NBC's Lester Holt explores the path a defender must take in order to tackle a ball carrier, and how this distance - called the "angle of pursuit" - can be calculated by using the Pythagorean Theorem to find the hypotenuse of a right triangle, and the distance of a defender's angle of pursuit. "Science of NFL Football" is a 10-part video series funded by the National Science Foundation and produced in partnership with the National Football League.
Science of NFL Football - Pythagorean Theorem
LESTER HOLT, reporting:
It's one of the most exciting chases in the NFL -- a receiver or running back making a bee-line for the end zone, with the defender in hot pursuit.
HARDY NICKERSON (Former NFL Linebacker): You identify the ball carrier. From there you want to close the distance between yourself and the ball carrier as quickly as possible.
Dr. JOHN ZIEGERT (Clemson University): They have to choose what direction and speed to run so that they get to the same place at the same time as the runner and can make the tackle.
HOLT: In football, the path the defender must take to intercept the ball carrier is called the "angle of pursuit". According to John Ziegert, an automotive engineer at Clemson University, this path is also a perfect illustration of a fundamental equation in geometry called the Pythagorean Theorem, discovered by the Greek mathematician Pythagoras more than 1,700 years ago.
ZIEGERT: Pythagorean Theorem is a basic theorem in plane geometry or Euclidean geometry that relates the lengths of the sides of any triangle where one of the angles is 90 degrees, called a right triangle.
HOLT: On a right triangle, the two adjacent sides, A and B, are called the legs. The longer side opposite the right angle, C, is called the hypotenuse. The Pythagorean Theorem simply states A-squared plus B-squared equals C-squared.
ZIEGERT: The Pythagorean theorem, which says that the square of the hypotenuse, the length of the hypotenuse, is equal to the sum of the squares of the lengths of the other two sides.
HOLT: Relating this to football, let's say the ball carrier is heading for the end zone 40 yards away. The defender stands 30 yards away and needs to intercept him. If these two distances are the legs of a right triangle, then the distance the defender needs to run is the hypotenuse. Using the Pythagorean Theorem, 30 yards times 30 yards added to 40 yards times 40 yards will give the length of the hypotenuse squared. To get the actual length, take the square root.
ZIEGERT: Forty squared plus 30 squared is equal to 2,500, which is 50 squared. So the distance of the hypotenuse is 50 yards.
NICKERSON: You got to be precise in what you are doing and you have to take the right angles especially in coverage.
HOLT: NFL players must react instinctively to cover this distance - and also gauge how fast they need to run to match their opponent's speed.
ZIEGERT: The defender now, if he chooses that angle of pursuit, he says, "Okay, I've got to cover this distance in the same amount of time it takes the runner to cover this distance.”
NICKERSON: If you are chasing a fast guy like a Marshall Faulk or you know some of those guys that can really burn. You know if you take the wrong angle, you’re done.
HOLT: The defender's angle of pursuit can be the difference between a touchdown and a game-saving tackle. It's also a perfect illustration of the properties of a right triangle, and the ABC's of the Pythagorean Theorem.
The citizens of Athens were fed up with the old "wise" man.
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