Natural number

${\displaystyle \sum _{i=1}^n{i}^3={\left(\frac{n(n+1)}{2}\right)}^2}$

${\displaystyle {(1-l)}^n={(1-l)}^{\frac{ln}{l}}=\underset{l\to 0}{lim}{e}^{-ln}}$
${\displaystyle Q_{ch}={\int }_{V_1}^{V_2}i\left(t\right)dt}$
where

Math equation input 2

${\displaystyle \sum _{i=1}^n{i}^3={\left(\frac{n(n+1)}{2}\right)}^2}$

\begin{gra ph}width=400; height=300; xmin=-6.3; xmax=6.3;
xscl=1; plot(3cos(x^2)) \end{graph}


Displacement: ${\displaystyle s=ut+\frac{1}{2}a{t}^2}$
Trigonometry: ${\displaystyle {tan}^{2}x+1={sec}^{2}x}$
Summation: ${\displaystyle \pi =4\sum _{i=1}^n\frac{{(-1)}^{k+1}}{2k-1}}$



${\displaystyle }$${\displaystyle f\left(x\right)=\sum _{n=0}^{\infty }\frac{f^{\left(n\right)}\left(a\right)}{n!}(x-a{)}^n}$${\displaystyle }$

${\displaystyle f\left(x\right)=\sum _{n=0}^{\infty }\frac{f^n\left(a\right)}{n!}{(x-a)}^n}$

Matrices

AB=(8451)(-851-15)=(8×-8+4×18×5+4×-155×-8+1×15×5+1×-15)

=(-60-20-3910)
Quadratic Equation

If ax2+bx+c=0, then

x=-b±b2-4ac2a
Fractions on Fractions

6x+232x+4=6x+2 ÷ 32x+4=6x+2×2(x+2)3=4
Roots

x3≠3x
Another matrix example

This next example was one I tried to create using WPMathPub but had trouble because it wasn’t very intuitive (see WPMathPub article).

[53cos26701-2sin5]

Now, that was much easier compared to WPMathPub! This is the code I used for the above ASCIIMathML:

[(5, 3, cos 2), (6, 7, 0), (1,-2, sin 5)]

In ASCIIMathML, it can be rendered easily like this:

3∫x2 dx+5∫x dx+9∫ dx


This is some example code:

\begin{gra ph}width=400; height=300; xmin=-6.3; xmax=6.3;
xscl=1; plot(3cos(x^2)) \end{graph}

Here is the resulting graph. Move your mouse cursor over the graph – it tells you the x- and y-coordinates of the cursor position.

1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 1 2 3 4 -1 -2 -3 -4
Update
width=400; height=300; xmin=-6.3; xmax=6.3;xscl=1; axes(); plot(3cos(x^2))

I’ll do a separate article soon about the graphing capabilities of ASCIIMathML.

axes(); plot(sin(x))

setBorder(0)
initPicture(-5,5)
axes(2, 1, "labels", 1)

stroke = "blue"
plot("sin(x)")

stroke = "red"
plot(["5*t*cos(pi*t)", "5*t*sin(pi*t)"],0,1)

stroke = "green"
strokewidth = "2"
marker = "arrowdot"
line([0,1], [pi/2,1])
dot([pi,0], "open", cpi)

text([-2.5,-2.5], "ASCIIsvg Example")

Type this	See that	Comment
${\displaystyle x^2+y_1+z_{12}^{34}}$	x2+y1+z1234	subscripts as in TeX, but numbers are treated as a unit
${\displaystyle {sin}^{-1}\left(x\right)}$	sin-1(x)	function names are treated as constants
${\displaystyle \frac{d}{dx}f\left(x\right)=\underset{h\to 0}{lim}\frac{f(x+h)-f\left(x\right)}{h}}$	ddxf(x)=limh→0f(x+h)-f(x)h	complex subscripts are bracketed, displayed under lim
${\displaystyle \frac{d}{dx}f\left(x\right)=\underset{h\to 0}{lim}\frac{f(x+h)-f\left(x\right)}{h}}$	ddxf(x)=limh→0f(x+h)-f(x)h	standard LaTeX notation is an alternative
${\displaystyle f\left(x\right)=\sum _{n=0}^{\infty }\frac{f^{\left(n\right)}\left(a\right)}{n!}{(x-a)}^n}$	f(x)=∑n=0∞f(n)(a)n!(x-a)n	f^((n))(a) must be bracketed, else the numerator is only a
${\displaystyle f\left(x\right)=\sum _{n=0}^{\infty }\frac{f^{\left(n\right)}\left(a\right)}{n!}(x-a{)}^n}$	f(x)=∑n=0∞f(n)(a)n!(x-a)n	standard LaTeX produces the same result
${\displaystyle {\int }_0^{1}f\left(x\right)dx}$	∫01f(x)dx	subscripts must come before superscripts
${\displaystyle \left[\begin{array}{cc}a& b\\ c& d\end{array}\right]\left(\begin{array}{c}n\\ k\end{array}\right)}$	[abcd](nk)	matrices and column vectors are simple to type
${\displaystyle \frac{x}{x}=\{\begin{array}{ll}1& ifx\ne 0\\ \text{undefined}& ifx=0\end{array}}$	xx={1ifx≠0undefinedifx=0	piecewise defined function are based on matrix notation
${\displaystyle a/b}$	a/b	use // for inline fractions
${\displaystyle \frac{\frac{a}{b}}{\frac{c}{d}}}$	abcd	with brackets, multiple fraction work as expected
${\displaystyle \frac{a}{b}/\frac{c}{d}}$	ab/cd	without brackets the parser chooses this particular expression
${\displaystyle \frac{(a\cdot b)}{c}}$	(a⋅b)c	only one level of brackets is removed; * gives standard product
${\displaystyle \sqrt{\sqrt{\sqrt[3]{x}}}}$	x3	spaces are optional, only serve to split strings that should not match
	〈a,b〉andxyuv	angle brackets and invisible brackets
	(a,b]={x∈ℝ|a	grouping brackets don't have to match
${\displaystyle abc-{123.45}^{-1.1}}$	abc-123.45-1.1	non-tokens are split into single characters, but decimal numbers are parsed with possible sign
${\displaystyle \widehat{ab}\overline{xy}\underline{A}\overrightarrow{v}\stackrel{.}{x}\stackrel{..}{y}}$	ab^xy¯A̲v→x.y..	accents can be used on any expression (work well in IE)
${\displaystyle AB3..ℬ..AB.AB}$	AB3..ℬ..AB.AB	font commands; can use any brackets around argument
	=defor=Δ(or:=)	symbols can be stacked
${\displaystyle {}_{ 92}^{238}U}$	92238U	prescripts simulated by subsuperscripts

Seven piece puzzle

Beijing tourist info

Information for travel in Beijing

Beijing Subway

as of 2010 at RMB2 one way, it is just super. However, the service can improve. Handicapped cannot ride certain route. also the gap between subway train and platform can be as big as six inches, a person can miss step and fall into the gap.

map of 2010 Beijing Subway