14 geometry, trigonometry and vectors

14.1 Geometric symbols

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]4 △ U+25b3 triangle
]0 ○ U+25cb circle
]7 □ U+25a1 square
]= ▭ U+25ad rectangle
]5 XXX rhombus
]6 ▱ U+25b1 parallelogram
]9 XXX diameter
]o ∠ U+2220 angle
]o ∡ U+2221 angle
]o ∢ U+2222 angle
]8 ∟ U+221f right angle
]31 XXX clockwise
]"3 XXX counterclockwise
.3 summary marker for Distance (horizontal bar over several letters)
.< summary marker for Arch (arch over several symbols)
.31 summary marking for Vector (arrow over several symbols)
31 Marker for vector (arrow over a symbol)
#' ⊥ U+22a5 perpendicular to
@= ∥ U+2225 parallel to

The symbols formed with key character ] can be written with or without a preceding and/or following space to be written. However, they must be clear of immediate to the right of them standing letters, for example by a case-sensitive indicator, be separated.

Summary marks over several symbols are just before the first of these symbols and are Projective. The end of the mark turns out after the general rules for projectives (see "10 Projective Technique"). The symbols for "perpendicular to" and "parallel to" are relative (see "5 Operation and Relations Characters").

14.2 Angular, hyperbolic and inversions

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$a Arc, arc
$s sin, sine
$c cos, cosine
$t tan, or tg; tangent
$\ cot, cot, ctg; cotangent
$- sec. secant
$< cosec, cosecant
$1s arcsin, arc sine
$1c arccos, arc cosine
$1t arctg, arctangent
$1\ arccot, arcctg arc cotangent
$13 arcsec arc sec
$1< arccosec arc cosec
$1s sinh, hyperbolic sine
$1c cosh, hyperbolic cosine
$1t tanh, hyperbolic tangent
$1\ coth, hyperbolic cotangent
$18s arsinh, arsh hyperbolic arc sine
$18c arcosh, arch hyperbolic arc cosine
$18t artanh, arth hyperbolic arc tangent
$18\ arcoth, arcth hyperbolic arc cotangent

These symbols apply to all variants of the shortcut in question. word symbols in inkprint, for example for tangles in the Spelling "tan" or "tg". Also, the symbol applies both for both uppercase and lowercase words. Starts the argument with an indicator mark (as for Numbers or uppercase or lowercase letters), may it be to the Connect symbol. In other cases, a space must be used be set between symbol and argument.

It is permissible to use these symbols with the general introductory characters for shortword symbols ] and those in the black to reproduce written letters. So resulting Expressions are longer, but may be appropriate there, where a closer correspondence with the inkprint is required. is derlich or a familiarity with isolated occurring Symbols can not be assumed.

The symbols are structured. Kotangens, Sekans and Kosekans are mathematical reciprocals of tangents, Cosine and sine. This is done by mirroring the second one Sign around the horizontal axis. The hyperbolic functions are activated by inserting the character 8 subscript h for "hyperbolic") formed. At the trigonome- tric functions means an inserted, subscript a 1 "Arc ...", in the hyperbolic functions "Area ...".

14.3 Vectors

Marking of vectors

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31 Right arrow (marking)
3 horizontal line (marking)
" 1. special typographic font
_ 2. special typographic font

Word symbols

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$g grad (gradient)
$d div (divergence)
$r curl

More symbols

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;\ Beginning of a new line
&n ∇ U+2207 Nabla

The notation of the vectors is used for transfers to Braille copied from the black lettering template.

Transfers or arrows over the vector belonging to the vector Symbols are called simple resp. summary mar- (see "8 Simple and concerted capturing marks").

Shown in bold or gothic letters Vectors come with one of the two indicator marks for special typographic fonts " or _ identified (see "3.4 Special typographic drawings").