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[math-fun] Hexagon puzzle
by dasimov＠earthlink.net 16 May '05

16 May '05

Puzzle: Let T denote the torus obtained by identifying each pair of opposite edges of a regular hexagon. For which positive integers N is it possible to cut T into N congruent regular hexagons? --Dan

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[math-fun] polyomino shelving
by Thane Plambeck 15 May '05

15 May '05

Pretty expensive, but if you've always wanted restackable, modular Tetris shelving here is your chance. http://www.inhabitat.com/entry_23.php -- Thane Plambeck http://www.plambeck.org/ehome.htm

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[math-fun] Fermat divisor question
by David Wilson 15 May '05

15 May '05

It is believed that the set of n >= 0 such that the Fermat number F(n) = 2^2^n+1 is composite is cofinite. Do we even know if it is infinite? - David W. Wilson "Truth is just truth -- You can't have opinions about the truth." - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"

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[math-fun] Misogynist math
by David Wilson 15 May '05

15 May '05

Disclaimer: My 15-year-old son has developed a rather dim view of girls which may in part be a backlash against the "Girlz rule, boyz drool" garbage that's going around in schools these days. At any rate, he showed me the following proof that women are evil. Though, I question the conclusion, I had to chuckle at the derivation. My apologies if this is an old joke in new guise. Theorem: Women are evil. Proof: Women require time and money: [1] women = time x money. But time is money: [2] time = money. and so [3] women = money^2. Now money is the root of all evil, [4] money = sqrt(evil), and so we conclude [5] women = evil. QED - David W. Wilson "Truth is just truth -- You can't have opinions about the truth." - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"

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RE: [math-fun] Re: Lotto & fortune cookies, from today's NYT
by dasimov＠earthlink.net 14 May '05

14 May '05

Rich wrote: << Thane contributes: << By Jennifer 8. Lee ... [Jennifer 8 Lee is no typo. That's her middle name: "8"] >> Clearly, 8 is her middle initial. Her middle name could be 88 or 8765 or even 8tricia. >> Or 8rocious. Because she wrote an incredibly stupid article recently (about how there's a new trend: hetero males getting together in a group of two in order to socialize!!!!!), I looked up some stuff about her, and she explains her adopting the 8. to distinguish herself from the many other Jennifer Lees. (And 8 because her background is Chinese and, she says, 8 is a very lucky number in Chinese culture.) So what do you call an "initial" that doesn't stand for anything? (Btw, such were once quite common in U.S. male given names.) --Dan

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Re: [math-fun] Waterman Polyhedra
by dasimov＠earthlink.net 13 May '05

13 May '05

I found the Moire effects of the radial coloring of the root 1001 and 3001 configurations (page 3) especially beautiful -- *and*, it reminds me of a computer graphics experiment I tried about 25 years ago: 1. Create a color table, from 0 to N-1, by using N (N large) consecutive colors equally spaced around a circular rainbow (e.g., follow the circle inscribed in the hexagon that bisects the RGB cube halfway between black (0 0 0) and white (1 1 1)). 2. Now on a preferably high-ish resolution screen whose pixels are indexed by (K,L) for 1 <= K <= xmax, 1 <= L <= ymax, color (K,L) with the color whose number is (K^2 + L^2) mod N. I'm sure many other people have also tried this experiment. I don't think I ever learned exactly why I got the Moire pattern that resulted, not dissimilar from Bourke's 1001 and 3001 configurations with radial coloring. --Dan

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[math-fun] Waterman Polyhedra
by David Wilson 13 May '05

13 May '05

The Waterman polyhedra are apparently the convex hulls of the centers of spheres in the fruitstand packing that lie within a fixed radius of a fixed point. For large distances, they closely approximate spheres. The original image is very large, and the lacework of polyhedron edges is clearly visible at full size. I have reduced it to a 1024x768 wallpaper, in which the polyhedral faces are not distinguishable, the overall impression is of a spherical fractal with with a network of great circles emphasized. http://astronomy.swin.edu.au/~pbourke/polyhedra/waterman/index.html - David W. Wilson "Truth is just truth -- You can't have opinions about the truth." - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"

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[math-fun] Math Matters II: LATimes: Glitch Trips Up Lottery's Derby
by Henry Baker 13 May '05

13 May '05

FYI -- http://www.latimes.com/news/local/la-me-derby13may13.story Glitch Trips Up Lottery's Derby Officials discover a programming error after a player questions lack of repeat numbers. By Nancy Vogel, Times Staff Writer SACRAMENTO Â Dave Andres, an insurance underwriter from Altadena, thought he alone was in the habit of scanning hundreds of winning numbers in the lottery's least-popular game, Daily Derby. He assumed no one else noticed that for 100 days running this winter, none of the winning times in the horse race-themed game had numbers that were repeated. He knew that players had to not only pick the right horses but also the last three digits of the winner's finishing time. And he saw that those numbers were always like 3.70 and 4.23, and never 1.33 or 4.24 Â even though the statistical probability is that duplicate numbers should appear 27% of the time. But Andres was not alone. An equally sharp-eyed Walnut man who noticed the same aberration described it in a letter to lottery officials last month. That led to the discovery of a computer software glitch that had denied 650 players a chance to win the game's grand prize over six months. "To whom it may concern. Something's been nagging me about the outcome of the last 150 or so Daily Derby race time draw results," began the handwritten April 18 letter from a man lottery officials refused to identify and can reach only by mail. California lottery officials quickly investigated, eager to plug any breach in the integrity of a state-sanctioned enterprise that last year saw a record $2.9 billion in sales. The problem was fixed last week. "This was taken seriously immediately," said California Lottery Director Chon Gutierrez. "It went from the marketing people to our security people, and they came up to us late on [April 29] and they said, 'We've looked at it and think there's a lot of merit to it.' " As a mea culpa to players, officials plan to take about $250,000 from their advertising budget and boost prizes in the Daily Derby game over the next couple of weeks. Gutierrez said the lottery from May 18 to June 1 would triple the race time prizes and augment the grand prize to roughly $300,000. Officials also plan to send the Walnut letter writer a thank-you gift. "This guy identified a real problem for us," Gutierrez said. There are two ways to win the $2 Daily Derby. Players can pick the top three horses in each race or pick the correct time it takes for a horse to win. Getting it all right nets a player the grand prize, which averaged $300,000 over the six months of the computer glitch and now stands at roughly $100,000. California lottery officials traced the problem to November, when a contractor was replacing the 7-year-old computer hardware and software that draws the winning numbers each day. The programmer inadvertently copied a line of software code that kept horses from appearing in more than one winning spot per race. The code guarantees that horse No. 8, for example, doesn't win both first and second place. But when the code was mistakenly applied to the race time, it blocked the computer from picking any number that repeated. "Now what I'd really like from you guys is a probability figure on this bizarre streak we've been getting for the last 159 Daily Derby race time draws," wrote the Walnut man. Andres, who didn't alert lottery officials to his discovery, said, "I just didn't think anybody else would be out there wasting their time with stuff like that." News of the glitch, Gutierrez said, has hurt lottery worker morale, especially in the unit that oversees the drawing of numbers. "They're just morose," he said. "They don't know what to say." The problem took just a few minutes to fix. Rebuilding the trust of Daily Derby fans may take more time. Though it generates only $200,000 of the lottery's $62 million in sales each week, lottery officials say its players are unusually loyal. >From November through April when the software problem existed, 650 of the 2,349 people who won the trifecta by picking the top three horses in the correct order had no chance of winning the grand prize because they picked a race time with a number that repeated. California lottery officials said they did not know how many people had no chance to win the average prize of $50 for picking the race time alone. Because it is a parimutuel game, all prizes are based on how many people play. Officials are trying to determine the names of the players affected Â they already know the time and place each player bought a ticket Â and are also reviewing other lottery games for software problems. The Daily Derby trouble comes as the California lottery is preparing to join an interstate jackpot game called Mega Millions, a move aimed at boosting jackpots and the roughly $1 billion each year that the lottery generates for California public schools. "The honesty and the integrity of the lottery is paramount to us," Gutierrez said. "Without it there can be no successful lottery. Whenever issues surface involving questions of integrity, they are dealt with instantly, aggressively and thoroughly. That was done in this case." Gutierrez said he hoped the situation did not lead to lawsuits. "We are dealing with this programming error in a forthright and direct fashion," Gutierrez said. "If litigation arises, we will deal with it appropriately. We believe we are treating our players fairly." This isn't the first time the lottery has tried to make amends with players. In 2002, embarrassed by revelations that 11 of its 137 popular Scratchers games had continued after all grand prizes had been awarded, the lottery took $2 million from its administrative budget to give away $1 million in prizes. The prizes were awarded randomly through a one-time contest that allowed anyone to enter by mailing their name, address and phone number to the lottery. Lottery officials said they did not know about the Scratchers problem until players filed a lawsuit. Andres, who plays the Daily Derby occasionally but prefers the Daily 3, said there was not much else the lottery could do. "It was clearly just a mistake," he said. "It seems like they're doing something to make amends." Like lottery officials, Andres said the computer glitch hurt some players but helped others. It improved the odds of winning for those players who picked race times with numbers that didn't repeat. Their odds of picking the race time correctly dropped from 1 in 1,000 to 1 in 720. Andres was one such player. "When I became convinced it was busted," he said, "I didn't use the duplicative approach." Still, he didn't win. After 10 years of playing, his biggest lottery win was $666 last year on Daily 3. "I'm not so good with numbers," Andres said, "it's just that after a while you look for patterns."

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[math-fun] Re: Lotto & fortune cookies, from today's NYT
by Schroeppel, Richard 12 May '05

12 May '05

Thane contributes ... >> By Jennifer 8. Lee >> ... > > [Jennifer 8 Lee is no typo. That's her middle name: "8"] Clearly, 8 is her middle initial. Her middle name could be 88 or 8765 or even 8tricia. Rich

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[math-fun] Nested polyhedral puzzle
by Daniel Asimov 11 May '05

11 May '05

A retired physicist named Wayne Daniel has created a 3D puzzle in the shape of an icosahedron, that -- as you peel off some of its pieces -- can become a dodecahedron, then an octahedron, then a cube, then a tetrahedron (all regular). See <http://www.nytimes.com/2005/05/10/science/10puzz.html>. (The article is available free through May 16; it requires signing up with your e-address and a password of your choice; you will not get any e-mail as a result, as long as you check that preference.) In hand-scuptured specialty woods, one of these puzzles is a mere $400. (So I'm hoping that Thane -- as a nice gesture -- will spring for one copy for each old-time math-funner. Just an idea. . .) --Dan

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