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GPF Archive: Wednesday, March 8, 2000

- posted by Gp @ 8:53 PM

ThunderK8S

- posted by Gp @ 8:53 PM

thunderk8spro

- posted by Gp @ 8:53 PM

IKP - Evolve Student Project

- posted by Gp @ 12:07 PM

Wired News: EFF Publishes Patent Hit List

- posted by Gp @ 12:05 PM

PUBPAT News > PUBPAT Adds Technical Experts, Seeks More

PUBPAT News > PUBPAT Adds Technical Experts, Seeks More: "PUBPAT Adds Technical Experts, Seeks More: Scientific Expertise Aids Non-Profit in Protecting the Public from the Harms of the Patent System

NEW YORK -- The Public Patent Foundation ('PUBPAT') announced today that four technical experts have joined its staff and that pro bono opportunities exist for any other technical experts who wish to assist PUBPAT's work against the harms caused by the patent system. The four technical experts joining PUBPAT have backgrounds in chemistry, microbiology and molecular genetics, computer science, and electrical engineering and will perform various activities, including reviewing and analyzing the validity and scope of patents within their respective fields of expertise."

- posted by Gp @ 11:58 AM

NewsForge | gLabels: Ready for prime time

- posted by Gp @ 8:40 AM

ARRLWeb: Utility Cuts Short BPL Trial that was Target of Amateur Complaints

- posted by Gp @ 7:10 AM

NASA Ames Research Center - Ames News

NASA Ames Research Center - Ames News: "Lunar bases that can travel on wheels, or even legs, will increase landing zone safety, provide equipment redundancy and improve the odds of making key discoveries by enabling crews to visit many lunar sites, according to Marc Cohen, a researcher at NASA's Ames Research Center, in California's Silicon Valley. Cohen recently presented his concept in a research paper at the 2004 American Institute of Physics Forum in Albuquerque, N.M."

- posted by Gp @ 7:02 AM

here

http://www.gpf-comics.com/d/19991220.html

- posted by Gp @ 8:29 PM

BBC NEWS | Science/Nature | Design wanted for Antarctic base

- posted by Gp @ 4:39 PM

Welcome

- posted by Gp @ 4:36 PM

Wired 12.07: Copy This Article & Win Quick Cash!

- posted by Gp @ 4:16 PM

About TELUS | Media | News Releases

- posted by Gp @ 4:13 PM

ACG | Imagine the possibilities...

- posted by Gp @ 3:57 PM

IODP Brochure (English)

- posted by Gp @ 2:55 PM

[cs/0406015] Zipf's law and the creation of musical context

- posted by Gp @ 2:54 PM

Tunes create context like language: Maths shows why tonal music is easy listening.

- posted by Gp @ 2:54 PM

News

- posted by Gp @ 2:51 PM

DBAzine.com: the online portal for database issues and solutions

- posted by Gp @ 2:51 PM

Date defends relational model

- posted by Gp @ 2:51 PM

Date defends relational model

- posted by Gp @ 2:51 PM

DATABASE DEBUNKINGS - HOME

- posted by Gp @ 2:50 PM

FOXNews.com - U.S. & World - Supreme Court Strikes Down Porn-Shield Law

- posted by Gp @ 2:50 PM

News

- posted by Gp @ 1:49 PM

ATrpms

- posted by Gp @ 12:53 PM

RPM Search

- posted by Gp @ 12:53 PM

rpmseek.com - The search engine for Linux rpm and Debian packages

- posted by Gp @ 11:58 AM

InformationWeek > IT Employment > Study: Technology, Not Outsourcing Is The Biggest Threat To Jobs > June 25, 2004

InformationWeek > IT Employment > Study: Technology, Not Outsourcing Is The Biggest Threat To Jobs > June 25, 2004

Strategy Analysis says technology that adds intelligence to computers is a bigger threat to jobs than low-wage countries.

- posted by Gp @ 9:14 AM

NOVALUG - Home Page

- posted by Gp @ 8:48 PM

tux.org: Home

- posted by Gp @ 8:48 PM

Mini-Box.Com

- posted by Gp @ 6:03 AM

Caffeine free coffee plant discovered. 23/06/2004. ABC News Online

Caffeine free coffee plant discovered. 23/06/2004. ABC News Online: "Caffeine free coffee plant discovered
Brazilian scientists say they have found a rare variety of coffee plant that should provide the world's first cup of naturally decaffeinated but full-tasting coffee.
The home of the plant is in Ethiopia, but its remarkable qualities were spotted by agricultural researchers in Sao Paulo.
They were screening three thousand coffee bushes that are being grown under a programme aimed at reducing caffeine content in coffee beans.
Three specimens were found to be 'almost completely free' of caffeine.
Decaffeinated coffee accounts for about 10 per cent of the world coffee market, but experts say demand would soar if a way were found to produce decaffeinated beans naturally."

- posted by Gp @ 4:40 AM

Physics News Update 689

Physics News Update 689: "Amorphous Steel
Amorphous steel, long a goal of metallurgists, has been fabricated for the first time by scientists at Oak Ridge National Lab. The amorphous steel produced has a hardness and strength more than twice that of the best ultra-high-strength conventional steel. Some amorphous (glassy) iron-based alloys have been employed in making transformer cores, the electrical devices which transform electricity from one voltage to another, and have reduced energy losses thereby by two-thirds. But not until now has glassy steel of the kind used in building structures been made. "

- posted by Gp @ 4:39 AM

21 Rules of Thumb � How Microsoft develops its Software

21 Rules of Thumb � How Microsoft develops its Software: "I will be presenting a session at TechEd in Amsterdam next week on the subject of software development � �21 Rules of Thumb � How Microsoft develops its Software�. As someone who has been involved with software development for over two decades, the whole area of how you actually bring together a team and get them to successfully deliver a project on time, is one worthy of a lot of attention, if only because it is so hard to do. Even before I joined Microsoft, ten years ago, I was interested in this topic, having been involved myself in a couple of projects that, I shall politely say, were somewhat �less than successful�.

So, just how do you get teams to work together successfully? I�ve written a few articles on it, interviewed people at Microsoft about it, and witnessed it first hand with teams inside and outside Microsoft. Jim McCarthy, who I have met and heard present, whilst at Microsoft, in the C++ team, wrote an article entitles �21 Rules of Thumb for Shipping Great Software on Time� (which I have enclosed at the end of my blog in its original form) and followed it up with a book �Dynamics of Software Development�. My session at TechEd is largely based on this article, and so if you are inspired by this session, then the best thing you can do is buy the book (and no, I don�t get any commission!) and start using it. (He also has a newer book �Software for Your Head: Core Protocols for Creating and Maintaining Shared Vision� which you may want to look at as well)"

- posted by Gp @ 4:38 AM

UA Scientists Help Create Spacecraft That Think for Themselves

- posted by Gp @ 4:38 AM

Researchers warn of infectious Web sites - News - ZDNet

Researchers warn of infectious Web sites - News - ZDNet: "update Security researchers warned Web surfers on Thursday to be on guard after uncovering evidence that widespread Web server compromises have turned corporate home pages into points of digital infection. "

- posted by Gp @ 4:34 AM

Wired 12.07: The Humanoid Race

Wired 12.07: The Humanoid Race: "It was an astounding request. A year ago, neuroscientist Mitsuo Kawato called on the Japanese government to commit 50 billion yen ($446 million) a year for the next three decades. The dream: an Apollo-like program to build a robot with the mental, physical, and emotional capabilities of a 5-year-old child. Kawato called his plan the Atom Project, named for the popular postwar cartoon Tetsuwan Atom (known as Astroboy in the US), the story of a superhero boy robot. "

- posted by Gp @ 4:34 AM

Wired 12.07: The Humanoid Race

- posted by Gp @ 4:34 AM

The Globe and Mail

The Globe and Mail: "Baltimore � If a robot does save the Hubble Space Telescope, it will be a robot designed by a Canadian company that has rescued the orbiting observatory once before."

- posted by Gp @ 4:34 AM

PCs out sick more than users - News - ZDNet

PCs out sick more than users - News - ZDNet: "The average UK PC is rendered unusable for the equivalent of around nine working days every year because the owner is cleaning up spam or fighting viruses. This is two days a year more than the average UK worker takes off as sick leave, according to Yahoo. "

- posted by Gp @ 4:27 AM

PCs out sick more than users - News - ZDNet

- posted by Gp @ 4:27 AM

Wired News: NASA Eyes Cash Prizes of Its Own

- posted by Gp @ 4:26 AM

Wired News: Rocket Hobbyists Dropping Hobby

- posted by Gp @ 4:26 AM

'Smart' Satellites That Think For Themselves

'Smart' Satellites That Think For Themselves: "Currently, satellites take pictures of whatever is in front of their cameras. But hydrologists from the University of Arizona (UA), working with the Jet Propulsion Laboratory (JPL) are creating spacecrafts that think for themselves. Their smart software, which is tested on NASA's EO-1 satellite, can be used on all kinds of spacecrafts. This software has three components: an image formation module, a science algorithm module, and a continuous planning module. This onboard planner reschedules what to film in conjunction with what the scientific algorithms have detected. This software has already detected floods in Australia and will be adapted to also detect volcano eruptions and changes in ice fields. In a next stage, it will be used in space, for instance to watch Jupiter's moons."

- posted by Gp @ 4:26 AM

US News Article | Reuters.com

- posted by Gp @ 4:26 AM

Student Theses

Student Theses: "Biometrics deals with identifying individuals with help of their biological data. Fingerprint scanning is the most common method of the biometric methods available today. The security of fingerprint scanners has however been questioned and previous studies have shown that fingerprint scanners can be fooled with artificial fingerprints, i.e. copies of real fingerprints. The fingerprint recognition systems are evolving and this study will discuss the situation of today.

Two approaches have been used to find out how good fingerprint recognition systems are in distinguishing between live fingers and artificial clones. The first approach is a literature study, while the second consists of experiments.

A literature study of liveness detection in fingerprint recognition systems has been performed. A description of different liveness detection methods is presented and discussed. Methods requiring extra hardware use temperature, pulse, blood pressure, electric resistance, etc., and methods using already existent information in the system use skin deformation, pores, perspiration, etc.

The experiments focus on making artificial fingerprints in gelatin from a latent fingerprint. Nine different systems were tested at the CeBIT trade fair in Germany and all were deceived. Three other different systems were put up against more extensive tests with three different subjects. All systems were circumvented with all subjects' artificial fingerprints, but with varying results. The results are analyzed and discussed, partly with help of the A/R value defined in this report."

- posted by Gp @ 4:26 AM

Yahoo! News - Scientist Sees Space Elevator in 15 Years

- posted by Gp @ 4:26 AM

- posted by Gp @ 4:20 AM

Mini-Box.Com

- posted by Gp @ 4:20 AM

Slashdot: News for nerds, stuff that matters

Slashdot: News for nerds, stuff that matters: "Women reason with the heart and are much less often wrong than men who reason with the head. -- DeLescure"

- posted by Gp @ 4:17 AM

Re: reprocess file in /var/mail

Re: reprocess file in /var/mail: "'Paul R. Morin' writes:
>I have a user with mail in their /var/mail/[user] spool. I need to
>requeue that mail file so all the messages are reprocessed and sent to a
>new destination as specified by the virtusertable. Can this be done
>with procmail, formail, etc?

Use formail to split the mailbox, feeding each message into sendmail:

formail -Y -n -s sendmail -odq user < /var/mail/user

Since you've already setup the virtusertable entry, no new mail should
be arriving in the mailbox, so you don't need to worry about locking it.
The '-odq' option to sendmail tells it to queue the message instead of
trying to send it out immeadiately. Once the above command finishes,
you can then 'run' the queue with something like:
sendmail -v -qRnew-address

where 'new-address' is the address that 'user's mail is being redirected
towards. That should be able to send all the messages with one SMTP
connection to the remote host."

- posted by Gp @ 10:17 PM

waste :: home

waste :: home: "Welcome
WASTE is an anonymous, secure, and encryped collaboration tool which allows users to both share ideas through the chat interface and share data through the download system. WASTE is RSA secured, and has been hearalded as the most secure P2P connection protocol currently in development. For technical information please see 'information', but for more information on download and installation, please see 'downloads'. Looking for other WASTE projects? Please choose 'projects', or if you are interested in the main WASTE sourceforge project, see 'sourceforge'. Or, if you just need some help with WASTE, see 'documentation'."

- posted by Gp @ 10:06 PM

SourceForge.net: Project Info - WASTE

- posted by Gp @ 10:05 PM

LinPHA -- The PHP Photo Archive

- posted by Gp @ 9:56 PM

SourceForge.net: Project Info - The PHP Photo Archive

- posted by Gp @ 9:33 PM

Mutt-i, GnuPG and PGP Howto

- posted by Gp @ 9:07 PM

21 Rules of Thumb � How Microsoft develops its Software

- posted by Gp @ 8:37 PM

Linux in Government: Winning in the Big Enterprise Space

Linux in Government: Winning in the Big Enterprise Space: "lder"

- posted by Gp @ 8:27 PM

Linux in Government: Winning in the Big Enterprise Space

Linux in Government: Winning in the Big Enterprise Space: "lder"

- posted by Gp @ 8:27 PM

TheStar.com - Rare gene may treat muscle deterioration

- posted by Gp @ 4:35 PM

Trillian Discussion Forums - Connection to Yahoo has failed -> Invalid Password <-

- posted by Gp @ 4:35 PM

Linux in Government: Winning in the Big Enterprise Space

- posted by Gp @ 4:35 PM

The New York Times > Science > A Very Muscular Baby Offers Hope Against Diseases

- posted by Gp @ 4:34 PM

CD trove is proving short on treasures

- posted by Gp @ 4:12 PM

Something Awful - The Internet Makes You Stupid

- posted by Gp @ 3:45 AM

id Software: Heretic

- posted by Gp @ 2:38 AM

id Software: Commander Keen (Invasions of the Vorticons Trilogy)

- posted by Gp @ 2:38 AM

The Official Dopefish Home Page

- posted by Gp @ 2:35 AM

Yet another Commander Keen page :)

- posted by Gp @ 2:13 AM

Public Commander Keen Forum @ www.ezboard.com

- posted by Gp @ 2:08 AM

3D Realms Site: A Look Back at Commander Keen

- posted by Gp @ 2:07 AM

RAID Tests

- posted by Gp @ 11:15 PM

Guide, How To, Tutorial and Article list

- posted by Gp @ 6:18 PM

The Official DVD Decrypter Website

- posted by Gp @ 6:18 PM

Guide, How To, Tutorial and Article list

- posted by Gp @ 5:20 PM

Afonic DVD Guides

- posted by Gp @ 5:13 PM

MTBradfield & Associates, LLC

- posted by Gp @ 4:44 PM

Linux & Wireless LANs

- posted by Gp @ 1:58 PM

LinuxQuestions.org - Interview with Jean Tourrilhes of HP - where Linux users come for help

- posted by Gp @ 1:58 PM

Index of /

- posted by Gp @ 1:26 PM

MythTV

- posted by Gp @ 1:26 PM

Get The Facts

- posted by Gp @ 1:09 PM

Hotmail bounces Gmail invitations - ZDNet UK News

- posted by Gp @ 1:03 PM

Ars Technica: KDE 3.2 Overview

- posted by Gp @ 1:00 PM

MSNBC - Private rocket ship breaks space barrier

- posted by Gp @ 12:58 PM

PCWorld.com - Company Makes Plans for Portable Fuel Cells

- posted by Gp @ 12:51 PM

Giving Mars Back its Heartbeat :: Astrobiology Magazine :: Search for Life in the Universe0

Giving Mars Back its Heartbeat :: Astrobiology Magazine :: Search for Life in the Universe

- posted by Gp @ 12:28 AM

Transcend TV-Box USB 2.0 TV Tuner -= www.bigbruin.com =-

- posted by Gp @ 12:24 AM

Astrobiology Magazine :: Search for Life in the Universe

- posted by Gp @ 12:23 AM

AutoPatcher.com - Home

- posted by Gp @ 12:19 AM

Order the Windows Security Update CD

- posted by Gp @ 12:14 AM

ACM Queue - Blaster Revisited - A second look at the cost of Blaster sheds new light on today's blended threats.

- posted by Gp @ 11:41 PM

Furdlog � Issues With Beastie Boys

- posted by Gp @ 11:36 PM

Stealth wallpaper could keep LANs secure - silicon.com

- posted by Gp @ 11:35 PM

The Statesman

- posted by Gp @ 6:05 PM

SignOnSanDiego.com > News > Business -- Glitches seen in Qualcomm cell chips

- posted by Gp @ 6:05 PM

Entertainment: People Article | Reuters.com

- posted by Gp @ 6:04 PM

STUFF : NATIONAL NEWS : EDUCATION - STORY : New Zealand's leading news and information website

- posted by Gp @ 6:02 PM

InformationWeek > Wireless > How To Really Surf The Net > June 18, 2004

- posted by Gp @ 6:02 PM

Entertainment: People Article | Reuters.com

- posted by Gp @ 6:02 PM

The New York Times > Science > To Surprise of Researchers, Comet Has a Personality

- posted by Gp @ 5:45 PM

[PDF] Secret Key Cryptography Using Graphics Cards

[PDF] Secret Key Cryptography Using Graphics Cards
File Format: PDF/Adobe Acrobat - View as HTML
... Al- though high-performance dedicated cryptographic accelerator cards have been commercially ... Pentium IV processor and Nvidia GeForce3 graphics card, a laptop ...
www.cs.columbia.edu/~library/TR-repository/ reports/reports-2004/cucs-002-04.pdf -

- posted by Gp @ 3:39 PM

LinuxDevCenter.com: Windows Compatibility for the Linux Desktop [Jun. 10, 2004]

- posted by Gp @ 2:09 PM

More Power to Firmware

- posted by Gp @ 2:08 PM

LWN: The Grumpy Editor's guide to terminal emulators

- posted by Gp @ 2:08 PM

Howstuffworks "How Turbochargers Work"

- posted by Gp @ 2:03 PM

Wikipedia PHP script development

- posted by Gp @ 1:38 PM

Howstuffworks "How Champ Cars Work"

- posted by Gp @ 1:27 PM

BBC Top Gear

- posted by Gp @ 1:18 PM

What does your firewall sound like? | Linux Gazette

- posted by Gp @ 1:18 PM

Halting problem - Wikipedia, the free encyclopedia

- posted by Gp @ 1:16 PM

Turing machine - Wikipedia, the free encyclopedia

- posted by Gp @ 1:15 PM

Hilbert space - Wikipedia, the free encyclopedia

- posted by Gp @ 1:07 PM

Quantum cryptography - Wikipedia, the free encyclopedia

- posted by Gp @ 1:05 PM

Causality - Wikipedia, the free encyclopedia

Causality - Wikipedia, the free encyclopedia: "Philosophy

In a strict reading, if A causes B, then A must always be followed by B. In this sense, sex does not cause pregnancy, nor does smoking cause cancer. In everyday usage, we therefore often take 'A causes B' to mean 'A causes an increase in the probability of B'.

The establishing of cause and effect, even with this relaxed reading, is notoriously difficult, expressed by the widely accepted statement 'correlation does not imply causation'. For instance, the observation that smokers have a dramatically increased lung cancer rate does not establish that smoking must be a cause of that increased cancer rate: maybe there exists a certain genetic defect which both causes cancer and a yearning for nicotine."

- posted by Gp @ 1:04 PM

EPR paradox - Wikipedia, the free encyclopedia

- posted by Gp @ 1:02 PM

Quantum Cryptography with Entangled Photons: Welcome!

- posted by Gp @ 1:01 PM

Quantum mechanics - Wikipedia, the free encyclopedia

- posted by Gp @ 12:52 PM

PhysicsWeb - News Resources

- posted by Gp @ 12:52 PM

PhysicsWeb - Teleportation breaks new ground

- posted by Gp @ 12:52 PM

Systems - Enterprise 450

- posted by Gp @ 10:30 AM

uncollected thoughts � Project ICECE

- posted by Gp @ 10:27 AM

- posted by Gp @ 10:26 AM

More Power to Firmware

- posted by Gp @ 10:18 PM

The New York Times > Technology > Circuits > Computers Chase the Checkered Flag

- posted by Gp @ 9:23 PM

Guardian Unlimited | Special reports | Inquiry call over police gun victim

- posted by Gp @ 9:20 PM

- posted by Gp @ 10:29 AM

NEWS.com.au | New stun gun uses UV laser (June 17, 2004)

- posted by Gp @ 10:27 AM

New Scientist

- posted by Gp @ 10:25 AM

Quantum entanglement - Wikipedia, the free encyclopedia

- posted by Gp @ 7:25 AM

CNN.com - Scientists�take step toward quantum computers - Jun 16, 2004

- posted by Gp @ 7:11 AM

LinuxDevCenter.com: Windows Compatibility for the Linux Desktop [Jun. 10, 2004]

- posted by Gp @ 7:09 AM

Censorship's Trial Balloons - What happens when wartime news gets censored? By Liam Callanan

- posted by Gp @ 6:56 AM

USC Viterbi School of Engineering

- posted by Gp @ 12:55 AM

TransHab

- posted by Gp @ 7:10 AM

Cinelerra

- posted by Gp @ 4:38 PM

g4u - Harddisk Image Cloning for PCs

- posted by Gp @ 4:38 PM

g4u - Harddisk Image Cloning for PCs

- posted by Gp @ 4:26 PM

CQC Intros: Quantum Computing

CQC Intros: Quantum Computing: "b"

- posted by Gp @ 4:24 PM

Qubit.org

- posted by Gp @ 3:42 PM

FhG Quantum Computing Services - Compute the Quantum

- posted by Gp @ 3:42 PM

SANS - Internet Storm Center - Cooperative Cyber Threat Monitor And Alert System - Current Infosec News and Analysis

- posted by Gp @ 3:40 PM

Welcome to the openMosixLOAF Project Website

- posted by Gp @ 4:54 PM

Linux4all LiveCD`s

- posted by Gp @ 4:49 PM

:: ClusterKnoppix - Main

- posted by Gp @ 4:41 PM

openMosix, an Open Source Linux Cluster Project

- posted by Gp @ 4:41 PM

Linux in Government: Federal Contracts, a New Era of Competition

- posted by Gp @ 2:19 AM

Opinion: Why Users Blame the Spatial Nautilius - OSNews.com

- posted by Gp @ 2:17 AM

Opinion: Why Users Blame the Spatial Nautilius - OSNews.com

- posted by Gp @ 7:55 PM

Xfce - Desktop Environment

- posted by Gp @ 6:00 PM

The Fast-Food Syndrome: The Linux Platform is Getting Fat - OSNews.com

- posted by Gp @ 6:00 PM

The Undead Zone - Why realistic graphics make humans look creepy. By Clive Thompson

- posted by Gp @ 5:59 PM

Oops! Firm accidentally eBays customer database | The Register

- posted by Gp @ 11:17 PM

New Scientist

- posted by Gp @ 4:46 PM

CNN.com - Think before you text - Jun 7, 2004

- posted by Gp @ 4:44 PM

LapLogic LapPads Review

- posted by Gp @ 4:24 PM

The New York Times > Technology > Nanotech Memory Chips Might Soon Be a Reality

- posted by Gp @ 4:23 PM

Leonardo Pisano --� Encyclop�dia Britannica

Leonardo Pisano --� Encyclop�dia Britannica

Life

Little is known about Leonardo's life beyond the few facts given in his mathematical writings. During Leonardo's boyhood his father, Guglielmo, a Pisan merchant, was appointed consul over the community of Pisan merchants in the North African port of Bugia (now Bejaïa, Alg.). Leonardo was sent to study calculation with an Arab master. He later went to Egypt, Syria, Greece, Sicily, and Provence, where he studied different numerical systems and methods of calculation.

When Leonardo's Liber abaci first appeared, Hindu-Arabic numerals were known to only a few European intellectuals through translations of the writings of the 9th-century Arab mathematician al-Khwarizmi. The first seven chapters dealt with the notation, explaining the principle of place value, by which the position of a figure determines whether it is a unit, 10, 100, and so forth, and demonstrating the use of the numerals in arithmetical operations. The techniques were then applied to such practical problems as profit margin, barter, money changing, conversion of weights and measures, partnerships, and interest. Most of the work was devoted to speculative mathematics—proportion (represented by such popular medieval techniques as the Rule of Three and the Rule of Five, which are rule-of-thumb methods of finding proportions), the Rule of False Position (a method by which a problem is worked out by a false assumption, then corrected by proportion), extraction of roots, and the properties of numbers, concluding with some geometry and algebra. In 1220 Leonardo produced a brief work, the Practica geometriae (“Practice of Geometry”), which included eight chapters of theorems based on Euclid's Elements and On Divisions.

The Liber abaci, which was widely copied and imitated, drew the attention of the Holy Roman emperor Frederick II. In the 1220s Leonardo was invited to appear before the emperor at Pisa, and there John of Palermo, a member of Frederick's scientific entourage, propounded a series of problems, three of which Leonardo presented in his books. The first two belonged to a favourite Arabic type, the indeterminate, which had been developed by the 3rd-century Greek mathematician Diophantus. This was an equation with two or more unknowns for which the solution must be in rational numbers (whole numbers or common fractions). The third problem was a third-degree equation (i.e., containing a cube), x3 + 2x2 + 10x = 20 (expressed in modern algebraic notation), which Leonardo solved by a trial-and-error method known as approximation; he arrived at the answer

in sexagesimal fractions (a fraction using the Babylonian number system that had a base of 60), which, when translated into modern decimals (1.3688081075), is correct to nine decimal places.
Contributions to number theory

For several years Leonardo corresponded with Frederick II and his scholars, exchanging problems with them. He dedicated his Liber quadratorum (1225; “Book of Square Numbers”) to Frederick. Devoted entirely to Diophantine equations of the second degree (i.e., containing squares), the Liber quadratorum is considered Leonardo's masterpiece. It is a systematically arranged collection of theorems, many invented by the author, who used his own proofs to work out general solutions. Probably his most creative work was in congruent numbers—numbers that give the same remainder when divided by a given number. He worked out an original solution for finding a number that, when added to or subtracted from a square number, leaves a square number. His statement that x2 + y2 and x2 - y2 could not both be squares was of great importance to the determination of the area of rational right triangles. Although the Liber abaci was more influential and broader in scope, the Liber quadratorum alone ranks Leonardo as the major contributor to number theory between Diophantus and the 17th-century French mathematician Pierre de Fermat.

Except for his role in spreading the use of the Hindu-Arabic numerals, Leonardo's contribution to mathematics has been largely overlooked. His name is known to modern mathematicians mainly because of the Fibonacci sequence (see below) derived from a problem in the Liber abaci:

A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?

The resulting number sequence, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 (Leonardo himself omitted the first term), in which each number is the sum of the two preceding numbers, is the first recursive number sequence (in which the relation between two or more successive terms can be expressed by a formula) known in Europe. Terms in the sequence were stated in a formula by the French-born mathematician Albert Girard in 1634: un + 2 = un + 1 + un, in which u represents the term and the subscript its rank in the sequence. The mathematician Robert Simson at the University of Glasgow in 1753 noted that, as the numbers increased in magnitude, the ratio between succeeding numbers approached the number a, the golden ratio, whose value is 1.6180 . . . , or (1 + Ö5)/2. In the 19th century the term Fibonacci sequence was coined by the French mathematician Edouard Lucas, and scientists began to discover such sequences in nature; for example, in the spirals of sunflower heads, in pine cones, in the regular descent (genealogy) of the male bee, in the related logarithmic (equiangular) spiral in snail shells, in the arrangement of leaf buds on a stem, and in animal horns.

- posted by Gp @ 12:48 AM

- posted by Gp @ 2:58 PM

Cluster Computing: Linux Taken to the Extreme

- posted by Gp @ 2:56 PM

Cluster Computing: Linux Taken to the Extreme

- posted by Gp @ 2:56 PM

Highly-parallel Integrated Virtual Environment

- posted by Gp @ 2:53 PM

Beowulf.Org The Beowulf Cluster Site

- posted by Gp @ 2:35 PM

Brads Publications

- posted by Gp @ 2:27 PM