A Jumbo Margin of Error

I was out in the neighborhood shopping for seafood and stopped by the local fishmonger. I inspected the jumbo shrimp, which were going for $17.99 a pound. I decided I’d take a pound, and placed my order.

The fishmonger threw a handful of shrimp on the scale. The pile weighed in 0.85 pounds, so he added a few more. The additional shrimp took the total over a pound, so he took one off. Slowly, this series of shrimp was converging to the appropriate limit.

Still a little over, the fishmonger exchanged two large shrimp with two smaller ones. This brought the total weight down to 0.95 pounds.

I turned my attention to the rest of my grocery list. It wasn’t until after I had cashed out and left the store that it hit me: The fishmonger had charged me $17.99 for the shrimp! That is, he charged me for a full pound, even though I only received 0.95 pounds.

Now, a 5% margin of error might not seem too bad, but because of the high cost of shrimp, that 5% error amounts to 90 cents! With all the attention paid to that weighing, I feel like he could have been a bit more accurate.  I would also hypothesize that the vast majority of weighing inaccuracies are of the “under” variety.

My inattentiveness here cost me a dollar, but at least I walked away with something to think about. And while the fishmonger may have won a dollar, he lost all my future business.

Wrapped Trapezoid

Wrapping up this gift was much more challenging than I expected.

But it got me thinking about how this could be an interesting project.  Questions such as “What’s the smallest square piece of wrapping paper that could do the job?” or “What kind of rectangle would work best?” are compelling and  easy to investigate.  And maybe someone could make a triangle or trapezoid do the job efficiently.  There’s a lot of room for creativity and exploration here.

The usual restrictions on tearing and cutting would apply, although relaxing those restrictions might create interesting problems, too.

It wasn’t easy, but I did pick up some unexpected ideas along the way.  And the gift was well-received, too!

A Good Math Story

This video lecture from the Princeton Public lecture series features psychologist Stanislas Dehaene and mathematician and author Steven Strogatz discussing math, learning, and teaching.

Dehaene, a leading researcher in how the brain acquires and processes mathematical knowledge, has some interesting things to say about whether mathematics is innate or learned.  He also describes some fascinating research conducted on number sense and geometric understanding in primitive societies.

What I enjoyed most in this lecture, however, are the two stories from Steven Strogatz about his personal experiences learning math.  At around the 23:30 mark, Strogatz tells the story of when he first became “really interested” in math.  Strogatz is a wonderful storyteller, and the tale should resonate with anyone who has discovered, or is discovering, their passion for math or science.

Strogatz’s second story is about his first experience being “weeded out” in an advanced math course in college.  This is a story I wish I had heard as a student, and it’s something I’ll definitely be sharing with my students from now on.

And for more on math and teaching from Professor Strogatz, check out how his book “The Calculus of Friendship” is a great read for advanced math students.

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