ASCIIMathML-SVG Pythagoras
Theorem: In a right-angled triangle with side-lengths `a`, `b` and `c`, where `c` is the length of the hypothenuse, `a^2+b^2=c^2`.
Proof: Consider a line through the right angle and perpendicular to the hypothenuse. This line
splits the hypothenuse into two pieces of length `d` and `c-d`. By similar triangles, `\frac{a}{c}=\frac{d}{a}` and `\frac{b}{c}=\frac{c-d}{b}`.
Therefore `a^2=c*d` and `b^2=c*(c-d)`, hence `a^2+b^2=c*d+c*(c-d)=c*d+c^2-c*d=c^2`.
agraph
width=600;
height=300;
initPicture(-6,6,-1,5);
A = [5,0];
B = [-5,0];
O = [0,0];
t = -2;
update2();
endagraph
Pointer coordinates: (x,y) Click coordinates: (x,y)
Move the pointer over the picture to see different right-angled triangles.
The proof given above applies to all of them.
agraph
width=600;
height=300;
initPicture(-6,6,0);
a = 2;
s = 5;
update4();
endagraph
Move the pointer over the left square. Can you see why
the red area + the
blue area = the green area? This is
what Pythagoras discovered! (Well, actually it was known long before his time,
but his name is attached to this fundamental result.)
 |
The original
ASCIIMathML and
ASCIIsvg
scripts have been developed by by
Peter Jipsen,
Chapman University (jipsen@chapman.edu)
LaTeXMathML has been
developed by Douglas Woodall (and exteded by Jeff Knisley), based on
ASCIIMathML
The version of ASCIIMathML used
here, is a modified and extended version, developed by
Dr.ir. S.A. Miedema
Other sources: An
ASCIIsvg manual by Robert Fant.
An
ASCIIsvg manual by Peter Jipsen. An
ASCIIMathML manual by James Gray.
Plugins and fonts required (depending on your browser):
MIT MathML
font packages,
MathPlayer,
Adobe SVGviewer
Look at:
http://www.w3.org/TR/SVG11/ for detailed information about SVG.
Look at: http://www.w3.org/Math/
for detailed information about MathML
Copyright ©
Dr.ir. S.A. Miedema, Delft University of Technology,
Faculty of Mechanical Engineering, Marine Technology & Materials Science
Department of Marine & Transport Technology,
The Chair of Dredging Engineering |
|