Quotable: I Do Hate Sums


I’ve been looking for quotes to put at the beginning of each chapter in my math games books. I found a delightful one by Mrs. LaTouche on the Mathematical Quotations Server, but when I looked up the original source, it was even better:

I am nearly driven wild with the Dorcas accounts, and by Mrs. Wakefield’s orders they are to be done now.

I do hate sums. There is no greater mistake than to call arithmetic an exact science. There are Permutations and Aberrations discernible to minds entirely noble like mine; subtle variations which ordinary accountants fail to discover; hidden laws of Number which it requires a mind like mine to perceive.

For instance, if you add a sum from the bottom up, and then again from the top down, the result is always different.

Again if you multiply a number by another number before you have had your tea, and then again after, the product will be different. It is also remarkable that the Post-tea product is more likely to agree with other people’s calculations than the Pre-tea result.

Try the experiment, and if you do not find it as I say, you are a mere sciolist*, a poor mechanical thinker, and not gifted as I am, with subtle perceptions.

Of course I find myself not appreciated as an accountant. Mrs. Wakefield made me give up the book to [my daughter] Rose and her governess (who are here), and was quite satisfied with the work of those inferior intellects.

— Maria Price La Touche
The Letters of A Noble Woman
London: George Allen & Sons, 1908

*sciolist: (archaic) A person who pretends to be knowledgeable and well informed. From late Latin sciolus (diminutive of Latin scius ‘knowing’, from scire ‘know’) + -ist.

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Reblog: Calculus Tidbits

[Feature photo above by Olga Lednichenko via Flickr (CC BY 2.0).]

This week I have a series of quotes about calculus from my first two years of blogging. The posts were so short that I won’t bother to link you back to them, but math humor keeps well over the years, and W. W. Sawyer is (as always) insightful.

I hope you enjoy this “Throw-back Thursday” blast from the Let’s Play Math! blog archives:

Finding the Limit

Eldest daughter had her first calculus lesson last night: finding the limit as delta-t approached zero. The teacher found the speed of a car at a given point by using the distance function, calculating the average speed over shorter and shorter time intervals. Dd summarized the lesson for me:

“If you want to divide by zero, you have to sneak up on it from behind.”

Harmonic Series Quotation

This kicked off my week with a laugh:

Today I said to the calculus students, “I know, you’re looking at this series and you don’t see what I’m warning you about. You look and it and you think, ‘I trust this series. I would take candy from this series. I would get in a car with this series.’ But I’m going to warn you, this series is out to get you. Always remember: The harmonic series diverges. Never forget it.”

—Rudbeckia Hirta
Learning Curves Blog: The Harmonic Series
quoting Alexandre Borovik

So You Think You Know Calculus?

Rudbeckia Hirta has a great idea for a new TV blockbuster:

Common Sense and Calculus


And here’s a quick quote from W. W. Sawyer’s Mathematician’s Delight:

If you cannot see what the exact speed is, begin to ask questions. Silly ones are the best to begin with. Is the speed a million miles an hour? Or one inch a century? Somewhere between these limits. Good. We now know something about the speed. Begin to bring the limits in, and see how close together they can be brought.

Study your own methods of thought. How do you know that the speed is less than a million miles an hour? What method, in fact, are you unconsciously using to estimate speed? Can this method be applied to get closer estimates?

You know what speed is. You would not believe a man who claimed to walk at 5 miles an hour, but took 3 hours to walk 6 miles. You have only to apply the same common sense to stones rolling down hillsides, and the calculus is at your command.

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Math That Is Fun: Infinite Primes

Oh, my! Ben Orlin over at Math with Bad Drawings just published my new favorite math proof ever:

I had a fight with Euclid on the nature of the primes.
It got a little heated – you know how the tension climbs.

It started out most civil, with a honeyed cup of tea;
we traded tales of scholars, like Descartes and Ptolemy.
But as the tea began to cool, our chatter did as well.
We’d had our fill of gossip. We sat silent for a spell.
That’s when Euclid turned to me, and said, “Hear this, my friend:
did you know the primes go on forever, with no end?” …


Click here to read the whole post at Math with Bad Drawings.

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Math Teachers at Play #58

No 58 - gold on blue[Feature photo (above) by Alex Kehr. Photo (right) by kirstyhall via flickr.]

Welcome to the Math Teachers At Play blog carnival — a smorgasbord of ideas for learning, teaching, and playing around with math from preschool to pre-college. If you like to learn new things and play around with ideas, you are sure to find something of interest.

Let the mathematical fun begin…


By tradition, we start the carnival with a pair of puzzles in honor of our 58th edition. Click to download the pdf:

How CRAZY Can You Make It


A Smith number is an integer the sum of whose digits is equal to the sum of the digits in its prime factorization.

Got that? Well, 58 will help us to get a better grasp on that definition. Observe:

58 = 2 × 29


5 + 8 = 13
2 + 2 + 9 = 13

And that’s all there is to it! I suppose we might say that 58′s last name is Smith. [Nah! Better not.]

  • What is the only Smith number that’s less than 10?
  • There are four more two-digit Smith numbers. Can you find them?

And now, on to the main attraction: the blog posts. Many articles were submitted by their authors; others were drawn from the immense backlog in my Google Reader. Enjoy!

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Have a Mathy Thanksgiving Dinner

Professional Mathemusician Vi Hart is back with more mathematical holiday fun. Enjoy!

Optimal Potatoes

Green Bean Matherole

Borromean Onion Rings

Thanksgiving Turduckenen-duckenen

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A Bit of Arithmetic Fun

Singing Banana (James Grime) recorded this video at the Mathematical Association annual conference dinner, 2011. I’ve shared it before, but that was over a holiday weekend, so many of you may have missed it. It relates, in a way, to our PUFM lesson this week.


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Super Bowl XLVI Math Worksheet and Football Comic

Lance Friedman of MathPlane.com has posted two bits of fun in honor of Super Bowl XLVI. (Click the images to go to Lance’s site.) And if you’re a homeschooler, Currclick is offering a Super Bowl Mini-Helper free this week.

NFL Math Quiz

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Square One TV: The Mathematics of Love

The Engineer was away on a business trip, and Kitten and I were in the mood to veg out on YouTube, so I hunted for some golden oldies. We used to watch Square One TV faithfully, back when my eldest was in first grade. I can’t believe they haven’t released this show on DVD!

We found recordings of my two favorite songs (“Nine, Nine, Nine” and “8% of My Love”), but the picture quality was horrible. This video was the runner-up:

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Elementary Arithmetic

My car makes a loud, scary, grinding noise, and of course the repair shop is closed until Tuesday — so instead of visiting relatives for the holiday weekend, I get a quiet “writer’s retreat” at home.

If you’re stuck at home, too, perhaps you’ll enjoy this bit of fun…

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MAA Found Math for the week of June 21, 2010

Math Teachers at Play #39

Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! If you like to learn new things and play around with ideas, you are sure to find something of interest.

Several of these articles were submitted by the bloggers; others were drawn from my overflowing blog reader. Don’t try to skim everything all at once, but take the time to enjoy browsing. Savor a few posts today, and then come back for another helping tomorrow or next week.

Most of the photos below are from the 2010 MAA Found Math Gallery; click each image for more details. Quotations are from Mike Cook’s Canonical List of Math Jokes.

Let the mathematical fun begin…

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Can You Find These AWOL Math Websites?

by √oхέƒx™ via flickr

In the course of my bloggy spring cleaning, I’ve made some terrible discoveries. Some of my favorite resources have disappeared off the internet. Or perhaps they’ve moved, and I just haven’t found their new homes.

Do you know where these websites went?

A Very Short History of Mathematics

This irreverant romp through the history of mathematics by W. W. O. Schlesinger and A. R. Curtis was read to the Adams Society (St. John’s College Mathematical Society) at their 25th anniversary dinner, Michaelmas Term, 1948.

Internet Archive’s Wayback Machine found a copy, but I’d love to replace this link with the article’s new location:

[Warning: Do not attempt to read this article while drinking coffee or other spittable beverage!]

Update: James Clare found the article’s new home here. Thank you!

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Best Math Humor, and a Few Teaching Tips

[Photo by T. Ruette.]

The Best of Blog project has become the monster that ate my life, but I am determined to finish the thing. [It’s done! :D] Meanwhile, I’m enjoying the chance to explore long-forgotten blog posts. If you’d like a laugh, try some of these…

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For Niner: A Bit of Calculus Fun

Students headed into finals week need to blow off some steam, so let’s have a little fun with calculus. Hey, Niner, does this look familiar?…

[10 Steps to Solving a Calculus Problem by hydriapotts.]

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Valentine’s Day: Say It with Music

If you have trouble seeing the video, it’s here on YouTube. For more information about the singers (and lyrics to this and other songs), check out the Klein Four webpage.

P.S.: You may also enjoy the Valentine’s Day Fail over at Abstruse Goose.

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Math Teachers at Play #8


[Photo by jaaron.]

Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! We accept entries from anyone who enjoys playing around with math, as long as the topic is relevant to students or teachers of preK-12th grade mathematics.

Some articles were submitted by their authors, other were drawn from the back-log in my blog reader, and I’ve spiced it all up with a few math jokes courtesy of the Mathematical humor collection of Andrej and Elena Cherkaev.

Let the mathematical fun begin…

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lefty clock

April Fool’s Day: Fun with Math Fallacies

Photo by RBerteig.

Take a break from “serious” math and have a little fun today with some classics of recreational mathematics. Do you have a favorite math or logic fallacy? Please share it in the Comments below.

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Happy Pi Day II

[Feature photo above by pauladamsmith.]

Now there is an ancient Greek letter,
And I think no other is better.
It isn’t too tall,
It might look very small,
But its digits, they go on forever.

— Scott
Mrs. Mitchell’s Virtual School

Time to Celebrate

Are your students doing anything special for \pi Day? After two months with no significant break, we are going stir crazy. We need a day off — and what better way could we spend it than to play math all afternoon?

If you need ideas, here are some great \pi pages:

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500 (?) and Counting

Photo by rileyroxx.

Could this be my 500th post? That doesn’t seem possible, even counting all those half-finished-and-then-deleted drafts. Well, at least it is my 500th something, according to the WordPress.com dashboard. And surely a 500th anything is worth a small celebration, right?

Maybe my students aren’t so bad, after all…

It has been awhile since I posted a link to Rudbeckia Hirta’s Learning Curves blog. Here are a few of her students’ recent bloopers:

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Quotations XIX: How Do We Learn Math?

He doesn’t learn algebra
in the algebra course;
he learns it in calculus.

I have been catching up on my Bloglines reading [procrastinating blogger at work — I should be going over the MathCounts lesson for Friday’s homeschool co-op class], and found the following quotation at Mathematics under the Microscope [old blog posts are no longer archived].

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That’s Mathematics

Things are still hectic, but at least the phone company guy found the problem and got our “extended DSL” service working. “Extended DSL” is what you get when you live out in the boonies. No guarantees that it will be faster than the ancient modem, but at least it doesn’t tie up the phone line anymore.

And it is a bit faster, so I finally get to enjoy You Tube. If the video doesn’t display properly, you can find it at this link:

Funny Math Problems

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Rewriting the History of Math

Here are a couple of quick links to math in the news:

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A Very Short History of Mathematics

This paper was read to the Adams Society (St. John’s College Mathematical Society) at their 25th anniversary dinner, Michaelmas Term, 1948. [Warning: Do not attempt to read this while drinking coffee or other spittable beverage!]

Hat tip: I found this through the math carnival at a mispelt bog.

Update: The original page has disappeared from the internet, or at least I cannot find it any more, but the Internet Archive Wayback Machine came to the rescue. After my plea for help, James Clare pointed me to the article’s new home.

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Quotations XIII: Mathematics Education Is Much More Complicated than You Expected

Registrations have been rolling in for our homeschool co-op, and the most popular classes are full already. Math doesn’t seem to be a “most popular” class. I can’t imagine why! Still, many of my students from last year are coming back for another go, and I am getting spill-over from the science class waiting list.

Anyway, I have started planning in earnest for our fall session. As usual, I look to those wiser than myself for inspiration…

Many teachers are concerned about the amount of material they must cover in a course. One cynic suggested a formula: since, he said, students on the average remember only about 40% of what you tell them, the thing to do is to cram into each course 250% of what you hope will stick.

Paul Halmos

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Math Jokes

Blame it on MathNotations and his Corny Math Jokes (which actually included one I hadn’t heard before) — or maybe I have been reading too many of Chickenfoot’s strange tales — but anyway, I’m in a mood for humor.

So here are a couple of old favorites:

Eric W. Weisstein
from MathWorld–A Wolfram Web Resource

Hat tip: These had gotten lost in the dustbunnies of my memory until I saw the Frivolous Theorem mentioned recently at Art of Problem Solving.

Edited to add: Scott at Grey Matters recently updated his Mathematical Humor post, which may be where I had originally read these. He links to several more great MathWorld jokes, including the ever-tasty Pizza Theorem.

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Have more fun on Let’s Play Math! blog: