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Template:Floor
[⧼Purge⧽ Template:Floor]
The {{floor}} mathematical formatting template and/or mathematical function template gives an HTML+CSS or a LaTeX formatted floor function of an expression and/or the numerical result of the floor of an expression (in which case it must evaluate to a real number).
Usage
- {{floor|expression}}
or
- {{floor|expression|format}}
where the last argument (format) is from
- htm: HTML+CSS [single line] (default);
- HTM: HTML+CSS [multiline];
- tex: LaTeX [single line];
- TEX: LaTeX [multiline];
- #: numerical result.
As an alternative to using LaTeX rendered PNG images (tex
or TEX
options), the htm
or HTM
options will produce an HTML+CSS formatted expression. (Do not use inside the <math>...</math>
tags.)
NOTE: To get rendered LaTeX, you must use the {{math}} template, since you cannot evaluate templates, parser functions or magic words inside the <math>...</math>
tags.
Examples
The code : before {{math|{{floor}}|&}} after
yields the text style HTML+CSS
- before
after⌊ ·⌋
The code : before {{math|{{floor|HTM}}|&}} after
yields the text style HTML+CSS
- before
after·
The code : before {{math|{{floor|tex}}|$}} after
yields the text style LaTeX
- before after
The code : before {{math|{{floor|TEX}}|$}} after
yields the text style LaTeX
- before after
The code : before {{math|{{floor|''x''}}|&}} after
yields the text style HTML+CSS
- before
after⌊ x⌋
The code : before {{math|{{floor|''x''|HTM}}|&}} after
yields the text style HTML+CSS
- before
afterx
The code : before {{math|{{floor|''x''|tex}}|$}} after
yields the text style LaTeX
- before after
The code : before {{math|{{floor|''x''|TEX}}|$}} after
yields the text style LaTeX
- before after
The code {{math|{{floor|''x''}}|&&}}
yields the display style HTML+CSS
⌊ x⌋ |
The code {{math|{{floor|''x''|HTM}}|&&}}
yields the display style HTML+CSS
|
The code {{math|{{floor|''x''|tex}}|$$}}
yields the display style LaTeX
The code {{math|{{floor|''x''|TEX}}|$$}}
yields the display style LaTeX
The code : before {{math|{{floor|5.3}} {{=}} {{floor|5.3|#}}|&}} after
yields the text style HTML+CSS
- before
after⌊ 5.3⌋= 5
The code : before {{math|{{floor|5.3|HTM}} {{=}} {{floor|5.3|#}}|&}} after
yields the text style HTML+CSS
- before
after= 55.3
The code : before {{math|{{floor|5.3|tex}} {{=}} {{floor|5.3|#}}|$}} after
yields the text style LaTeX
- before after
The code : before {{math|{{floor|5.3|TEX}} {{=}} {{floor|5.3|#}}|$}} after
yields the text style LaTeX
- before after
The code {{indent}}{{math|{{floor|5.3}} {{=}} {{floor|5.3|#}}|&&}}
yields the display style HTML+CSS
⌊ 5.3⌋ = 5 |
The code {{indent}}{{math|{{floor|5.3|HTM}} {{=}} {{floor|5.3|#}}|&&}}
yields the display style HTML+CSS
|
The code {{indent}}{{math|{{floor|5.3|tex}} {{=}} {{floor|5.3|#}}|$$}}
yields the display style LaTeX
The code {{indent}}{{math|{{floor|5.3|TEX}} {{=}} {{floor|5.3|#}}|$$}}
yields the display style LaTeX
Willans’s formula
Starting from Wilson’s theorem, C. P. Willans derived the following formula for then |
The code
{{indent}}{{math| ''p''{{sub|''n''|HTM}} {{=}} 1 + <!-- -->{{sum|''m''{{=}}1|2{{^|''n''|80%}}|HTM}}<!-- -->{{floor|<!-- -->{{root|''n''|<big>''n''</big>}} <!-- -->{{(|<!-- -->{{sum|''x''{{=}}1|''m''|HTM}}<!-- -->{{floor|cos{{^|2}} {{Gr|pi}} {{frac|(''x'' {{op|-}} 1)! + 1|''x''|HTM}}|HTM}}{{nbsp}}<!-- -->|)}}{{^|{{^|{{^|{{op|-}}1{{op|/}}''n''}}|100%}}|100%}} |HTM}}. | tex = p_n = 1 + \sum_{m=1}^{2^n} {{floor| \sqrt[n]{n} \left( \sum_{x=1}^{m} {{floor| \cos^2 \pi \frac{(x-1)! + 1}{x} |TEX}} \right)^{-1/n } |TEX}} . |&&}}
yields the display style HTML+CSS
pn = 1 +
|
and, with the $$
argument to {{math}}, yields the display style LaTeX
See also
Notes
- ↑ Henry S. Warren, Hacker’s Delight, Addison-Wesley Professional (2003), p.273.
- ↑ Willans’s formulas