- published: 30 Jun 2012
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Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria (e.g. "two counties over"). In mathematics, a distance function or metric is a generalization of the concept of physical distance. A metric is a function that behaves according to a specific set of rules, and provides a concrete way of describing what it means for elements of some space to be "close to" or "far away from" each other.
In most cases, "distance from A to B" is interchangeable with "distance between B and A".
In neutral geometry, the distance between (x1.) and (x2) is the length of the line segment between them:
In analytic geometry, the distance between two points of the xy-plane can be found using the distance formula. The distance between (x1, y1) and (x2, y2) is given by:
Similarly, given points (x1, y1, z1) and (x2, y2, z2) in three-space, the distance between them is:
These formulae are easily derived by constructing a right triangle with a leg on the hypotenuse of another (with the other leg orthogonal to the plane that contains the 1st triangle) and applying the Pythagorean theorem.
Jason Mraz ( /məˈræz/; born June 23, 1977 in Mechanicsville, Virginia) is an American singer-songwriter. Mraz released his debut album, Waiting for My Rocket to Come, which contained the hit single "The Remedy (I Won't Worry)", in 2002, but it was not until the release of his second album, Mr. A-Z, in 2005, that Mraz achieved major commercial success. The album peaked at number five on the Billboard 200 and sold over 100,000 copies in the US. In 2008, Mraz released his third studio album, We Sing. We Dance. We Steal Things. The album debuted at number three on the Billboard 200 and was a commercial success worldwide, peaking in the top ten of many international charts.
Mraz's international breakthrough came with the release of the single "I'm Yours" from the album We Sing. We Dance. We Steal Things. The single peaked at number six on the Billboard Hot 100, giving Mraz his first top ten single. The song was on the Hot 100 for 76 weeks, beating the previous record of 69 weeks held by LeAnn Rimes' "How Do I Live". The song was a huge commercial success in the US, receiving a 5x platinum certification from the RIAA for sales of over five million. The song was successful internationally, topping the charts in New Zealand and Norway and peaking in the top ten of multiple international charts.
Evan Mitchell Lowenstein and Jaron David Lowenstein (born March 18, 1974) are American musicians and identical twin brothers who performed as Evan and Jaron. Evan and Jaron have recorded three studio albums and charted three singles on the Pop Songs charts. The duo's highest-peaking single is "Crazy for This Girl," which peaked at #15 on the Billboard Hot 100 in 2000.
They began performing in the folk-pop genre in coffee houses in their hometown of Atlanta, Georgia. In 1994, their live album, Live at KaLo's Coffee House, was released, and drew some attention. After touring for a year, in 1996 they released a second independent album, Not from Concentrate and performed at the 1996 Atlanta Olympics. While touring they were noticed by Jimmy Buffett, who signed them to Island Records, the label on which they released We've Never Heard Of You, Either in 1998.
In 2000, the duo released Evan and Jaron for Columbia Records. The album included hit singles "Crazy for This Girl", "From My Head to My Heart", and "The Distance." At the height of their success, Evan started a family and the touring ceased. Their most recent album, Half Dozen, offered more of an Americana/country sound and included six songs as well as three additional bonus tracks.