Pythagoras' Nightmare

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Project by ChuckV posted 10-07-2012 09:44 PM 20790 views 5 times favorited 26 comments Add to Favorites Watch

My 8 and 10 year-old boys are playing Fall Little League. They have two great coaches, and I want to give them something in thanks for all of their effort, time and patience. I decided to make boxes in the shape of home plate.

This boxes feature Paul’s (shipwright’s) wooden hinges. The carcase is black walnut and the top is ash, as are baseball bats. The finish is Danish Oil.

Here are all the pieces for one box:

This close-up of a top shows how it attaches to the rest of the lid (the top is upside down here):

I used rubber bands to provide the clamping pressure during the glue-up:


What does this have to do with Pythagoras? To determine the dimensions of the box lids, I used this sketch showing the official dimensions:

It is not possible to make a figure in this shape. If it were, the right triangle on the back of the plate would have sides 12, 12, 17. As Mr. P. knew, this means that 12×12 + 12×12 = 17×17, or 288 = 289. So, I guess that no baseball game has ever been played according to the rules!

The actual rule doesn’t explicitly say that the point on the plate has to be 90 degrees, but it does say that the two 12” edges must coincide with the first and third base lines, which implies 90 degrees. Here is the official wording:
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 pitcher’s plate, and the two 12-inch edges coinciding with the first and third base lines.

End of useless trivia for now.

-- “Big man, pig man, ha ha, charade you are.” ― R. Waters

26 comments so far

View Kookaburra's profile


748 posts in 2129 days

#1 posted 10-07-2012 09:58 PM

Really nice – and what a great thing for you to do. Gifts that touch on an special interest of the recipient are rare enough – and you made these especially for the coaches. 50 years from now, the coaches kids are going to have these as a special reminder of their dads’ days on the field. Until then, the coaches are going to smile every time they use the box. Kudos to you!

(I’m a former Little League umpire who never even got thanks!)

-- Kay - Just a girl who loves wood.

View daltxguy's profile


1373 posts in 3818 days

#2 posted 10-07-2012 10:43 PM

Obviously, they didn’t account for kerf!
US ranks 31st among ‘wealthy’ nations in math proficiency. They should have sent the baseball diamond design problem to Korea which ranked near #1.
Massachusetts, however, is tops in the nation, so it is no wonder that this would he pointed out by you!

Lovely box, beautiful joinery and a very nice gesture on your part.

-- If you can't joint it, bead it!

View Oldtool's profile


2547 posts in 2095 days

#3 posted 10-07-2012 11:10 PM

Nice work, good looking boxes.

-- "I am a firm believer in the people. If given the truth, they can be depended upon to meet any national crisis. The point is to bring them the real facts." - Abraham Lincoln

View Jim Jakosh's profile

Jim Jakosh

20071 posts in 3010 days

#4 posted 10-07-2012 11:43 PM

Very neat boxes!!!!!!!!!!!!!!..............Jim

-- Jim Jakosh.....Practical Wood Products...........Learn something new every day!! Variety is the Spice of Life!!

View gfadvm's profile


14940 posts in 2594 days

#5 posted 10-08-2012 01:07 AM

Those are very nice boxes and the integral Shipwright hinges are perfect! The whole math calculations thing escapes me!

-- " I'll try to be nicer, if you'll try to be smarter" gfadvm

View jumbojack's profile


1673 posts in 2528 days

#6 posted 10-08-2012 01:39 AM

A very fine gift.
I umpired little league and pony league for sixteen years as a volunteer. I enjoyed the love/hate relationship on the field. Baseball umpires share a unique experience as you are king from the time the ball is put in play right up until the last out. How often does one get to be the undisputed ruler of anything for any amount of time.
I did a little managering and coaching, after, those guys are heros. It is a nearly thankless job. Thank you for doing something nice for some truly unsung heros.

-- Made in America, with American made tools....Shopsmith

View oldnovice's profile


6543 posts in 3272 days

#7 posted 10-08-2012 05:42 AM

It is really going to be a good keepsake for the coaches!

Nobody ever said that baseball is a game of inches!

-- "I never met a board I didn't like!"

View lab7654's profile


266 posts in 2151 days

#8 posted 10-08-2012 11:34 AM

Nice boxes! I’m a fan of any project that challenges me with math. To me, it makes the design process much more fun.

-- Tristin King -- When in doubt, sand it.

View JohnEinNJ's profile


94 posts in 2252 days

#9 posted 10-08-2012 02:46 PM

so, which dimension did you cheat on? Did you make the “square” end 12 * sqrt(2) = 16.97”, or the sides sqrt(289/2) = 12.02”?

View helluvawreck's profile


30129 posts in 2771 days

#10 posted 10-08-2012 03:35 PM

Unusual and nicely done.

helluvawreck aka Charles

-- If a man does not keep pace with his companions, perhaps it is because he hears a different drummer. Let him step to the music which he hears, however measured or far away. Henry David Thoreau

View a1Jim's profile


116902 posts in 3481 days

#11 posted 10-08-2012 03:38 PM

Cool design and build,it looks great.

-- Custom furniture

View ChuckV's profile


3095 posts in 3432 days

#12 posted 10-08-2012 07:23 PM

JohnEinNJ -

I think that my ruler is defective. Both sqrt(2) and sqrt(289/2) seem to be missing. I might have to return the ruler!

I actually made these a little less than half the real size. I cut all the pieces to final size except for the ones forming the “point” Then I “snuck up” on both the length and the angle.

-- “Big man, pig man, ha ha, charade you are.” ― R. Waters

View DS's profile


2855 posts in 2325 days

#13 posted 10-08-2012 08:12 PM

Very nice boxes.

The math, as stated in the rule, does create slightly longer than 12” sides, but, they could just be referring to “nominal” 12” sides just to keep the rule verbage simple.

Did I mention, cool boxes?

-- "Hard work is not defined by the difficulty of the task as much as a person's desire to perform it.", DS251

View shipwright's profile


7894 posts in 2702 days

#14 posted 10-08-2012 08:30 PM

Absolutely the best project shaped like a home plate in the last 24 hours, beyond any doubt.

I’d like them even if they looked like second base.
Thanks for the hinge credit. You get an “A” on them.

-- Paul M ..............If God wanted us to have fiberglass boats he would have given us fibreglass trees.

View Dave's profile


11426 posts in 2744 days

#15 posted 10-09-2012 12:24 AM

Chuck that is a true Home Run. When I first saw it I thought of the time capsule we but under our home base my 10th grade year. Nice job and well done.

-- Superdav "No matter where you go - there you are."

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