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25 April 2005

Vleeptron Complaint Dept.: besbol PizzQ


SteveHeath said...

Is the A squared + B sguared = C squared equation only valid on Right Triangles?

If not, then the answer is 60.5 squared + Our Answer = 90 squared.

So it's the square root of 4339.75
....65'10'' seems about right.

OR my equation is only for Right Triangles and I'm stumped.
10:09 PM

SteveHeath said...

Another Very Important Calculation applicable here is that if whether I score this pizza slice or not, I'm pretty sure I've got at least a couple days worth of meals at that short list of Northampton dives you've offered up as prizes for past years of trivial pursuit success by us.

If I can just square away (pun!) a couple more meals, I can visit you and Mrs Elmer for a weekend and eat for free the whole way!
10:12 PM

SteveHeath said...

Oops, shoulda read 4439.75 which has a SR of about 66feet7inches
4:20 PM

SteveHeath said...

Simply coincidence BTW, that this late insight came to me at the posted time stamp.
4:21 PM

SteveHeath said...

I refuse to particpate in this Contest Chapter [What happened to Candide & Friends in Europe in 1755?] (as if I would even have a freakin' guess on THIS one) until I learn if I've gained more Vleeptron food with my edge-u-kated guess about the distance between the pitchers mound and first base.

With folded arms in Clearwater

S

===============

Okay, let's start with Steve's Complaint: Is the distance from the Pitcher's Mound to First Base the Square Root of 4439.75 ?

No. No pizza slice for that.

I know you're not drunk, Steve, but surely this is an appropriate moment to tell the only joke that ever escaped from calculus class: Don't drink and derive.

But you are stumbling around The Pythagorean Theorem as if your mind was on Other Things, like that gorgeous redhead named Ananda in the seat next to you in Geometry Class.

"Geometry class was great,
I'm so glad I learned all that stuff.
Hardly a day goes by that I don't have to do a proof."

-- a comedian whose name
I have alas forgotten


You are this much right:

1. It's a Pythagorean Triangle Thing. Here's everything you need to know:

x² + y² = z²

2. Yes, Pythagoras only sits up and barks if the triangle has one right angle in it somewhere.

And fortunately, this triangle does.

Here, by the way, is Step 1 of the amazing book "How to Solve It" by Polya:

1. DRAW A PICTURE

The original PizzaQ had a Very Annoying Condition in it: Every number in The Answer must be a Whole Number (a Positive Integer). You can put these Whole Numbers together with any arrangement of Addition, Subtraction, Multiplication, Division, and Square Root.

But I'm not trashing your answer because it violates The Annoying Condition. Your answer is Just Wrong.

"It's not even wrong!"
-- Wolfgang Pauli, trashing somebody's
new theory of quantum physics

If someone sends me an answer in a decimal fraction, like 63.2204389370042... and it's right-ish, hmmm, okay, I may relent and credit you the pizza. I can't keep fighting this Doh New World where Tiffani and Todd and Scott and Annika use their 30-digit display Texas Instruments overpriced piece-o-crap graphing calculators and think "This is the answer!"

Only 2500-year-old geezers still know how to come up with The Perfectly Precise Exact Ancient-Greek-Style Whole Number Answers anymore.

No! I won't relent!
SOMEBODY has to keep Planet Earth straight! Somebody has to maintain High Standards around this rock!

Okay, now Draw The Damned Picture of the Besbol Diamond. The Diamond is just a Square. Every side is 90 feet long.

Draw two straight lines:

1. From top to bottom corners, and
2. From left to right corners.

They intersect in the Center of the Diamond.

But the Pitcher is not at the Center. Because of the circa-1875 printer's error in the Rule Book, the distance from the bottom corner (Home Plate) straight up vertical to the Pitcher is 60 feet 6 inches.

Ya need that in Whole Numbers? Okay, that distance is 121/2 feet.

(Get rid of those dumb inches immediately. All you people who went Metric because they didn't want Napoleon to kill them: 1 foot = 12 inches)

Now you're all heading correctly down The Bunny Trail toward The Perfect Answer. Pizza awaits. (Or an endive, or a bag of chips, or a bottle of Old Vleeptron beer.)

9 Comments:

Blogger SteveHeath said...

I'll address this special post (I'M A STAR! she cried with joy!) later this evening after work when I can take off my socks to better access my personal calculator.

12:54  
Blogger Amy said...

Has anyone solved this to your satisfaction yet? :)

If not...Mike and I got into a late night discussion over it that went something like "WHAT? I DON'T UNDERSTAND HOW YOU'RE GETTING THIS!" (just kidding...it was late and both of our brains were going on the fritz). This was like 2 weeks ago.

Anyway, I did draw a little figure, but since it was so late, I accidentally put the pitcher's mound closer to home plate than I should have. Maybe I'll post it somewhere.

And just as a warning, this might be a long and bass-ackward way to do this.

I first calculated the distance between home and second. Just to get those lengths. It is 1080 x sqrt (2) inches. Given that Bob told us that the distance from the pitcher's mound to home is 60 feet, 6 inches (or 726 inches), that makes the distance between the pitcher and second (1080 x sqrt(2)) - 726 inches. And...um...I'm calling this variable "Y" so I don't have to keep typing that out :)

Now, I drew a line from pitcher's mound to somewhere between first and second so that it makes a 90 degree angle (this stuff is so much easier with those right triangles). And since I bisected another 90 degree angle from the line before, dropping that last line makes a 45-45-90 right triangle. So the two unknown sides are figured out with the help of Mr. Pythagorus and his theorem. That makes one of those short sides equal to sqrt (Y/2).

Moving on. Calculate the other part of that side between first and second. 1080 - sqrt (Y/2). Then a^2 + b^2 = c^2 thing again to calculate the final and ultimate, unreduced distance between the pitcher and first. A = 1080 - sqrt (Y/2). B = sqrt (Y/2). Therefore:

(1080 - sqrt (Y/2)^2 + (sqrt (Y/2)^2 = C^2

Woof...

Filling in for Y again:

(1080 - sqrt (((1080 x sqrt(2)) - 726)/2)^2 + (sqrt (((1080 x sqrt(2)) - 726)/2)^2 = C^2

(So...take the square root of that whole left side to solve for C...which is your answer).

Gimme a bit and I'll punch it through the calculator...teehee...

(Either that, or I'll have figured out an easier, less convoluted way to do it).

How's that for ya?

03:26  
Blogger Amy said...

Okay so there was an easier way, methinks. If only I had integrated the comments that you wrote into my brain I would have figured it out. But I was just going off of what late-night-brain told me 2 weeks ago.

So here goes attempt number 2, a bit less kooky of an answer.

I drew the two lines to make an X thru the center of that there diamond. The length of which, as I stated in the last post is 1080 x sqrt (2) inches.

THOSE make a 90 degree angle in the middle...duh. But anyway, since the mound is off center, I'll get to that part in a second. Distance to the real center of that diamond is (1080/sqrt(2)). Therefore, the distance to the mound to the real center of the field is (1080/sqrt(2)) - ((1080 x sqrt(2)) - 726 inches). Yeah...I'm calling that variable "N".

And that gives us two sides (the little tiny bit that I just calculated and the distance from the center to first).

(Okay, this answer is turning out to be just as convoluted as my other).

(1080/sqrt(2))^2 + ((1080/sqrt(2)) - ((1080 x sqrt(2)) - 726 inches))^2

= answer^2

Ugh...I could really use some pizza of any kind right now.

03:48  
Blogger Bob Merkin said...

I can't believe you've done this in inches rather than in feet. Now I have to work the whole thing out again. Ouch ouch ouch.

20:59  
Blogger Mike said...

It actually makes much more sense to me, given the requirements that you set forth. One of the distances you provided was 60 feet 6 inches. You either convert that to inches, use a base 12 number system, or use 60.5 feet. Since you said right off that you just wanted whole numbers, the 60.5 is out, and using base 12 seems a bit outlandish don't you think? Doing it in inches gives you all whole numbers, no decimals. Just like you asked. :)

21:36  
Blogger Bob Merkin said...

I didn't say it was wrong to do it in inches. I didn't even say it was Evil. But the World o Besbol is a World of Feet, not of inches. When you think besbol, you think feet. 90 feet from one base to the next. 310 feet from Home to Left Field at Fenway Park. (With, occasionally, some inches left over.)

I grudgingly avknowledge that from a purely arithmetical standpoint, it does make sense to do it in inches. It was just unexpected. I think by Saturday I'll have the leisure and clarity to check Amy's answer. I guess I just have to divide everything by 12. Ouch ouch ouch.

04:50  
Blogger Bob Merkin said...

Hiya Amy --

I'm having a little ambiguity trouble evaluating your expression

(1080/sqrt(2))^2 + ((1080/sqrt(2)) - ((1080 x sqrt(2)) - 726 inches))^2

= answer^2

... which probably ain't your fault, it's just by nature unwieldy.

Hmmm ... maybe just this one time, could you rewrite the expression using this grouping symbol hierarchy:

{ [ ( ) ] }

and I'm guessing that will clear up my ambiguity. Or your ambiguity. Or steve's. Or mike's.

And pleeeeeze get rid of that word "inches" which is in a real odd place, I'll just assume everything's in inches.

(Sometimes I get something that's in the ballpark ... and sometimes I get something that wants me to take the square root of a negative.)

07:47  
Blogger Mike said...

Actually, you'll have to multiply everything by 12, not divide. I'm not sure what type of units you'd be working in if you divided. Something unique to Vleeptron possibly? :)

11:30  
Blogger Bob Merkin said...

I'll either have to multiply my answer by 12 to make it agree (or not agree) with Amy's, or I'll have to divide Amy's answer by 12 to make it agree (or not agree) with my answer.

I'd like to compare decimal fractions on a 4-banger, but because I'm an Ancient Greek Geezer on the Vleeptron PizzaQ Honor Program, I'll do it polynomially. I can handle that even if I gotta divide one polynomial by another. We learned how to do that in 10th grade. Ouch ouch ouch. Made my fucking brane bleed. But it's saved my life more than once in the Yukon.

12:27  

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