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    Parker Owens
  • Parker Owens
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  • 09/25/2017
  • 1,226 Words
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Stories posted in this category are works of fiction. Names, places, characters, events, and incidents are created by the authors' imaginations or are used fictitiously. Any resemblances to actual persons (living or dead), organizations, companies, events, or locales are entirely coincidental.
Note: While authors are asked to place warnings on their stories for some moderated content, everyone has different thresholds, and it is your responsibility as a reader to avoid stories or stop reading if something bothers you. 

Cut the Cake - 1. Cut the Cake

There really is a math problem in here. Truly. Otherwise, just enjoy the cake. But leave me the frosting. Happy National Math Story Day, Drew.

My problem began when my boyfriend made me a cake.

Okay, let me back up a second. It was my birthday, and Jimmy decided a celebration was in order. Normally, I try to avoid birthdays and things like that. Too much bother over yet another year past. But Jimmy is such a sweetheart, and really, I'm kind of new at the whole boyfriend thing, so when he trailed the hint in front of me, I didn't voice any objection.

"What kind of cake do you like?" He queried.

This was a normal question-for-the-sake-of-information thing, right? I mean, we've discovered some lovely things about one another over the past few months, but how can you convey every personal piece of information in such a short time. We're nerds, not cyborgs.

"Carrot cake," I replied without hesitation. I love a good carrot cake.

"Aaaand, what plans do we have this week?"

I sighed. Now I'd have to look at the calendar. I rose from my chair. "Let me go see." I returned from the kitchen calendar a moment later. "Nothing that I can see."

Jimmy smiled one of his mischievous smiles – the kind which skewered my heart in the first place. "Great."

All this leads to this past weekend: I had to work doing some tutoring on Saturday, but Jimmy seemed unusually okay with that. When I got back to the apartment, I smelled the unmistakable scents of spice and baking.

I opened the door. "Hey, Jimmy, what have been up to?" I called out.

"You're home early," his voice echoed from the kitchen. I heard the clatter of a pan in the sink.

Walking into the kitchen, I found Jimmy up to his elbows in soapy water. And on the counter, a large rectangular sheet cake. Carrot cake. I strongly suspected cream cheese frosting, too. I love cream cheese frosting. Almost as much as Jimmy. Don't tell him I said that.

"Just what did you do?" I demanded.

"Nothing. Just a little birthday cake."

"Little? That thing's the size of football field."

"But it's a carrot cake. You said you liked carrot cake."

"I do. And it smells incredible. But it's enormous."

"Well, I thought maybe you'd be willing to share a little with all our friends."

My eyes narrowed. "Friends? Share carrot cake?"

My boyfriend turned and hugged me with soapy arms. "I just thought maybe a few friends coming over to celebrate your birthday would be a good thing. That's not a bad idea, is it?"

I wanted to shout. This is where Jimmy and I are different – he's gregarious, a friend of all the world. I'm shy, retiring, and terrible at small talk. This could be a disaster.

"Jimmy, I'm just…" The look of apprehension on Jimmy's face silenced anything else I was going to say. How can a man of our age look like such a kid? "…oh, all right. Fine, I guess that's all right."

I wasn't going to be enthusiastic.

But Jimmy smiled back at me just the same. "Thank you. You'll see. It's going to be fantastic."

My acquiescence earned me a kiss. I forgot about being irritated for few moments.

"Who's coming?"

"Friends. Val and Dave and AC from across the street. That first year teacher from school, Drew; the English woman, what's her name? Oh, and tim said he was coming, and maybe his husband, too. And your brother and his wife, they're coming early."

"Why early?"

"To help with setup. They'll be here in under an hour."

"Setup? I thought this was just a few friends."

"Oh, don't worry, there's plenty of cake."

"As long as I get half the frosting."

"Only half?" Jimmy teased.

"Hey, carrot cake is my favorite." I kissed Jimmy again. "Well, almost my favorite."

"I think we're going to have to make a quick trip to the store for some soft drinks, though."

"Oh?"

"Well, I bought plenty of prosecco, but I kind of forgot about the other stuff."

"I can go get that," I volunteered.

"For your own party? No way."

"Sure, why not? I can go."

"We'll both go," Jimmy insisted.

"What about my brother? What if he and Jeannine come early?"

"We can leave the door unlocked, with a note. They're trustworthy."

I cocked an eyebrow at Jimmy. He and I have gotten to understand each other pretty well, but he clearly doesn't know my brother.

"Come on, let me just finish these, and we can go. The sooner we get out the door, the sooner we get back."

And so we made a whirlwind trip to the store, leaving the cake to cool and a note for my brother and his wife.

Forty minutes later, we burst in the door, laughing and breathless from hustling up the stairs. We might possibly have kissed on the landing. You can review the security camera tapes if you want.

"Hey, brother mine, happy birthday." I received a one-arm bro-hug. "Working on setting up the bar here," my older sibling pointed out proudly.

"Thanks. Let me put these packages down in the kitchen."

I hate jarring surprises. I got one the moment I entered the kitchen. There on the counter was the cake – that big beautiful, rectangular cake. My big beautiful carrot cake.

And there, in a completely random spot in that lovely, beautifully frosted cake, was a rectangular hole. Someone had taken a rectangle of cake out. And not a corner or a side piece, this was rectangular hole was cut in a strange, capricious and arbitrary spot. No way to miss it. No easy way to accommodate it.

And someone had taken a rectangle's worth of frosting.

 

At least I knew it hadn’t been Jimmy. That left my brother as the culprit. Surely Jeannine wouldn't do a thing like that. My angry shout brought Jimmy and Jeannine running.

"Where's that brother of mine?"

"Paul, what's the matter?"

I pointed. Jimmy's mouth fell open; Jeannine's was set in a thin, grim line.

"How do I get half the frosting now?"

So call me irrational. You have my number.

"Wait, wait, wait a second, love," Jimmy was thinking furiously, I could tell. "Calm down."

I was going to kill my brother. I know, he's always been a big boy, and there was certainly a lot of cake – carrot cake – but still. I mean, even if I didn't want a birthday, or a party, or any of that, there was the matter of my frosting.

"Paul, it'll be fine," Jimmy was placating. "Look. All I have to do is draw one single, straight line. Just one straight line, see? And then you'll have exactly half of the frosting."

I was being silly, of course.

For one thing, Jimmy was absolutely right. I could still have exactly half of the remaining frosting. I love having a dork like me for a boyfriend. All he had to do was cut along that one single straight line, and the cake – and the frosting – would be cut precisely in half.

But more importantly, I needed to share. I had Jimmy, and he was enough.

 

 

Math Question: What was the single straight line that cut the remaining cake exactly in half? How did Jimmy know where to draw that line?

You can leave solutions and explanations here. Or just leave a comment. Hope you enjoyed one of the longest word problems on GA.
Copyright © 2017 Parker Owens; All Rights Reserved.
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Stories posted in this category are works of fiction. Names, places, characters, events, and incidents are created by the authors' imaginations or are used fictitiously. Any resemblances to actual persons (living or dead), organizations, companies, events, or locales are entirely coincidental.
Note: While authors are asked to place warnings on their stories for some moderated content, everyone has different thresholds, and it is your responsibility as a reader to avoid stories or stop reading if something bothers you. 
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Parker Owens
1 minute ago, Dr. John NYC said:

Loved algebra but was terrible at geometry & trig. Stretching back almost half a century, I was originally excited that i could solve it. Then , I realized that the rectangle was in an arbitrary place. After some more thought, I think I have the solution, but I can't figure out how to make it hidden text writing from my iPhone. So I have to wait until I get home. 

 

Oh, the story was absolutely delicious! My mouth was watering thinking about a giant carrot cake.  🎂 🍽👏🏽

 

Thank you for reading the story, and reacting to it. Geometry is the best way to handle this, though it may turn out that your straightedge gets sticky.  Drawing it out on paper may be a better way to try out what to do, though modeling it with actual carrot cake would be more delicious. Have fun!

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Lux Apollo
1 hour ago, Parker Owens said:

 

Thank you, Lux. I am very glad you read it. 

Meant to ask if the guest list was being referential or if I was just reading into it too much?

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JeffreyL

Enjoyed the story and carrot cake! To do the math I need a picture or a more detailed explanation of where the missing piece was. Thanks for this bit of fun!

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Parker Owens
19 hours ago, Lux Apollo said:

Meant to ask if the guest list was being referential or if I was just reading into it too much?

No, not particularly referential...just done for fun...

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Parker Owens
12 minutes ago, JeffreyL said:

Enjoyed the story and carrot cake! To do the math I need a picture or a more detailed explanation of where the missing piece was. Thanks for this bit of fun!

 

I am glad you enjoyed the story. I will have to work on getting an image to post for this...

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Defiance19

That was pretty cool Parker. I knew I wouldn’t attempt to figure any of this out, so I enjoyed the story with a single minded focus!! 

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Parker Owens
3 hours ago, Defiance19 said:

That was pretty cool Parker. I knew I wouldn’t attempt to figure any of this out, so I enjoyed the story with a single minded focus!! 

 

Thanks for giving Paul and Jimmy a chance; and maybe the solution to the math question will occur to you sometime when you least expect it...

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xleroc
On 9/25/2017 at 5:13 PM, JaySeale said:

Before the hole was cut: any straight line that goes thru the center of the cake cuts the cake in half.  By same reason, any straight line that goes thru the center of the hole cuts the hole in half.  So, the unique straight line that goes thru both the center of the cake and the center of the hole cuts the original cake in half, but also places half the hole on each side.  Thus, half the remaining cake is also on each side.

From another math nerd, this is the correct answer.  I was about to write something similar, but JaySeale beat me to it.

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Parker Owens
4 hours ago, xleroc said:

From another math nerd, this is the correct answer.  I was about to write something similar, but JaySeale beat me to it.

 

Indeed it is!  I hope you enjoyed Jimmy and Paul and the tiny math problem baked into the carrot cake. 

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booklove

OK. I am a story- not a math-lover. So I would cut the cake horizontally and divide the underlaying part between the guests and LEAVE ALL THE ICING FOR PAUL...

No, I dont like creamcheese icing, so sue me.

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Parker Owens
19 hours ago, booklove said:

OK. I am a story- not a math-lover. So I would cut the cake horizontally and divide the underlaying part between the guests and LEAVE ALL THE ICING FOR PAUL...

No, I dont like creamcheese icing, so sue me.

 

Paul will definitely not sue you! I am glad you liked the story, even if there was a math problem buried in it. Thanks for taking time to read it and comment. 

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Pedro1954

Thanks for another delightful tale. Well it had to be delightful with carrot cake in it!

Problem:

First Iteration: The cake has been set to cool as the boys go to shop. Frosting would not be applied until cool.Therefore divide horizontally as the least intellectually challenging solution. Paul and Jimmy share the bowl of frosting after everyone else has gone home.

Second iteration.The problem states the cake is already frosted. My geometry skills are too rusty to have arrived at Jay's solution which I immediately saw was both elegant and correct.

Third iteration: The question is the wrong one. The cake is intended for sharing. Paul cuts off enough for himself (and Jimmy) and leaves the crumbs to be fought over by the other guests. (I think someone else had suggested this)

Fourth iteration: The question becomes irrelevant. Pointing at his mother, who is eyeing up the cake and whose BMI is sub-optimal ( or should that be supra-optimal), the neighbour's kid says "a moment on the lips, a lifetime on the hips." The boys' guilt trip over the implied carb loading makes them lose the appetite for the cake.

 

Corollary: Paul's brother is relieved of his glass of prosecco before he has a chance to drink it to be replaced by a mug of builders tea and a badge denoting him as designated driver for all the guests.

 

Lemma. The original question/solution is still valid if the hole or cake is circular. What are the conditions on the shape of the hole and cake for the solution still to be valid? Is it that the shapes should have two planes of symmetry at right angles? Or is it only necessary to be able to identify the centres of mass of the cake and the missing piece?

 

Pleas Sir! Are we doing Algebra next week? Or 3-D calculus?

Edited by Pedro1954
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Parker Owens

@Pedro1954 Your comprehensive remarks left me laughing and delighted. I particularly applaud :

6 hours ago, Pedro1954 said:

Corollary: Paul's brother is relieved of his glass of prosecco before he has a chance to drink it to be replaced by a mug of builders tea and a badge denoting him as designated driver....

 

But the icing on the cake (so to speak) was your wonderful Lemma, which will be foisted upon my calculus class at the earliest suitable opportunity. Awesome. 

 

And I am glad these characters appealed to you. Paul and Jimmy seem like an interesting pair. 

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Pedro1954

Foisted on your calculus class? Sorry I thought you said 'frosted'.

 

Will there be one super-nerd who suggests mapping the cake to a different space such that the hole becomes infinitesimally small....?

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Parker Owens
6 hours ago, Pedro1954 said:

Foisted on your calculus class? Sorry I thought you said 'frosted'.

 

Will there be one super-nerd who suggests mapping the cake to a different space such that the hole becomes infinitesimally small....?

 

You have me laughing. Alas, I fear I don't have such a super-nerd this year. But that sounds like fun....and frosted!  :) I prefer that any day.

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pondman

The cake was bad enough, but when it became friends, that crossed the line. I would have left him and friends on their own.  I hate birthdays and people who feel the need to make it a big deal....Trust me, he would have paid for the party big time. After knowing he did not want a big deal, he goes behind his back and does that anyways. Final straw, he would be wearing that cake, before I walked out.

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Parker Owens
16 minutes ago, pondman said:

The cake was bad enough, but when it became friends, that crossed the line. I would have left him and friends on their own.  I hate birthdays and people who feel the need to make it a big deal....Trust me, he would have paid for the party big time. After knowing he did not want a big deal, he goes behind his back and does that anyways. Final straw, he would be wearing that cake, before I walked out.

You and Paul could have hung out together. Maybe he’d have shared some icing with you too. Still, it’s amazing the things we do for love - like solve math problems... thank you very, very much for reading and responding to this. 

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pondman

Its a good thing Jimmy was not my BF. He would have had a sink full of cake and Id be gone. He could have his party with me.  Disrespecting his bf wishes is got to be good for some huge fight, maybe even lead to a break up.

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Parker Owens
41 minutes ago, pondman said:

Its a good thing Jimmy was not my BF. He would have had a sink full of cake and Id be gone. He could have his party with me.  Disrespecting his bf wishes is got to be good for some huge fight, maybe even lead to a break up.

I can imagine they must have quarreled afterwards. Perhaps something holds them together. 

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pondman
On 9/25/2017 at 9:01 PM, Parker Owens said:

 

Love your thinking. What a pity Jimmy made a more mundane, standard carrot cake. 

 

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RevSimon

I love carrot cake and especially the frosting. I love this story too. But what sort of person excises a rectangle of cake from a whole sheet cake? Taking a corner piece to maximise the amount of frosting I can understand, but to try and cut down into the cake and then lift out a piece is bonkers. It would be a mess and leave crumbs and disturbed frosting. But this is a story so set aside my disbelief and pedantry, it happened so how to get half the cake and frosting? First is it half the original or half the remaining? The hole was cut from the whole “in a completely random spot”. This math problem, which you say is actually geometry, is missing data, so you being a word smith I think you take half of each half, add a single line and get ha-ha!

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Parker Owens
16 hours ago, RevSimon said:

I love carrot cake and especially the frosting. I love this story too. But what sort of person excises a rectangle of cake from a whole sheet cake? Taking a corner piece to maximise the amount of frosting I can understand, but to try and cut down into the cake and then lift out a piece is bonkers. It would be a mess and leave crumbs and disturbed frosting. But this is a story so set aside my disbelief and pedantry, it happened so how to get half the cake and frosting? First is it half the original or half the remaining? The hole was cut from the whole “in a completely random spot”. This math problem, which you say is actually geometry, is missing data, so you being a word smith I think you take half of each half, add a single line and get ha-ha!

You’re quite correct; I should have said half the remaining frosting, if I wanted exactitude. This geometric problem is fun to pose to students; it was even more fun to present in story form. Thanks for trying it out. 

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