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Monday's Programming Question

There is a sequence of numbers in mathematics that is sometimes known as the hailstone sequence. The German mathematician, Lothar Collatz, proposed that for any number it's possible to make...

If maths is boring what is the answer?

Mathematician Marcus du Sautoy has an imaginative formula to bring his subject alive in the classroom.

Sept. 23, 1846: Neptune Right Where They Said It Would Be

1846: German astronomer Johann Gottfried Galle, knowing exactly where to look, confirms the existence of an eighth planet in the solar system, Neptune. Galle was not the first astronomer to see Neptune -- Galileo, puzzled by the changing position of what he thought was a fixed star, had sketched the movement in 1613 but never published his findings. Others had seen it, too, but Galle, working at the Berlin Observatory, was the first to observe Neptune while understanding exactly what he was looking at. By the time Galle fixed his gaze upon Neptune, the existence of a planet beyond Uranus was widely predicted and its position had been intensely calculated. In fact, other astronomers were quarreling over who owned the priority of discovery. A Frenchman, Urbain Le Verrier, had worked out a complicated set of mathematical predictions based on anomalies in Uranus' orbit, and those, in fact, were what Galle was using when he spotted Neptune. Le Verrier had also taken care to make his predictions public. Meanwhile, the young British mathematician John Couch Adams, working independently, had reached similar conclusions, but confined himself to sharing the data with colleagues at Cambridge University. The key to their calculations was Uranus. Irregularities had been observed in the planet's orbit, irregularities that suggested possible gravitational interference by another heavenly body. French astronomer Alexis Bouvard first noted this in 1821, when he published observations of Uranus' orbit. By 1846, Le Verrier had not only completed his calculations for an eighth planet, but had determined its mass and orbital path. When his work was met with indifference by the French astronomical fraternity, Verrier sent his data to Galle in Berlin, who -- assisted by his student Heinrich Louis d'Arrest -- discovered Neptune that same night. Galle found Neptune less than 1 degree from the position Le Verrier predicted it would be. Adams was a gracious loser, giving full credit to Le Verrier for the information leading to Galle's discovery. Others in England, however, were less diplomatic, and in addition to some cross-Channel rancor, there was also criticism of those who could have been expected to act as Adams' mentors. A proposal by the suddenly interested Paris Observatory to call the new planet Le Verrier went nowhere, and the name Neptune was eventually selected. Source: Various Wired.com

Euler started the Sudoku craze? - Sure hope he doesn't expect royalities!!

"Tim Preston, publishing director of Puzzler Media, Britain's biggest seller of crossword and cryptogram puzzles in books, magazines and syndication, said Sudoku can be traced to the work of 18th century mathematician Leonhard Euler. The Basel, Switzerland, native, who spent much of his life serving the Russian court in St. Petersburg, enjoyed posing puzzles. His vast output included the Latin Square, arrangements of groups on numbers in grids that do not repeat vertically or horizontally. 'The thing about most puzzles,' Preston said, 'once you get inside them and you know how to do them, they can be quite addictive.'" Sure hope he doesn't - talk about a LOT Of interest on a 200 year payment!! Robert sudoku Sudoku

Science of Star Wars

In 1999, astrophysicist and mathematician Jeanne Cavelos wrote a book titled The Science of Star Wars: An Astrophysicist's Independent Examination of Space Travel, Aliens, Planets, and Robots as Portrayed in the Star Wars Films and Books. Timed with the release of The Clone Wars, Scientific American has posted excerpts from Cavelos's book, including bits about the power of the Death Star, light speed travel, and Darth Vader's bionics. From SciAm: The Death Star: Could It Destroy A Planet? The Death Star's planet-destroying weapon is said in the Star Wars Encyclopedia to be a super-laser. While a laser is basically just light, it is light that can be focused onto a precise spot and can have high, extremely concentrated power. Lasers can produce a steady beam for long periods, or they can produce a very intense beam in short pulses, occurring thousands or millions of times per second. The amplified light of lasers can also be very powerful. A series of pulses can drill through hard materials like titanium or diamond. A megawatt laser can burn a hole through a jet up to six miles away?though it needs to maintain contact with the aircraft for one to two seconds. In a 1998 test, MlRACL, a 2.2-megawatt laser, was able to hit a satellite in Earth orbit. MlRACL purposely did not destroy the satellite, since the test was designed merely to show that the laser could target and hit the satellite. But researchers say the laser could just as easily have melted it. Thus it seems the lasers we have today would be capable of doing many of the things we see in Star Wars. We could injure or kill people; we could burn structures or melt holes in walls; we could destroy targeted areas of spaceships, assuming we could keep a beam on them for long enough. The main difference between Star Wars lasers and ours is the size. While we can create lasers that emit extremely powerful energies, we need to pump great energies into them to make them work. That energy source takes space, which the Death Star, at least, provides. Science of Star Wars (SciAm), Buy Science of Star Wars (Amazon)...

Aug. 7, 1944: Harvard, IBM Dedicate Mark I Computer

1944: Harvard and IBM dedicate the Mark I computer. Also known as the IBM Automatic Sequence Controlled Calculator, or ASCC, the pioneering computer was notable for producing reliable results and its ability to run 24/7. Harvard electrical engineer Howard Aiken first dreamt up a large-scale calculator in 1937. He knew he needed a corporate partner and first courted Monroe Calculator Company, which turned him down. Aiken went back to the drawing board and came up with a proposal that convinced IBM, whose big product at the time was a punch-card processor. A big plus in the proposal was that it used so many existing IBM components in a new way. Clair Lake, Frank Hamilton and Benjamin Durfee finished the Harvard computer at Endicott, New York, in January 1943. They demonstrated it to the Harvard faculty members in December, and then took it apart, packed it up and shipped it off to Cambridge, where it was rebuilt in the basement of the physics lab. The Mark I was a monster: 55 feet long and 8 feet high. It weighed five tons and contained 760,000 components, including 3,000 rotating counter wheels and 1,400 rotary-dial switches, along with an assortment of shafts, clutches and electromagnetic relays, all linked together with 500 miles of wire. Its clickety-clack sounded like a "roomful of ladies knitting." You fed instructions in on paper tape, and loaded the data on punch cards. It could only perform operations in the precise linear order it received instructions. The tape could not run backward. The Mark I could handle 23-decimal-place numbers and perform addition, subtraction, multiplication and division. It was also programmed with subroutines for logarithms and trigonometry. It was slow, taking three to five seconds to do a multiplication. It gave you results through two outputs: teletypewriter and punch card. Mathematician Grace Hopper of the U.S. Naval Reserve joined Aiken's team at Harvard and was instrumental in keeping the Mark I running. She repaired it one day by removing a moth that had fouled the Mark I's electromechanical innards, becoming the first person to debug a computer. She then coined the term computer bug. When the time neared to dedicate the Mark I, in August 1944, the Harvard News Office put out a press release giving all the credit for the machine to Aiken. IBM chief Thomas J. Watson was himself so put out that his firm's work was not being acknowledged that he threatened to return to New York, boycotting the dedication and luncheon festivities. Cooler heads prevailed, and Watson stayed for the hoopla, but Aiken and Watson never got over their turf tiff. Years later, when Thomas J. Watson Jr. made a peace offering of a consultant gig at IBM, Aiken refused to sign a nondisclosure agreement. Hopper and Aiken (also USNR) used the Mark I to help the Navy produce tables for aiming artillery shells and bombs in the closing year of World War II. The electromagnetic machine remained in use until 1959, by which time it was left in the dust by true electronic computers using first vacuum tubes, then transistors, then chips. And for all of the Mark I's advances, German engineer Konrad Zuse's Z3 model from 1941 may have preceded it as the world's first fully functional, programmable computer. Aiken went on to build the Mark II in 1947, the same year he founded the Harvard Computation Laboratory and predicted, "Only six electronic digital computers would be required to satisfy the computing needs of the entire United States." Source: Various

Ancient clock displays Olympic calendar and astronomical cycles

The Antikythera Mechanism is a two-thousand year-old clock made in Greece that was discovered a century ago in a shipwreck. Two years ago, scientists studying the bits and pieces that survived under the sea were able to figure out that the device was used to calculate astronomical cycles. Now though, British mathematician Tony Freeth, part of the original research group, has determined that the Antikythera Mechanism also shows the timetables of the Olympic Games. Freeth and his colleagues published their findings in this week's issue of the science journal Nature. The magazine also posted a fascinating video telling the clock's story. It's a marvelous tale of technology, history, and curiosity. From Nature News: The device had intermeshed toothed wheels that represent calendar cycles. By turning the wheels, a user could figure out the relationships between astronomical cycles to deduce the relative positions of the Sun and Moon and forecast eclipses. But after two millennia under the sea off the island of Antikythera, near Crete, all that remains of the device are 82 fragments of flaking bronze, including parts of 30 gear-wheels2. The numbers of gear teeth are crucial, but must be inferred from the partial wheels that remain. And most of the inscriptions are hidden under corrosion and surface accretions. To read them, the researchers used a method called microfocus X-ray computed tomography, which provides X-ray images of slices through the sample, revealing inscriptions buried beneath the mechanism's surface. Antikythera Mechanism video "Complex clock combines calendars" Nature News article "Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism" paper...

Was ancient Greek 'calculator' used to teach astronomy?

Inscriptions on a 2000-year-old clockwork device suggest it was inspired by earlier devices made by the great Greek mathematician Archimedes