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Calculating By Hand

10.15.03

Mathematics and science are two subjects that often require computers and calculators. With the press of a button, complex problems are solved. But, it wasn't always that fast or easy. When NASA was developing the Saturn V rocket, many of the calculations were done by hand.

Calculators and computers have been around for half a century. However, only in the last 20 years has their use become widespread. In the past, engineers used a slide rule. Slide rules are used to solve multiplication, division, and trigonometry problems. Commonly used functions were listed on a table or chart to save repetition and to reduce the chance of error. These functions are now available within a computer or a calculator.

Computers have been used for years. In the past, a user would enter information on data cards.These data cards were put into an electronic reader. The results were then printed out on special dot-matrix green-striped paper.

Larry Mullins is an aerospace engineer at NASA's Marshall Space Flight Center in Alabama. He remembers 40 years ago when there were rooms full of people using calculators. They would spend up to 3 months calculating a single trajectory for a launch. Every calculation was checked, and then checked again for errors. Today, the trajectory sequence can be laid out in minutes using a computer.

NASA's space program relies heavily on computers. Automated systems can work thousands of times faster than humans and without error. Computers are also used for long-range weather forecasting. In the medical field, computer images are used to map the progression of disease and to prepare the best treatments.

Computers and calculators make solving mathematics problems faster, but they do not change the basics. "One plus one is still two," Mullins says. It is important for students to learn the basic concepts of mathematics. This would include memorizing multiplication and division tables. Computers aren't smart. They are just robots that do what we tell them.

Mathematics really isn't difficult, says Mullins. It's the attitude you bring to the work that makes the difference. "If you feel you can't do it, then it will be hard, but basic arithmetic is conceptually simple. Algebra is a fascinating series of puzzles and brainteasers. Once you learn the concepts, you instruct the computers, and they speed up the calculations to help you get the work done faster."