## Rulebook Specs for Home Plate are Impossible

*May 9, 2011 at 2:00 am* *Chad Upton* *
17 comments *

By Chad Upton | Editor

The earliest known reference to “baseball” comes from a 1744 British publication called, “A Little Pretty Pocket-Book” by John Newbery. At the time, the field was triangular and used poles instead of bases. This game was brought to America sometime before 1791, when the first American reference is found in a town bylaw for Pittsfield, Massachusetts.

Of course, the game has changed a lot since then. The infield is has gome from triangular to “diamond” (square) shaped. Home base was originally a round metal plate, which is why it is often called “home plate.” Home plate became a square shape in the 1870s, making it jus t like the rest of the bases.

The rear point of home plate sat at the intersection of the baselines from first and third bases. Although this point never changed, in the year 1900, home plated went from four sides to five.

The front of the base was squared in relation to the pitcher. This was done to make it easier for the pitcher to see the left and right edges of the base. When the base was a square, there was only a small point on each side, which was difficult to see and could easily be covered with dirt. Having a long edge rather than a small point also makes it easier for the umpire to see if the ball passes over the base and make an appropriate call.

The official Major League Baseball rulebook specifies the dimensions for home plate. They say it should be a 12 inch square with two corners filled in so one edge (facing the pitcher) is 17 inches. It also specifies that the two sides should be 8.5 inches. That sounds good on paper, but that is an impossible shape to create — according to Pythagorean theorem. If the 12 inch sides are supposed to be at a right angle to each other, then the hypotenuse would be 17 inches according to the rulebook. Mathematically, the hypotenuse would have to be 16.9 inches.

Some would say it’s a small difference, but it’s actually a large difference in modern day manufacturing tolerances. Either way, the point stands: nobody can create a home plate with the exact specifications set in the rulebook.

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Sources: MLB.com, wikipedia (baseball, home plate), MAA

Photo: JC Derr (cc / graphics overlaid)

Entry filed under: Sports. Tags: base, baseball, home, homebase, homeplate, math, pentagon, plate, pythagorean.

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1.Rachel | May 9, 2011 at 5:38 amHow is that shape impossible to create mathematically?

2.Chad Upton | May 9, 2011 at 7:51 amAccording to Pythagorean theorem, the hypotenuse would have to be 16.9 inches rather than the 17 inches specified in the rulebook.

3.rocco jibraltar | September 27, 2012 at 4:38 pm“according to the pythagorean theorem,” the square root of (8.5^2)*2 [or 72.25*2 or 144.5] is 12.02081528017131, so i’m guessing that they use the 17 inch front measurement as the standard, then take the two, 8.5 inch sides back at 45º angles, and finally bring the last two sides together at 135º angles, using a devil-be-hanged attitude on the ~.02081528017 inches difference in length.

just my 2¢.

4.rocco jibraltar | September 27, 2012 at 4:42 pmwhoops. sorry. the “45º” i mentioned, below, should have been “90º.” saw the mistake after entering, and i don’t see an ‘edit’ option.

5.Mark | October 29, 2017 at 8:18 pmFor a 12″ square the diagonal would be 16.97.

6.markus | May 30, 2014 at 6:32 pmDid you not even read it?

7.Kraig | May 9, 2011 at 4:57 pmIt’s probably because they didn’t have a strong sense of math back when they made the change, OR they just rounded up.

8.mridley1013 | April 16, 2012 at 11:58 amActually, if you read the MLB rule book, it says that the two 12 inch sides must come together to a point, but never says it must be a right angle. Therefore, the angle is actually slightly larger to adhere to the dimensions.

9.colin | April 19, 2012 at 6:43 pmit says square, and the definition of a square is four equal sides, meeting at four right angles . therefore, it must be at a right angle.

10.mridley1013 | April 19, 2012 at 9:35 pmActual definition:

1.05

Home base shall be marked by a five-sided slab of whitened rubber. It shall be a 17-inch square with two of the corners removed so that one edge is 17 inches long, two adjacent sides are 81/2 inches and the remaining two sides are 12 inches and set at an angle to make a point. It shall be set in the ground with the point at the intersection of the lines extending from home base to first base and to third base; with the 17-inch edge facing the pitchers plate, and the two 12-inch edges coinciding with the first and third base lines. The top edges of home base shall be beveled and the base shall be fixed in the ground level with the ground surface. (See drawing D in Diagram 2.)

11.colin | April 24, 2012 at 3:19 pmagain, it says square

12.mridley1013 | April 24, 2012 at 3:38 pmYes, the original shape is a square, so the two corners closest to the pitching mound are right angles, but it has two sides removed. The removal of these sides leave an angle slightly larger than 90 degrees.

13.Hahn | June 27, 2012 at 1:56 amIf you start with a 17-inch square and follow the directions, the two “12-inch” sides calculate as 12.02081… inches (about 21 thousandths of an inch or about 5 sheets of 80gsm copy paper) more that the “12-inch” specification which is insignificant in terms of the game.

An angle of 90 degrees is formed at their intersection.

The critical measurement is the original 17-inches as this determines whether the ball is in the strike zone.

14.Steve Nastasiuk | March 16, 2013 at 11:42 amThe above rule book excerpt says:”the two 12-inch edges coinciding with the first and third base lines”. Since the 1st and 3rd baselines are set at 90 degrees the angle at the “point” has to be 90 degrees. I intend to be taking measurements of several home plates and baseball fields in the near future. These shall eventually be incorporated into a blog post tentatively titled: “Home Plate Umpires Disprove Pythagorean Theorem at http://mathonthemckenzie.blogspot.com/

15.Troy | July 23, 2016 at 2:34 pmThe rules don’t specify the distance from the front of the plate to the apex. Though you begin with a 17 X 17 square, the removal of the corners does not specify that the intersection of the cut (the apex) be at the edge of the square.

Since the rules do specify that the edges be 17, 8.5, 8.5, 12 & 12, and that the 12″ sides form the base lines, and that the field is a square ( meaning that the resultant angle between the 12″ sides is by definition a right angle), that leaves the distance from the front of the plate to the point at 16.9706 inches.

16.s. Myshrall | June 5, 2017 at 4:26 pmWhat is the diff between the “apex”, and the rear of home plate ?

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