From Quito, trace a longitude line to the north pole then make a 90-degree turn to the right and head straight back down. First, let's pick a city on the equator-for simplicity, say it's Quito, Ecuador, on the Pacific coast of South America. You can see this distinction if you draw a right triangle on a globe. On spheres and other shapes, it may not be. In fact, it is only the shortest one on football fields and other flat surfaces.
If the points on the triangle were places to visit in a city, you probably wouldn't bother walking along a and b if you could directly take c.īut the hypotenuse isn't always the shortest route. The "c" is the hypotenuse, and although it represents the longest side of a right triangle, it is the shortest path between the two points on either end. Greek mathematician Pythagoras, as a² + b² = c². You might know this relation, discovered by the 5th-century B.C. In chasing down the ball-carrier, the defender basically runs along the diagonal of a right triangle, in which the sum of the squares of the sides equals the square of that diagonal. In the Pythagorean theorem episode of NBC Learn's "The Science of NFL Football," you see that a defender in the middle of the field must take the proper angle of pursuit to catch a ball-carrier making a dash down the sideline for the end zone.
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