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When I was an undergraduate, someone presented to me a proof of the Fundamental Theorem of Calculus using entirely vegetables. I found this incredibly fun at the time, but I can't remember who presented it to me and my internet searching has not been successful.

The proof involved pinning various vegetables to a board and using their locations as variable names. I hope to find a reference for this -- obviously it's a bit of a longshot.

I was at the University of Michigan and it probably happened around 2004. But I have no reason to believe it was invented at that location or that time.

Chris Cunningham
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    What a title! I thought this was going to be about "eating one's vegetables"…i.e. having to see a proof as a typical Calculus student. – Jon Bannon Sep 19 '14 at 11:27
  • Are you sure it wasn't original? I may try to do a robust search for it... in 30s I tracked down a column in a similar spirit: http://opinionator.blogs.nytimes.com/2010/04/18/it-slices-it-dices/ (Steven Strogatz: "From this perspective, the lasting legacy of integral calculus is a Veg-O-Matic view of the universe.") – Benjamin Dickman Sep 22 '14 at 05:54
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    @BenjaminDickman Ha, no -- I mean literally vegetables, tacked to a board. It may have been original from whoever showed it to us. – Chris Cunningham Sep 22 '14 at 18:34
  • Your undergraduate transcripts, with a pointed question about teachers and assistants, should narrow it down to a handful, direct questions nail it down. – vonbrand Aug 07 '15 at 15:36
  • the last time i heard this joke someone claimed they had invented a new vegetable - the calculus, a hybrid of calabrese, a cucumber and a lettuce. Calabrese is a type of broccoli, does this help? – JMP Aug 09 '15 at 09:02
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    In what way this particular explanation of the fundamental theorem of calculus is important? Does it allow to grasp certain concepts better than other explanations? Are vegetables essential for the explanation, or were used just for fun? How the explanation will change if vegetables are replaced with other objects? I am surprised this question got so many upvotes. – Rusty Core Apr 29 '19 at 17:48
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    I assumed at the time of writing that maybe this was a well-known exposition something like Flatland. As it turns out, it wasn't well-known at all and was an idiosyncratic presentation by one specific graduate student. If you don't think it's a good reference-request, feel free to downvote it. – Chris Cunningham Apr 29 '19 at 20:30
  • Did the fact that those were vegetables play any role at all? Or were they just fancy names for the variables? – Federico Poloni May 30 '19 at 16:25
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    @FedericoPoloni I found the person I was looking for (5 years later) and hope to have a video to share later this summer. I don't remember the details. – Chris Cunningham May 31 '19 at 20:40
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    Apparently some kind of automated process bumped this. The person who has the primary source is getting the video digitized, although it didn't happen this summer. I'll post the video as an answer when it arrives. – Chris Cunningham Aug 26 '19 at 12:46
  • As it turns out the purpose of the vegetables is that some of them are shaped like points, some of them are longer and so are better for representing lines, and the banana is good for when the squeeze theorem comes into play. – Chris Cunningham Oct 30 '19 at 16:47

2 Answers2

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I am grateful to Mark Conger for finding a video of this presentation and getting the University of Michigan to digitize it. It isn't produced in the style of math youtube content, because that was presumably not the goal of QED TV, which I do not know the history of. But it is found! I finally have a link to the video! Here it is:

  • The video spends a lot of time on preliminaries, which you can skip by going to about 13:40.
  • Since you have likely proved FTC before, I would recommend you start watching at 17:55, which is when the vegetables appear.

https://umich.app.box.com/s/5lwbiroohcfwfk6yy13wqrz6yqadq76r

The vegetables are used to represent various things that appear in the proof: Legend of Vegetables

And the final product when h has approached zero (Carrot has approached Asparagus) looks like this:

h has approached zero; the banana is squeezed.

Chris Cunningham
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I remember this anecdotal version, I don't know whether or not it matches yours.

The Fundamental Theorem of Calculus stated using vegetables:

$$\int_{carrot}^{potato}vegetable(turnip)d(turnip)$$ $$=stew(potato)-stew(carrot)$$ where $$stew'=vegetable$$

My tutor said you end up with potato stew with no carrots. I asked what happened to the turnips?

JMP
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    This does not seem to attempt to answer the question as asked. Please [edit] your post so that it actually answers the question. (Otherwise this post might be removed.) – quid Aug 15 '15 at 09:18
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    @quid; howzat?? – JMP Aug 15 '15 at 09:26
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    Your edit does help a bit, thanks for that. It still does not seem much like an answer to a reference request for that proof of FTC. – quid Aug 15 '15 at 09:35
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    @quid; it might help jog a memory or two... – JMP Aug 15 '15 at 09:36