The 2 dimensional determinant of a matrix can be interpreted as the area of a parallelogram as shown in the following diagram. Numeric Example Compare that with the old fashioned area of two triangles that make up the parallelogram: Using Pythagoras: This carries on through higher dimensions. Read more…
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…
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…
Research Links The Maximum Entropy Principle – The distribution with the maximum entropy is the distribution nature chooses Maximum Entropy Distribution for Random Variable of Extent [0,Infinity] and a Mean Value Mu Quantum Harmonic Oscillator: Wavefunctions Hermite polynomials In many physical systems the question arises what is the probability Read more…
How to display mathcad files in a webpage. Export MathCad document as HTML
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…
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…
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…
If you were trying to reverse engineer a database of a blind e commerce site like MercadoLivre it appears you only need to have 6 ish levels of connection to be able to connect everyone. This is something I have wondered about and now realize the 6 degrees applies to Read more…
When you look at the Hubbart peak oil graph is is tempting to read off the peak shown as is. The problem with this is in years past we could have each year predicted peak oil following rapidly. This is because oil is found on an ongoing basis. It is Read more…