Home base in baseball is a five-sided shape. Rule 2.02 in MLB’s handbook precisely defines how to construct the shape.

Home plate is made as a 17 inch square with two corners removed. The top edge is 17 inches, and its two adjacent sides are 8.5 inches. The remaining two sides are defined to be 12 inches each and they meet at a right angle.

But there’s something wrong with this figure. It’s mathematically impossible!

Can you figure out why? Let’s assume that all angles and the dimensions of 17 and 8.5 are correct. What should be the length of the remaining two sides? Can you figure it out?

Watch the video for a solution.

Baseball’s Home Plate Is Impossible Mathematically

Or keep reading.

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"All will be well if you use your mind for your decisions, and mind only your decisions." Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon. .

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Answer To Baseball’s Home Plate Is Impossible Mathematically

Let’s connect the two points that are opposite the sloping lines. This side has a length of 17 inches, and it divides home plate into an upper rectangle and a lower isosceles right triangle.

The isosceles right triangle has a hypotenuse of 17 inches. If each leg of the triangle has a length x, then by the Pythagorean Theorem the sum of the squares of the legs has to be the square of the hypotenuse.

x2 + x2 = 172

2x2 = 172

x2 = 172/2

x = 17/√2 ≈ 12.02 inches

Technically the sloping sides should be slightly longer than 12 inches!

While the error is quite small, baseball is a game of inches. Maybe the next iteration of the rulebook can include the language the sides should be “approximately 12 inches” to be completely mathematically correct.

But this rule for home plate has been in the books since 1900. So it stands to reason baseball will continue with this tradition, even if it’s slightly mathematically incorrect.

Sources

Rule 2.02 in 2017 MLB handbook

http://mlb.mlb.com/mlb/downloads/y2016/official_baseball_rules.pdf

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 8½ 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 pitcher’s 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 Appendix 2.)

*Note: drawing D in Appendix 2 indicates the 12 inch sides span a right angle of 90 degrees.

MLB Field Dimensions

http://m.mlb.com/glossary/rules/field-dimensions

Home plate is a 17-inch square of whitened rubber with two of the corners removed so that one edge is 17 inches long, two adjacent sides are 8 1/2 inches each and the remaining two sides are 12 inches each and set at an angle to make a point. The 17-inch side faces the pitcher’s plate, and the two 12-inch edges coincide with the first- and third-base lines. The back tip of home plate must be 127 feet, 3 and 3/8 inches away from second base.

Now I know

http://nowiknow.com/why-every-baseball-game-breaks-the-rules/

Via NY Post

http://nypost.com/2016/10/05/americas-pastime-is-based-on-impossible-math/

MathWorld

http://mathworld.wolfram.com/HomePlate.html

Math on the McKenzie

http://mathonthemckenzie.blogspot.com/2013/05/pythagorean-geometry-confounds-home.html

The Mathematical Tourist

http://mathtourist.blogspot.com/2010/06/pythagoras-at-plate.html