Mojo
02-18-07, 06:56 PM
Alexander Yee likes big numbers. Yee, a Palo Alto High School alumnus and freshman at Northwestern University, broke the world record for calculating digits of the Euler-Mascheroni constant in December 2006 using his laptop and an original computer program. Yee first began working on his program in his AP Java Class at Paly, where one homework assignment required a program that could add, subtract, multiply and divide very big numbers. After the class, he continued working on the program, which he has temporarily named the "Big Number Java Library."
http://voice.paly.net/media/images/2007-02-12-this-one-dammit.jpg
"Around October 2006, I realized that I could top the world record, so it became a top priority, over my homework, over my grades," Yee said. "I figured that if I didn't break it now, someone would break it later. 116 million isn't that much more than 108 million after all."
Yee's current program can not only add, subtract, multiply and divide numbers with millions of digits, but can also calculate radicals, trigonometric and inverse functions, factorials and normal distribution to millions of digits. Yee then specified his program to calculate the Euler-Mascheroni Constant.
The Euler-Mascheroni constant '' is the limit as 'n' approaches infinity of the difference between the harmonic series and the natural log of 'n.' Yee recently calculated 116, 580, 041 digits using algorithms he obtained online.Yee said he fiddled with his program until its speed was unparalleled. The difficulty lay not in using the algorithm, but in using it efficiently. With more speed, Yee could have calculated even greater than 116,000,000 digits, but he was eager to break the world record.
"My program is very fast, but it is not optimized," Yee said. "I can see a few places to improve it to make it ten times faster, but I'm done with it. I already broke the world record."
Yee couldn't find the 108,000,000 digits found formerly by Gourdon and P. Demichel, and thus could not compare his results with theirs. To verify his own results, he calculated the constant to 16,000,000 digits twice using two completely separate algorithms.
"You can't just compute the digits, because you don't know if they're right," Yee said. "For example, Mascheroni calculated 32 digits but he only got the first 19 right."
Yee's calculation took 38 and a half hours. The verification, using a slower algorithm, took 48 hours. The digits are now available online at http://euler.isozilla.com. Yee said that he feels his world record is now complete, as it has been posted on Mathworld, the Internet's leading mathematics reference resource.
"The guy at Mathworld said that he would try to verify it, so if they put it up, it means that either they verified it, or they concluded that I'm correct," Yee said.
According to Ed Pegg Jr., a Mathworld employee, the addition of Yee's claim does not mean that Mathworld has verified it or completely backed Yee's calculations.
"Actually, if it's non-controversial and a believable source, we'll usually add it to the encyclopedia," Pegg said of adding Yee's calculations to Mathworld.
However, Yee is sure his calculations are correct.
"If anything goes wrong, the two separate calculations won't match at the end," Yee said. "If they do, there is a 100 percent chance that it is correct."
Yee is now concentrating on the value of his program itself. He said that he hopes to improve the speed of his program.
If his program is truly novel, Yee said he is considering a patent, although another option would be to sell it to Sun Microsystems.
Meanwhile, he's already thinking about his future.
"It's a world record; why shouldn't I try to break it?" Yee said. "But it also looks good on my resume."
tartar source (http://voice.paly.net/view_story.php?id=5059)
http://voice.paly.net/media/images/2007-02-12-this-one-dammit.jpg
"Around October 2006, I realized that I could top the world record, so it became a top priority, over my homework, over my grades," Yee said. "I figured that if I didn't break it now, someone would break it later. 116 million isn't that much more than 108 million after all."
Yee's current program can not only add, subtract, multiply and divide numbers with millions of digits, but can also calculate radicals, trigonometric and inverse functions, factorials and normal distribution to millions of digits. Yee then specified his program to calculate the Euler-Mascheroni Constant.
The Euler-Mascheroni constant '' is the limit as 'n' approaches infinity of the difference between the harmonic series and the natural log of 'n.' Yee recently calculated 116, 580, 041 digits using algorithms he obtained online.Yee said he fiddled with his program until its speed was unparalleled. The difficulty lay not in using the algorithm, but in using it efficiently. With more speed, Yee could have calculated even greater than 116,000,000 digits, but he was eager to break the world record.
"My program is very fast, but it is not optimized," Yee said. "I can see a few places to improve it to make it ten times faster, but I'm done with it. I already broke the world record."
Yee couldn't find the 108,000,000 digits found formerly by Gourdon and P. Demichel, and thus could not compare his results with theirs. To verify his own results, he calculated the constant to 16,000,000 digits twice using two completely separate algorithms.
"You can't just compute the digits, because you don't know if they're right," Yee said. "For example, Mascheroni calculated 32 digits but he only got the first 19 right."
Yee's calculation took 38 and a half hours. The verification, using a slower algorithm, took 48 hours. The digits are now available online at http://euler.isozilla.com. Yee said that he feels his world record is now complete, as it has been posted on Mathworld, the Internet's leading mathematics reference resource.
"The guy at Mathworld said that he would try to verify it, so if they put it up, it means that either they verified it, or they concluded that I'm correct," Yee said.
According to Ed Pegg Jr., a Mathworld employee, the addition of Yee's claim does not mean that Mathworld has verified it or completely backed Yee's calculations.
"Actually, if it's non-controversial and a believable source, we'll usually add it to the encyclopedia," Pegg said of adding Yee's calculations to Mathworld.
However, Yee is sure his calculations are correct.
"If anything goes wrong, the two separate calculations won't match at the end," Yee said. "If they do, there is a 100 percent chance that it is correct."
Yee is now concentrating on the value of his program itself. He said that he hopes to improve the speed of his program.
If his program is truly novel, Yee said he is considering a patent, although another option would be to sell it to Sun Microsystems.
Meanwhile, he's already thinking about his future.
"It's a world record; why shouldn't I try to break it?" Yee said. "But it also looks good on my resume."
tartar source (http://voice.paly.net/view_story.php?id=5059)