed in the braille cells immediately following the shape indicator. The sign of shape must be spaced according to the assigned meaning of the shape. If, for example, it represents an omitted sign of operation, it would be spaced according to the rules for omission signs.

Two-celled shapes: letter or letters suggests shape

Many shape symbols are displayed with the shape indicator followed by a letter or letters that suggests the shape. Combining the shape indicator with other letters allows for a variety of shapes to be displayed in braille. The shape indicator followed by an s represents a star. The shape indicator followed by a letter t represents a triangle. The shape indicator followed by dots two-four-six represents an angle symbol.

#### Spacing with Signs of Shapes

A shape symbol that identifies a letter or letters, or a numeral or numerals, must be separated from the identified character or characters, by a space. Signs of shape are mathematical symbols. They are to be punctuated according to the guidelines for applying marks of punctuation to mathematical symbols. In particular, when shapes are made plural or possessive with an apostrophe ;s, the punctuation indicator is inserted, unspaced, between the shape sign and the apostrophe.

When a sign of shape has a plural or a possessive ending, the sign of shape and its associated space have been interrupted and are no longer considered to be a single unit. The letter or letters following the space after the ;s or apostrophe ;s, therefore, are not considered to be part of an identified sign of shape. The letter or letters identifying the shape, following the shape indicator, shape symbol, and ;s or apostrophe ;s, would be brailled according to the rules for the use and non-use of the English letter indicator. That is, a single letter requires the English letter indicator. Two or more letters in a series do not require the English letter indicator.

### Example 1

$△ABC$
⠫⠞⠀⠠⠁⠠⠃⠠⠉

### Example 2

$△A$
⠫⠞⠀⠠⠁

### Example 3

$\angle 1$
⠫⠪⠀⠼⠂

### Example 4

$\angle MNO$
⠫⠪⠀⠠⠍⠠⠝⠠⠕

### Example 5

$\text{A}\phantom{\rule{.3em}{0ex}}△\phantom{\rule{.3em}{0ex}}\text{has three sides.}$
⠠⠁⠀⠫⠞⠀⠓⠁⠎⠀⠞⠓⠗⠑⠑⠀⠎⠊⠙⠑⠎⠲

### Example 6

Before UEB, the punctuation indicator saw a lot of use as, in Nemeth, it needs to appear between any literary punctuation and mathematical character. With UEB, however, these situations are rare since Nemeth mode is usually ended before punctuation. As such, this Tutorial will not extensively cover the punctuation indicator but below is an example of its use.

$\text{Are}\phantom{\rule{.3em}{0ex}}△\text{'s}\phantom{\rule{.3em}{0ex}}A\phantom{\rule{.3em}{0ex}}\text{and}\phantom{\rule{.3em}{0ex}}B\phantom{\rule{.3em}{0ex}}\text{acute?}$
⠠⠁⠗⠑⠀⠸⠩⠀⠫⠞⠸⠄⠎⠀⠰⠠⠁⠀⠠⠄⠁⠝⠙⠀⠰⠠⠃⠀⠸⠱⠀⠁⠉⠥⠞⠑⠦

### Example 7

$△\text{s}\phantom{\rule{.3em}{0ex}}\mathrm{ABC}\phantom{\rule{.3em}{0ex}}\text{and}\phantom{\rule{.3em}{0ex}}\mathrm{DEF}$
⠸⠩⠀⠫⠞⠎⠀⠠⠁⠠⠃⠠⠉⠀⠠⠄⠁⠝⠙⠀⠠⠙⠠⠑⠠⠋⠀⠸⠱

### Example 8

(with signs of comparison)

$\angle 1=85°$
⠫⠪⠀⠼⠂⠀⠨⠅⠀⠼⠦⠢⠘⠨⠡

### Example 9

$\angle ABC=100°$
⠫⠪⠀⠠⠁⠠⠃⠠⠉⠀⠨⠅⠀⠼⠂⠴⠴⠘⠨⠡

### Example 10

(with operations)

$\angle 1+\angle 2$
⠫⠪⠀⠼⠂⠬⠫⠪⠀⠼⠆

### Example 11

$\angle ABC>\angle XYZ$
⠫⠪⠀⠠⠁⠠⠃⠠⠉⠀⠨⠂⠀⠫⠪⠀⠠⠭⠠⠽⠠⠵