(FORTUNE Magazine) – ''Why must we learn this stuff, and where are we ever going to use it?'' According to Alfred S. Posamentier, professor of mathematics education at New York's City College, that question endlessly haunts folks in his line of work. Posamentier complained in a letter to the New York Times the other day that the tyros he teaches do not understand the relevance of, say, the Pythagorean theorem, and fail to appreciate how their lives would be enriched if only they continually bore in mind that a squared + b squared = c squared (meaning that in a right triangle the square of the hypotenuse is equal to the sum of the squares of the other two legs). And yet somehow one senses that few City College students will be gripped by the prof's example of life enrichment. The letter cited his application of the Pythagorean theorem to a recent news event: that ''near miss'' of Reagan's helicopter by a private plane flying over Santa Barbara. The Times, Posamentier sternly reminded the editors, had said that the private plane came ''within 200 feet'' of the helicopter. Elsewhere, however, the paper's report indicated that this was the minimum horizontal distance separating the aircraft, and that the vertical distance was 150 feet. The letter triumphantly observed that the vertical and horizontal distances could be thought of as the legs of a right triangle, with the hypotenuse representing the actual distance between the plane and the helicopter. And since 150 squared + 200 squared works out to 62,500 (250 squared), the distance had to be at least 250 feet. But as we were saying, who cares? More meaningful to your average urban matriculator, one intuits, are certain Euclidean events occurring on a regular basis except when the race track is closed. Plane geometry is, in fact, enormously useful in horse handicapping, typically in calculations about how much farther thoroughbreds run when they go outside on the turn. If you think of the turn as a semicircle, then a horse who takes the turn eight feet from the rail covers about 19 feet more than one two feet from the rail (because the radii of their respective semicircles differ by pi, or 3.14, times six). Turf analysts also turn frequently to the Pythagorean theorem, or at least a fellow we know was invoking it recently in preparation for the Travers Stakes, run at Saratoga on August 22. This party was strongly predisposed toward Temperate Sil, a medium-priced horse (he went off at 5 to 1) with an outside post position. Since Temperate Sil was a notoriously fast starter, it was obvious to one and all that jockey Willie Shoemaker would try to get him to the rail before the first turn, which was 350 yards from the starting gate. Question, answerable only via the magic of plane geometry: How much farther would the horse have to run in order to get there? His position at the start was about 12 yards from the rail. If you think of that distance as the base of a right triangle, and the 350 yards to the turn as a second leg, then the steed's course is the square root of (350 squared + 12 squared), which works out to 350.21 yards -- only seven or eight inches more than a horse at the rail would be running. Viewing this difference as trivial, our friend bet big on the horse.

| Shoemaker got him to the rail, all right, but couldn't keep him in front, and he regrettably finished eighth in a field of nine. In selling the students on the everyday uses of plane geometry, it might pay to search out an example with a happier ending. The prof can find one in any old Racing Form.