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Anyone who has taken a high school geometry class has at least a dim recollection of the number called pi. But in his new book The Golden Ratio, author Mario Livio examines the mysteries of pi's lesser-known cousin, phi -- a number that has both counfounded and amazed mathematicians since antiquity.

European and Russian space officials meet next week to discuss how to pay for Russian flights carrying critical supplies to the International Space Station. With NASA's shuttle fleet grounded, Russia now bears a greater role in keeping the station afloat. NPR's Eric Niiler reports on the imperfect international partnership now playing a crucial role in the space station's survival.

In his first briefing since the war began, Gen. Tommy Franks, commander of U.S. forces, says American and British troops are pushing rapidly into Iraq. He says thousands of Iraqi soldiers have surrendered or deserted and negotiations with Iraqi officials are ongoing. NPR's Jennifer Ludden reports.

Mark Woollen and Michael Greenfeld are both in the business of creating film trailers – the two-and-a half minute edited teasers that promote upcoming feature films. Woollen is the founder of Mark Woollen and Associates and their recent movie trailers include About Schmidt, Pianist, Antwone Fisher and The Ring. Greenfeld is partner and co-CEO of Antfarm. Recent Antfarm campaigns include Chicago, Lord of the Rings, The Two Towers, Catch Me If You Can and Harry Potter and The Chamber of Secrets. The Golden Trailers Awards were held last week.

U.S. expedition forces sweep across Kuwait's border into southern Iraq, preparing the battlefield for larger assaults. Airstrikes continue in Baghdad as the U.S. military tries to take out key Iraqi defenses there. NPR's Jennifer Ludden reports.

NPR's Tom Goldman, Cheryl Corley and David Molpus report from around the country on reaction to President Bush's speech Monday night, and the seemingly imminent war.

President Bush gives Saddam Hussein and his sons 48 hours to leave Iraq or face "the full force and might" of the American military "at a time of our choosing." In a prime-time address to the nation, Mr. Bush says: "The United Nations Security Council has not lived up to its responsibilities. So we will rise to ours." Hear NPR coverage and analysis.

In the first U.S. combat death, a U.S. Marine is killed in southern Iraq. Earlier, four U.S. Marines and eight British soldiers are killed in the accidental crash of a U.S. helicopter near the Kuwait-Iraq border. Hear NPR's John Burnett.

U.S. and British military forces take control of portions of southern Iraq, but Pentagon officials say their main attack on the country has yet to begin. U.S. Marines say they have encountered only light resistance. Hear NPR's Steve Inskeep and NPR's Eric Westervelt.

The first single from Surrender is a chunky-boot strut through a floral pop fantasia.