Crane School Blog: Focus on Learning

Featuring articles written by Crane Staffulty

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Mathematical Endeavors
Richard Downey

In 1974, an SR-71 reconnaissance plane of the U.S. Air Force reached London a scant one hour and 54 minutes after leaving New York. I was inspired by the thought of such speed. Even the supersonic Concorde, celebrated for its astonishingly swift travel, took two and one-half hours.

In 1974, an SR-71 reconnaissance plane of the U.S. Air Force reached London a scant one hour and 54 minutes after leaving New York. I was inspired by the thought of such speed. Even the supersonic Concorde, celebrated for its astonishingly swift travel, took two and one-half hours.
 
Speed seems a simple concept at first. We are all familiar with miles per hour, a ratio of distance to time. However, speed makes sense only in relation to a point of reference. As you stride along the moving walkway at the airport, your speed in relation to the conveyor belt is different from your speed in relation to the tiled floor. Similarly, a boat sails at one speed in relation to the water, another compared to the shore, and yet another in relation to a passing yacht.
 
Distance can also be more challenging to measure than one might imagine. It may be gauged from a starting point, from a destination, or from any other location. Imagine the complexity of measuring the changing distances between points in motion. This was one piece in the puzzle of the interplanetary Cassini-Huygens mission, which parachuted a probe onto a moon of Saturn. The objective was to launch a spacecraft from Earth, which was rotating on its axis and revolving about the sun, and steer it to the moving target of Titan, which was orbiting Saturn as the ringed planet itself was continually changing its position relative to Earth.
 
Younger students who have yet to pilot a plane or drive a car may lack the intuitive feeling for speed and direction that can facilitate an understanding of relative motion. The traditional “Train A leaves the station at 9:00” problems that linger in our adult memories (or nightmares) offer at least an intellectual appreciation. They require students to identify essential components of distance, rate, and time, and then to assemble them into a mathematical model. Eventually, students suggest and test a tentative solution. I suspect that those who developed the mathematics essential to the success of Cassini-Huygens once embarked upon their own studies of motion in a similar fashion.
 
Some find mathematics a cold endeavor; others find it moving.
 
Richard Downey
Upper School Math Teacher

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