## Topological Graph Theory References

Topological Network Theory References Graph Theory and Its Engineering Applications  By Wai-Kai Chen Books by Sundaram Seshu     ( google search:   inauthor:"Sundaram Seshu" ) Linear Graphs and Network Theory PDF – Sundaram Seshu Linear Graphs and Network Theory DjVu – Sundaram Seshu Linear Network Analysis – Seshu; Norman Balabanian Topological Read more…

## Animated Geometric Proof of Pythagoras Theorem using shearing transform

What is most interesting about the following geometric proof is that it uses a shearing transform.  This transform exploits the fact that a parallelogram of equal height and length has equal area.  This gives it a fluid pouring aspect. Alot of different proofs of Pythagorean theorem.

## Two 2 dimensional determinant of a matrix animation showing it is equal to the area of the parallelogram

The 2 dimensional determinant of a matrix can be interpreted as the area of a parallelogram as shown in the following diagram. This carries on through higher dimensions.  Below depicts a 3 variable system. The rows r1, r2, r3 are vectors each. The various summations taken 1, 2 and 3 Read more…

## WordPress WP-Latex Plugin for rendering Mathematics

I found another math rendering plugin refered to here: http://www.illigal.uiuc.edu/web/kumara/2007/04/10/latex-math-plugin-for-wordpress/ It is based on LaTeX. Note To Self:  Kumara Sastry  appears to be an interesting an talented person.  He studies in the area of genetic algorithms.  An idea I have is to study talented people and make a blog and the Read more…

## Cube Sequences

13=1 13+23=9  = 32                          13+23+33=36 = 62 13+23+33+43=100 = 102 13+23+33+43+53=225 = 152 …. 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16…. These are triangular numbers are in bold:  1+2 =3 1+2+3=6 1+2+3+4=10           ( n(n+1)/2 )2= n2(n+1)2/4 A question I have in my mind is that Fermat’s last theorem states: If an integer n is greater than Read more…

## Derivation of the Normal Gaussian distribution from physical principles

In many physical systems the question arises what is the probability distribution that describes a system with a given expected energy E  over the interval from -infinity to + infinity?     Again you will use the maximum entropy principle to determine this. The constraints are as follows:         …. sum over Read more…

## MathCad File display in webpages

How to display mathcad files in a webpage. Export MathCad document as HTML

## The Mathematics Plugin that allows the equations to be typeset on this blog – wpMathPub

The beautiful equation tying pi, 1, 0, e and i all together.  You have to love that. I am using wpmathpub. The wpmathpub math publisher plugin for WordPress.org blogs is now available directly from WordPress.org’s plugin site. The WordPress.org hosted version manages several promotional and support features: Overview of the Read more…

## The Maximum Entropy Principle – The distribution with the maximum entropy is the distribution nature chooses

In a previous article entropy was defined as the expected number of bits in a binary number required to enumerate all the outcomes.  This was expressed as follows: entropy= H(x)=   In physics ( nature ) it is found that the probability distribution that represents a physical process is the Read more…

## What is Entropy?

There are many mathematical definitions of entropy.  The mental picture I find most useful is to imagine the following:   you are put in a room and your job is to label everything in the room with a sharpy indelible marker and masking tape.   You are asked to label everything in Read more…