Articles, Blog

Baseball’s Home Plate Is IMPOSSIBLE Mathematically

Baseball’s Home Plate Is IMPOSSIBLE Mathematically

Hey, this is Presh Talwalkar Baseball is a game of traditions and rules. Rule 2.02 two of the MLB handbook carefully defines home plate by the following geometric construction. The home base is defined as a square where one side is 17 inches. Two corners are removed. The two adjacent sides measure 8 and 1/2 inches and the remaining two sides measure 12 inches and meet at a right angle. There’s only one problem with this very carefully defined construction It’s an impossible shape mathematically. This creates an interesting geometric little puzzle. If we were to say the dimensions of 17 inches and 8 and 1/2 inches as well as the following right angles are correct, what would be the correct measure of the remaining sides? That is, can you solve for the correct value of x to make home-plate geometrically possible? Can you figure it out? Give this problem a try and when you’re ready to keep watching the video for the solution. So how can we solve for the correct value of x? Will divide the shape into two different shapes. We’ll draw a line connecting the two sides of 8 and 1/2 inches. This creates an upper rectangle and a lower isosceles right triangle. Because the upper shape is a rectangle we know that this length will be 17 inches. Now we can focus on the isosceles right triangle. By the Pythagorean theorem x squared plus x squared is equal to 17 squared. This means 2x squared is equal to 17 squared, which means x squared is equal to 17 squared divided by 2. And so x is equal to 17 divided by the square root of 2, which is approximately 12.02, which is slightly larger than the 12 inches that’s defined in the handbook. If MLB wanted to be mathematically correct, it could say in the next iteration of its handbook that the two remaining sides should measure about 12 inches. Did you figure it out? Thanks for watching this video. Please subscribe to my channel I make videos on math. You can catch me on my blog Mind Your Decisions which you can follow on Facebook, Google+ and Patreon. You can catch me on social media @preshtalwalkar, and if you like this video please check out my books. There are links in the video description.


Been playing baseball since I was 5 (21 now) and never really thought about the math behind home plate! Always fun to learn more about the sport that has made up such a big part of my life.

I figured it out by the 45 45 90 triangle, each side is x, then hypo is x sqrt(2), which is equal to 17"

Took me all of 3 seconds to realize that the sides of the part cut away was 8.5, 8.5, and by identity, the length must be 8.5xsqrt(2)

2 other possibilities 1.a rectangle 16.973 × 8.5 and a isoscele triangle with 12"× 12" × 16.973" neing square and width and length bieng of.027 of a inch small, which is like disecting a fine hair. Or 2 being out of squarre on each side where the two 12 inch sides of the Isosceles tringle meets the long end of rectangle bieng out of square .054" on each side.

You can calculate this also byusibg the triangle that was cut out. Its side is 8.5 inches so the hypotenusa is 8.5 * sqrt(2).

The difference is about half a millimeter so so the error is within measuring tolerances

If they use metric system like the rest of the world won't be approximate but it will all be exact to a mm

Its simple. The answer is 12.02 so what is your problem. Most people would round down especially since .02 inches is only half a millimeter You try distinguish half a millimeter when cutting anything thicker than paper

You don't really need a calculator to show this. It's enough to show that sqrt(12^2+12^12)=12*sqrt(2), which cannot be simplified to 17. Assuming that the rules are interpreted correctly, but I don't even know what a "base" is.

I used the triangel that was cut off. sides need to be 8.5 ( 17 – 8.5 and 17 split in two for the corner ) Than a² + b² = c²
now i'm happy that for once I could work a question without extra help.

Lengths given in anything except metres are only ever approximate anyway ….. Only measurements in SI units are accurate.

12.0208 inches. (A²+B²=C²)
B (Which is half of 17") = 8.5"
Therefore C=12.02081528017131 (which I rounded down to 12.0208")

You went way overboard with the complicated algebra.
Simple in your head math shows that forget the 12" and the home plate is perfectly matched 17/2=8.5 done.
It was done with inches not decimals.

I don’t see why you can’t just assume 17 inches in wrong, when you do, just using the Pythagorean theorem, you find out the hypotenuse should be 16.97 inches.

All other measurements given had two sig figs. Therefore, the answer need only have two sig figs. 12 is fine as opposed to 12.02 because of that.

Oh poo…. a measurement of .02 in the 1800s? Get real. Do it the other way and the base should be 16.97. Nitpicky and silly.

Where does it say that the home plate must be planar? If it is cut from a hyperbola, this is definitely possible, and the curvature would likely not be noticeable.

Well, I'm just happy that I solved this one
I used to be really bad at math, but I'm trying very hard to become good

Presh, at 0:34 you mention that MLB rule 2.02 mentions the 12” sides meet at a “right angle.” I believe you are mistaken.
I reviewed rule 2.02 you linked in the video description but do not find any reference to a “right angle” in the description of the home plate.
Can you provide the reference you actually used?
Were you assuming the 12” sides were supposed to meet in a right angle?

It is correct because it is limited by the smallest significant digits, IIRC. I came up with 16.97…, and that can only yield an accuracy of 17. Then there's tolerances and propagation of error. – things are getting foggy. Empirical testing will let one know if they chose correctly.

I solved it a different way. The remaining sides are 8.5 inches. Since both legs are equal in a right triangle you could then use the equation Xsqrt2. In this case 8.5sqrt2 is about 12.02

Mathematicians: I scoured the universe looking for inconsistencies. Guess what! Baseball home plates are 0.02 inches out!! That's a massive 0.166666666…% error!
Engineer: Meh. Thats close enough.
People watching baseball: What are those two pitch invaders doing with that ruler?

The MLB handbook says the dimensions are 17/8.5/12 and they meet at a point. The diagram in the appendix makes it appear that home plate is the bottom right triangle of the baseball diamond, but it doesn't put the "right angle" marker like it does for the other bases; only that the 1st base line and the 3rd base line form a right angle. Looking online, find the MLB groundskeeper blog where they state the point of home plate meets the imaginary lines from 1st and 3rd base. In reality, those lines are usually marked with a chalk line that is several inches wide, so there is quite a large tolerance for the "line".

You might be better to ask what angle is the point at home plate, you can use the cosine rule (note that interestingly 17^2 = 12^2 + 12^2 + 1 (I wouldn't be surprised if a mathematician was consulted when they were codifying the rules who pointed out that this shape very nearly worked… like fermat near misses on the simpsons). Anyway, the angle is actually 92.4.

Given that 12 is really anything greater than 11.5 and less than 12.5, it is mathmetically correct. Had it said 12.00 then your statement would be correct

Kin yew say "rounding error", boys and girls?
If the triangle's sides are taken as accurate, the angle cyphers to 90°11'56.2"
If the right angle is insisted upon, logarithmic error for the sides is 0.173% (1.73 micropartes)
Neither discrepancy is worth the math meany's tantrum. Namas té.

I used a different method, I considered x as the diagonal of a smaller square with the side of 8.5… Still resulted 12.02

I imagined the base was a square rotated to look like a diamond with two right triangles at the top then solved a^2+b^2=c^2 to get the same answer. Anyone else do the same thing?

My work: 8.5^2+(17/2)^2 =144.5

Can i use pythagoreom theorem, because I did and i got a completely different answer, around 54

You could have just as easily taken the size of the edges that were removed. Half of 17 is 8.5 so the missing length of the side is 8.5. 8.5^2+8.5^2 = 144.5.
√144.5 ≈12.02

12.0208" Given it starts with a square of 17", the two verticals are cut at 8.5", so the removed triangles are 8.5" right triangles. That gives the hypotenuse of (8.5^2 + 8.5^2)^0.5.

Pretty sure this doesn't matter because machines (or people) that make baseball plates are not accurate to the 1/50 inches anyway. .02 inches is less than than the thickness of a pencil lead.

For anyone thinking it might be a problem rooted in turning metric measurements into imperial, it's not. The metric measurements state that the front edge is 43 cm and the triangle sides are 30 cm. However, The Pythagorean Theorem puts the triangular sides just over 30.4 cm.

Thankfully, the angles match up at least; the two angles connected to the triangular sides are 135° each.

I think this math is wrong as you said pythagorian theorem would be A squared + B squared = C squared. So 12 squared + 12 squared = Desired length squared
144+144=desired length squared. therefore 288 = desired length squared and since 17 squared = 289 the length should be just below 17 inches. Also the fact that the triangle is stated to be isoceles but when solved for is actually and equilateral triangle is kinda funny.

To make the shape geometrically possible, we could set the angle θ ≈ 90.20°, X ≈ 12.02", or side c ≈ 16.97". Rounding any of these results to the nearest whole number would result in the indicated dimensions which, while inaccurate in purely academic math terms, is perfectly acceptable in real world engineering terms as it falls within the indicated tolerances.
Sure, it's correct to say that 12 ≠ 12.02 but it is also correct to say that 12 ≈ 12.02 and that 12.02 is close enough to 12 that the difference is rather insignificant.

The dimensions of the plate could be precisely correct with a truncated corner omitted which would have a length of .028"… Roughly.

Even 12.02 isn't correct, you'd have to write the equation to be accurate, 12" is info enough for the game, this is a good little warm up problem tho

People who don’t understand how significant digits are used should not be making videos about mathematics. Other videos from this person are not as bad so I guess they have just run out of material.

It would be 12.02 if the plate was 2 seperate shapes together, but its not, its one shape. the corners of the triangle do not extend completely as far as it would if it was a clean cut seperate shape. So when i measures out, you will lose approx .02 inches due to the slight radius that takes side of the isosceles into the side of the rectangle. Its practical math, not theoretical math, which in a way goes against the laws of mathematics, but is very real difference.

The guys that make them don't measure anything. They just mix, form, cut, box, and ship.

Leave a Comment

Your email address will not be published. Required fields are marked *