Mathematics
For your Tuesday morning meditation: what do you get when you cross the Mandelbrot set with Eastern religion? Buddhabrot:
Melinda Green made this amazing picture, has more on her website, plus links to more creations and instructions for making your own.
Sleep is such an essential part of human existence that we spend about a third of our lives doing it -- some more successfully than others. Sleep disorders afflict some 50-70 million people in the United States and are a major cause of disease and injury. People who suffer from disturbed sleep have an increased risk of heart attack, stroke, hypertension, obesity, depression, and accidents. Nearly a fifth of all serious car crashes, in fact, are linked to sleeplessness.
Diagnosing sleep disorders is not necessarily easy. In standard "sleep studies," people spend one or more nights at…
The Shortest Path Problem in a Dynamic Network.
A method is needed by which efficient new network routes can rapidly becalculated to route traffic away from problem paths and nodes. Apossible method is proposed. I propose to call it the Wentrok heuristic.
What Is The Quickest Route From Newtork To Wentrok?
A network is only as efficient as the algorithm used to control its traffic. The most efficient use of resources is achieved when all traffic encounters the least physically possible delay in going from A to B. In real life, this might apply to the internet or to road traffic. …
This is the second of a two part blog on commutative encryption.Part one was Using Encryption to Block Spam.
In part one, I showed a commutative encryption scheme. In that scheme, the encryption is not a substitution cypher, but a transposition cypher. In cryptology it is a useful fiction to describe messages as if all messages begin as ordinary text, made up of alphanumeric chunks. Historically, that was the case, but in this digital age a 'message' can be anything that might be sent as a file across a network. That file could be anything from a simple text email to…
Using Encryption to Block Spam
Tackling the problem of spam is a problem in communication. If spam is noise as against wanted communications, then the spam problem is a signal to noise filtering problem. Unwanted emails, especially broadcast spam emails, consume about 80% of currently available bandwidth. We need to filter out the 80% noise so as to increase the efficiency of the web in distributing the 20% of traffic that is the wanted signal.
In using the internet we find spam in various forms. The most widely known is the spam email. Less widely known is comment spam. Comment spam…
Well, OK, Excel is not going to replace Matlab or Mathematica or whatever other similar industrial-strength computing tool you use. But this amazing site shows you how to do some powerful computation just using Excel. Need a differential equation solver? Need to simulate a random walk, or chemical reactions kinetics?This stuff isn't necessarily that complicated, but it's not always obvious how to implement this in Excel. Engineers-Excel.com has some great tips and even spreadsheet templates for scientific computing on a piece of software that you a) don't have to…
Pumpkin warning: to be read before midnight.
http://arxiv.org/abs/0903.5321
6 out of every 10 university students, regardless their field of study, get anxious when it comes to mathematics, according to a research work carried out at the University of Granada. There are significant differences between men and women in this sense, as men suffer less anxiety when it comes to deal with mathematical tasks (47% of men against 62% of women).
The research was carried out by professors Patricia Pérez-Tyteca, Enrique Castro, Isidoro Segovia, Encarnación Castro and Francisco Fernández, of the department of Didactics of Mathematics of the UGR, and Francisco Cano of the…
DEFINITIONSParcelatories, or Partitions, is a mathematical function of Combinatory Analysis which indicates how many possible forms an Whole Number can be obtained from the sum of others smaller Whole Numbers.
An example usually mentioned is the Parcelatories of the number 10.
The number 10 can be obtained from 42 different additions. The list below contains all possible counts:
Unlike the pure combination of elements, the Parcelatories are bounded by the value of the sum of its parts. As can be seen, the five Parcelatories of 10 with 2 parcels (1+9, 2+8, 3+7, 4+6, 5+5) doesn't match the…
This blog is not about music, unless it be the 'music of the spheres'.
It is a sad fact that, throughout recorded history, many books have been irretrievably lost. In many cases, had these books survived, they may have given some insight into the life and character of their authors. Such is the case with all but one of the books of the geometer Hipparchus.
If people think of ancient geometers at all, they usually think of Euclid or Pythagorus. If they think of ancient astronomers at all, they usually think of Plato or Ptolemy. Poor Hipparchus! What did he ever do to deserve such obscurity?…