Because I "interact" with a lot of baseball-related social media posts, my feeds fill with the questions, observations, and provocations of other fans. Recently, I saw someone wonder about the distance between the pitching rubber and first base. The question aroused in my nerdy soul a memory from junior high, when I realized in math class one day that this "Pythagorean Theorem" could answer a question I'd wondered about—namely, whether the pitching rubber is closer to home plate or second base. I knew that it was 60 feet, 6 inches from the rubber to the plate and 90 feet between consecutive bases. Now I was practically being directed to notice that, according to Pythagoras, the distance from the plate to second base was the product of 90 feet and the square root of 2: that's 127.28 feet or, rounding to the nearest inch, 127 feet, 3 inches. So the pitcher throws from a point that's more than 6 feet closer to the plate than it is to second base. The math contradicted my impression from watching on TV, where the ubiquitous zoomed-in view from the centerfield camera has a foreshortening effect.

The question about the distance from the rubber to first base elicited in the answers a lot of error, and I suspect that the source for the correct answers was usually not math but Google. A couple people mentioned the Law of Cosines, which works, but to me it seems simpler just to consider another right triangle: one leg goes from first base to the point where the diamond's diagonals intersect (the "center" of the diamond), the other leg goes from the diamond's center to the point in the middle of the pitching rubber that's 60.5 feet from home plate, and the hypotenuse connects that point on the rubber to first base. The first leg is half of 127.28 feet: 63.64 feet. The second leg is 63.64 less 60.5 equals 3.14 feet. So the hypotenuse, which is the distance from the rubber to first base, is the square root of the sums of the squares of 63.64 and 3.14, and that turns out to be [drum roll, pressing buttons on calculator] 63.72 feet, or, if you prefer, essentially 63 feet, 9 inches.

To cavilers, yes, the world in which people play baseball is not the world of Euclid, where instead of having things that take up space, like bases and pitching rubbers, there are "points." When talking about "the distance between the rubber and first base," then, you have to make choices about what *points* to use. Another way of describing the above solution to the problem would be to say that in a triangle in which a side measuring 60.5 feet forms a 45-degree angle with a side measuring 90 feet, the length of the third side, to the nearest inch, is 63 feet, 9 inches.

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