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Featured article: April 15, 2007

The first few thousand terms and partial sums of the series

In mathematics, 1 − 2 + 3 − 4 + · · · is the infinite series whose terms are the successive positive integers, given alternating signs. The series diverges, meaning that its sequence of partial sums (1, −1, 2, −2, …) does not tend towards any finite limit. Nonetheless, Leonhard Euler claimed that 1 − 2 + 3 − 4 + · · · = 14. Starting in 1890, Ernesto Cesàro, Émile Borel, and others investigated well-defined methods to assign generalized sums to divergent series – including new interpretations of Euler's attempts. Many of these summability methods assign to 1 − 2 + 3 − 4 + · · · a "sum" of 14 after all. Cesàro summation is one of the few methods that does not sum 1 − 2 + 3 − 4 + · · ·, so the series is an example where a slightly stronger method, such as Abel summation, is required. The series 1 − 2 + 3 − 4 + · · · is closely related to Grandi's series 1 − 1 + 1 − 1 + · · ·. Euler treated these two as special cases of 1 − 2n + 3n − 4n + · · · for arbitrary n, a line of research extending his work on the Basel problem and leading towards the functional equations of what we now know as the Dirichlet eta function and the Riemann zeta function. (more...)

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Featured picture: June 5, 2007

Bassoons

Two views of a Renard bassoon, a woodwind instrument in the double reed family that plays in the tenor range and below. The instrument is made of black maple, with silver-plated nickel silver keys.

The bassoon evolved from the dulcian. Although the process of evolution from its predecessor is unknown, the bassoon much as it appears in its current form appeared in a late 17th century painting, and a three-keyed bassoon has been dated to 1699. The modern bassoon exists in two distinct primary forms, the Buffet system and the Heckel system. The Buffet system is played primarily in France but also in Belgium and parts of Latin America, while the Heckel system is played in the majority of the world.

Photo credit: Gregory Maxwell

Featured list: List of Colorado Avalanche players

This is a complete list of ice hockey players who have played for the Colorado Avalanche in the National Hockey League (NHL). It includes players that have played at least one match, either in the NHL regular season or in the NHL playoffs. The Colorado Avalanche franchise was originally founded in Quebec, Canada with the name Quebec Nordiques. In 1995, the franchise moved to Denver, Colorado and since then 12 goaltenders and 141 skaters have wore its jersey. The Avalanche have won the Stanley Cup twice with a total of 41 players. Six of them were part of both Stanley Cup winning rosters.

Goaltenders

Patrick Roy, goalie for the Avalanche between 1995 and 2003 and two-time Stanley Cup winner
Patrick Roy, goalie for the Avalanche between 1995 and 2003 and two-time Stanley Cup winner
Nat Seasons Regular Season Playoffs SC winner
GP W P GAA SV% GP W P GAA SV%
Aebischer, David Flag of Switzerland 2000-2006 174 89 5 2.35 .917 13 6 0 2.07 .928 2001
Billington, Craig Flag of Canada 1996-1999 67 30 2 2.61 .912 3 0 0 4.00 .905
Budaj, Peter Flag of Slovakia 2005-2007 91 45 3 2.75 .903 3 0 0 4.00 .905
Denis, Marc Flag of Canada 1996-2000 28 10 2 2.55 .922

Skaters

Nat Pos Seasons Regular Season Playoffs SC winner
GP G A P PIM GP G A P PIM
Andreychuk, Dave Flag of Canada LW 1999-2000 14 1 2 3 2 17 3 2 5 18
Arnason, Tyler Flag of United States C 2006-2007 82 16 33 49 26
Aubin, Serge Flag of Canada C 1998-2000
2002-2003
82 6 7 13 70 22 0 1 1 10
Babenko, Yuri Flag of Russia C 2000-2001 3 0 0 0 0

Featured topic: Christ Illusion


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Featured article "Eyes of the Insane"

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