Baseball is played on a field of geometric regularity. The baseball "diamond," for instance, is properly a square, 30 yards on each side.

Official league rules also specify the size and shape of home plate:

*Home base shall be marked by a five-sided slab of whitened rubber. It shall be a 12-inch square with two of the corners filled in so that one edge is 17 inches long, two are 8 1/2 inches and two are 12 inches.*But something isn't quite right. The diagram implies the existence of a right triangle with sides 12, 12, and 17. If it were truly a right triangle, the Pythagorean theorem would hold, and 12

^{2}+ 12^{2}would be the same as 17^{2}. It's not: 12^{2}+ 12^{2}= 288 and 17^{2}= 289.So, the dimensions of home plate (an irregular pentagon) are not mathematically correct.

But there's a difference between measured numbers (accurate to a certain number of significant digits) and purely mathematical numbers. To the degree of accuracy required to construct a workable home plate, 17 is as good as (and certainly more measurable than) the more exact value of 12 times the square root of 2.

The history of baseball sheds some light on how the dimensions of home plate came about.

The playing field has been the same shape and size since the rules of baseball were first published more than 140 years ago. The size, placement, and shape of the bases, however, have changed over the years.

Initially, the rules insisted that bases be 1 square foot in area (most simply, a 1 foot by 1 foot square). Out on the field, the center of each base sat directly over a corner of the infield square. Home plate started as a circular iron plate, painted white, with a diameter not less than 9 inches. By the 1870s, however, home plate had become a square just like the other bases.

In 1877, the width of the bases was increased to 15 inches but home plate stayed at 12 inches. First and third base were moved to their present positions, where they fit snugly inside the corners of the square that defines the infield. This change was made so that umpires could call foul balls more easily. Second base, however, still stuck out of the square, where it remains to this day.

The year 1900 saw the introduction of the five-sided home plate, with a flat side rather than a point facing the pitcher. The extra rubber made it easier for both umpires and pitchers to judge when a ball "cut the corner," especially when dirt happened to cover the corners of home plate.

*Original version posted March 25, 1996.*

*Updated July 12, 2004; June 30, 2010.*

**References**:

Bradley, M.J. 1996. Building home plate: Field of dreams of reality.

*Mathematics Magazine*69 (February): 44-45.Kreutzer, P., and T. Kerley. 1990.

*Little League's Official How-to-Play Baseball Book*. New York: Doubleday.Peterson, I. 2002. Pythagoras plays ball. In

*Mathematical Treks: From Surreal Numbers to Magic Circles*. Mathematical Association of America.Thorp, J., and P. Palmer, eds. 1995.

*Total Baseball*, 4th ed. New York: Viking.