In a forum recently, during a discussion about the differences between cricket and baseball, I made the comment that if you could bounce the ball on the way to Home Plate then someone like English test bowler Jimmy Anderson who is known for having an extraordinary ability to hit the same mark on a cricket pitch, would likely sail through every Major League Baseball side.
The reason for this is that Jimmy Anderson is aiming to knock down a set of stumps which are only 9 inches in width, whereas the Home Plate in baseball is 17 inches across. With 17 inches of space to aim at, I think that even I as a rank amateur could do considerable damage to a Major League Baseball side.
If you only need 3 outs in an inning an there are 9 innings for a side in a baseball game, then you only need 27 deliveries to completely eliminate every player in all innings. 27 deliveries is less than 5 overs; which is well within the work rate of any half decent bowler. In one churches B-Grade match because we were short of confident bowlers, I ended up bowling 28 overs in a day. Four bowlers operated from the other end and even they all bowled 7 overs each; which is about the same as a good efficient Major League Baseball pitcher.
In that thread, someone posted the two diagrams of a set of cricket stumps and of Home Plate in baseball. However, even upon basic interrogation, the standard diagram of Home Plate bothered me. The reason for this is that the corner at the bottom is shown as a right triangle and yet every single number on the diagram is a rational number. Probably locked away in the minds of anyone who has done High School trigonometry are the values for sin 45° and cos 45° which are both 1/√2. √2 is not rational.
Without even doing any maths at all, I already knew that the standard diagram of Home Plate and probably the rules which underpin is, are mathematically impossible. As someone who works in an accounting office, where being cent perfect is the standard to aim for, I think that I have developed a professional sense of obsessive compulsive pedantry. In a glorious twist of hypocritic inconsistency, I quite often gumby up everything but when it comes to maths which has rules, and the possibility to attain perfection, what would be considered to be a psychological disorder (OCD) is transformed into hyper-diligence in the field of mathematics.
If you have too many rules, then you are in Germany.
If you don't have enough rules, then you are in France.
If you have rules and they are silly, then you are in England.
If you have rules and they are wrong, then you are in America.
Here is the relevant rule:
https://www.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.
- Field Dimensions, Home Plate, Major League Baseball
Home Plate can be thought of as a 17 inch by 8.5 inch box, with a triangle attached. Ignore that box. It is fine. The triangle is a great big nonsensical schnibbity-nibbity schnick-nuck-neigh woo-woo.
The isosceles right triangle (if you can call it that) has a hypotenuse of 17 inches. We know this because the front of home plate is the front part of that 17-inch square. 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.
a² = b² + c²
But since both of the two corner cut sides are identical, then b² = c²
17² = b² + b²
17² = 2b²
or
289 = 2b²
144.5 = b²
We have a problem. 12² = 144.
If the hypotenuse is 17 inches long then the length of those two sides is actually ≈ 12.02 inches.
If on the other hand, the two sides are 12 inches each, and this is a right triangle, then again using the Pythagorean Theorem the sum of the squares of the legs has to be the square of the hypotenuse; we get:
a² = b² + c²
a² = 12² + 12²
² = 288
a ≈ 16.97
If the two sides are 12 inches long then the length of the hypotenuse is actually ≈ 16.97 inches.
We could very well assume that all of the side lengths are correct. If this is true, then:
sinA = 12/17
A ≈ 44.90°
B ≈ 44.90°
C ≈ 90.20°
Here's the fun thing... I LOVE THIS.
I love that the only people that this is ever likely to trouble, are mathematicians who find this interesting, and high school students in maths class who now have a real world exercise to do maths upon. Of those two kinds of people, the mathematicians are going to go into an apoplectic rage about the real world not fitting with what the maths says, and the high school students are likely to be bored and grumpy as they stare out of the window.
I love that 12/17 is a good approximation of √2 because 17 is a number that doesn't really appear anywhere sensible in maths. I love that this exercise with a minor amount of annoyance has given me a fun new approximation of √2. I love that near enough is good enough because who in the real world honestly cares a jot that the dimensions are all out but less than even 1%. All kinds of stuff is designed to be within tolerance levels and in this case, for a thing where literally nobody in the world is going to get out a tape measure and argue over 0.03 of an inch, this is perfectly fine.
Best of all, I really love that you can have a set of rules which defines things yet contains mathematical impossibilities. I love that Baseball and even Major League Baseball has gone "Ah ha ha! We don't care!" and danced around like a porkchop with the rules. Near enough IS good enough. Good enough is good enough.
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