Reimann-hexagon

Math Teachers at Play #70

800px-Brauchtum_gesteck_70_1[Feature photo above by David Reimann via Bridges 2013 Gallery. Number 70 (right) from Wikimedia Commons (CC-BY-SA-3.0-2.5-2.0-1.0).]

Do you enjoy math? I hope so! If not, browsing this post just may change your mind.

Welcome to the 70th edition of the Math Teachers At Play math education blog carnival — a smorgasbord of 42+ links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college. Let the mathematical fun begin!

By tradition, we start the carnival with a puzzle in honor of our 70th edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

Click here to continue reading.

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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?” …

15-eu-must-be-clidding

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


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Math That Is Beautiful

One of the sections in my book encourages parents to make beautiful math with their children. If you have trouble imagining that math can be beautiful, check out this video:

How many mathematical objects could you identify? Cristóbal Vila describes them all on his page Inspirations from Maths.


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HexaFlexaParty This Weekend!

Sunday, October 21, is the worldwide hexaflexagon party in honor of Martin Gardner’s birthday. Gardner’s article about hexaflexagons launched his career as a recreational math guru who inspired people all around the world to love math.

Here’s how to join in the fun:

Hexaflexagon History

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What Is a Proof?

I’ve been enjoying the Introduction to Mathematical Thinking course by Keith Devlin. For the first few weeks, we mostly talked about language, especially the language of logical thinking. This week, we started working on proofs.

For a bit of fun, the professor emailed a link to this video. My daughter Kitten enjoyed it, and I hope you do, too.

Full lesson available at Ted-Ed.


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Who Killed Professor X?

What a Fun Book!

professorX

Who Killed Professor X? is a work of fiction based on actual incidents, and its heroes are real people who left their mark on the history of mathematics. The murder takes place in Paris in 1900, and the suspects are the greatest mathematicians of all time. Each suspect’s statement to the police leads to a mathematical problem, the solution of which requires some knowledge of secondary-school mathematics. But you don’t have to solve the puzzles in order to enjoy the book.

Fourteen pages of endnote biographies explain which parts of the mystery are true, which details are fictional, and which are both (true incidents slightly modified for the sake of the story).

I ordered Who Killed Professor X? from The Book Depository (free shipping worldwide!), and it only took 5 days to arrive here in the middle of the Midwest. My daughter Kitten, voracious as always, devoured it in one sitting — and even though she hasn’t studied high school geometry yet, she was able to work a couple of the problems.


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Happy Birthday, Einstein (Part 3)

In 1905, when he was 26 years old, Albert Einstein rocked the scientific world with a series of papers that changed our understanding of the nature of the universe. At MinutePhysics, the celebration continues:

More Einstein Videos


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Happy Birthday, Einstein (Part 2)

Today would be Albert Einstein’s 133rd birthday. At MinutePhysics, the celebration continues:

More Einstein Videos


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Happy Birthday, Einstein!

March 14th is Pi Day, and it’s also Albert Einstein’s birthday. In honor of Einstein, MinutePhysics is posting a series of videos on his “wonder year” of 1905, when he published several papers that eventually earned him the Nobel Prize.

More Einstein Videos


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What I’m Reading: Fermat’s Enigma

Homeschooling is much more than just doing school at home — it’s a lifelong lifestyle of learning. And thanks to the modern miracle of inter-library loan, even those of us who live in the middle of nowhere can get just about any book sent directly to our tiny home-town libraries.

As I mentioned in Math Teachers at Play 46, I’m trying to add more living books about math to our homeschool schedule, including my own self-education reading. So, a copy of Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem finally showed up at my library, and I am thoroughly enjoying it.

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Review/Giveaway and Fibonacci Puzzle

Thanks to author Keith Devlin’s generosity, I am giving away FIVE copies of his new e-book Leonardo and Steve: The Young Genius Who Beat Apple to Market by 800 Years (at the end of this review post), PLUS a signed copy of his latest print book, The Man of Numbers: Fibonacci’s Arithmetic Revolution.

What Leonardo did was every bit as revolutionary as the personal computer pioneers who in the 1980s took computing from a small group of “computer types” and made computers available to, and usable by, anyone. Like them, most of the credit for inventing and developing the methods Leonardo described in Liber Abbaci* goes to others, in particular Indian and Arabic scholars over many centuries. Leonardo’s role was to “package” and “sell” the new methods to the world.

The appearance of Leonardo’s book not only prepared the stage for the development of modern (symbolic) algebra, and hence modern mathematics, it also marked the beginning of the modern financial system and the way of doing business that depends on sophisticated banking methods.

Keith Devlin
Fibonacci’s ‘Numbers’: The Man Behind The Math
excerpt from The Man of Numbers

* Leonardo of Pisa, also known as Fibonacci, used two b’s in the word “calculation” (abbaci) to distinguish his methods from the use of an abacus.

Can You Solve This Fibonacci Puzzle?

If you want a chance to win a personally signed copy of The Man of Numbers: Fibonacci’s Arithmetic Revolution, all you have to do is solve this riddle.

Email me your answer.

Do NOT give your answer as a comment here! If that email link doesn’t work for you, then copy my address by hand: lets play math [no spaces] at gmail dot com.

Here is the puzzle:

The Fibonacci sequence arises in the solution to a problem about a breeding rabbit population that Leonardo gave in Liber Abbaci.

But there is evidence that in another book he gave the problem in terms of different creatures. What were they?

[Hint: The answer is in the e-book, Leonardo & Steve. But this is a no-purchase-necessary contest: There are at least two places to find the answer online, if you search carefully.]

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Free Math from Dover Publications

I love Dover books, don’t you? They publish so-o-o-o-o many interesting titles at reasonable prices. I always have several Dover books on my wishlist, waiting for my next free gift card from Swagbucks.

But you don’t have to wait to enjoy free math from Dover books. Sign up for the Dover Sampler, and each week they will send an email with links to content from all sorts of books. Or try the Dover Children’s Sampler and Dover Teacher’s Sampler for coloring books, mazes, literature, and more. All the Dover samplers are completely free, and you can cancel at any time.

From Last Week’s Sampler

Last week’s email included a section on “Exploring Mathematics”:

And that’s only the beginning. Below, I’ve listed a wide variety of math-related links collected from past samplers (though be warned: Dover does change its page links from time to time). Download, print, enjoy!

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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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Bloggy Spring Cleaning Continues

Still on course with my state-sponsored blog overhaul, and Google Reader insists on displaying every old post as new. What a nuisance! The email feed seems unaffected. (And not everyone is having the problem with Reader, either — see Comments below.)

Amazon won the reader poll (and it’s my favorite, too), so I’m converting all my old affiliate book links to just-plain Amazon links. At the same time, I’m checking for dead links and other dust bunnies among the old posts. I’ve worked my way up to June 2007 — four more years to go — and then I’ll start on my blogroll (a monster task!) and other pages.

Like normal housecleaning, it never ends …

Does Anyone Know Where the La Habra Math Timeline Went?

The worst news so far is that the La Habra Math History Timeline has disappeared. What a shame! Does anyone out there know where it might have gone? I would love to link to its new site.

Thanks to the Wayback Machine, here’s a glimpse at the old site. Math discoveries, publications, and other tidbits — from paleolithic number bones to the present:

I changed the links on my Math Resources page to the wayback pages, too. My apologies to those who got sent to a junk site by the old, defunct links.


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Renée’s Platonic Mobile

Alexandria Jones struggled to think of a Christmas gift that a one-month-old baby could enjoy, but finally she got an idea.

She cut empty cereal boxes to make regular polygons: 6 squares, 12 regular pentagons, and 32 equilateral triangles. Using small pieces of masking tape, she carefully formed the five Platonic solids. Then she mixed flour and water into a runny paste. She tore an old newspaper into small strips and soaked them in the paste. She covered each solid with a thin layer of paper.

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Egyptian Math: Fractions

I have been enjoying James Tanton’s website. In this video, Tanton explains a foolproof method for creating Egyptian fractions:

See more posts on Egyptian math.


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Free Math History: Number Stories of Long Ago

David Eugene Smith tells how arithmetic developed in different cultures. The file is available from Google Reader, if you are in the U.S., but international readers have had trouble finding the book. If you’d like to download a copy, it will be featured this Monday at the Homeschool Freebie of the Day site.

Math History from the Story Teller

“Night after night he told these tales of the ages past, stories unlike the make believes they had often heard, stories of what might really have happened when the world was young, stories that the Crowd said were ‘different’ because they told of much that was new, much that was curious, and much that was interesting. . . .”


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Math Project: Measure the Earth

Tomorrow, September 23, is the equinox — when night and day are equally balanced (or would be, if the sun appeared as a point, rather than a disc). If we lived on the equator, the sun would appear directly overhead at noon and would cast no shadow. Therefore, it’s a great day to perform Eratosthenes’ experiment of measuring the earth:

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Math History Tidbits: The Battling Bernoullis

July 27th is Alex’s birthday. She shares it with Johann Bernoulli, an irascible mathematician from the late 17th century. This coincidence intrigued her enough that she wrote a research paper on Johann and his mathematical brother, titled “Jeering Jacob and Jealous Johann.”

Of course, to make the alliteration work, she had to mispronounce Johann’s name — but she figured he kinda deserved that. Read the historical tidbits below to find out why one writer said the Bernoulli brothers were “the kind of people who give arrogance a bad name.”*

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One Day Only: Number Stories of Long Ago

For all those who missed it last time, now is your chance: Number Stories of Long Ago will be available Tuesday, January 20, from Homeschool Freebie of the Day.

David Eugene Smith tells stories set in different historical eras, showing how different mathematical concepts were developed and became a part of civilization. Wonderful!

For Those Who Missed It

If you missed the Homeschool Freebies edition, Number Stories of Long Ago is also available as a real book or (at least in the U.S.) as a scanned library book from Google Books.

Or try downloading a copy for your Kindle (or Nook, Kobo, Sony Reader, etc.):


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Math History Tidbits: Agnesi, Euler, and China

Alexandria JonesI’ve fallen behind on my project of transcribing my Alexandria Jones stories. Finally, here are a few more tidbits from math history, along with links to relevant Internet sites and a few math puzzles for your students to try.

I hope you find them interesting.

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A Mathematician for President

[Image courtesy of the Images of American Political History.]

In 1876, a politician made mathematical history. James Abram Garfield, the honorable Congressman from Ohio, published a brand new proof of the Pythagorean Theorem in The New England Journal of Education. He concluded, “We think it something on which the members of both houses can unite without distinction of party.”

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Number Stories Is Back, Very Limited Time Only

If you missed Number Stories of Long Ago last time, it is available as a free downloadable pdf file at the Homeschool Freebie of the Day Labor Day Weekend/End of Summer Bash.

This offer should work for those who live outside the U.S. and were unable to read the Google Books file.

But act quickly!

The offer is only good “until Monday night” — and I don’t know which time zone they’re in.


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Free Math History: Number Stories of Long Ago

If you teach elementary children, check out this read-aloud math history resource from Homeschool Freebie of the Day:

Number Stories of Long Ago
by David Eugene Smith

[This download is available for one day only. If you missed it, see the end of this post for other ways to get the book.]

From the Preface

“These are the stories that were really told in the crisp autumn evenings, the Story Teller sitting by the fire that burned in the great fireplace in the cottage by the sea. These are the stories as he told them to the Tease and the rest of the circle of friends known as the Crowd. Sitting by the fire and listening to the stories, in the lights and shadows of the dancing flames they could see the forms of Ching and Lugal and all the rest with their curious dress of long ago…”

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euclid

Euclid’s Geometric Algebra

Picture from MacTutor Archives.

After the Pythagorean crisis with the square root of two, Greek mathematicians tried to avoid working with numbers. Instead, the Greeks used geometry to demonstrate mathematical concepts. A line can be drawn any length, so straight lines became a sort of non-algebraic variable.

You can see an example of this in The Pythagorean Proof, where Alexandria Jones represented the sides of her triangle by the letters a and b. These sides may be any length. The sizes of the squares will change with the triangle sides, but the relationship a^2 + b^2 = c^2 is always true for every right triangle.

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Math History on the Internet

[Image from the MacTutor Archive.]

The story of mathematics is the story of interesting people. What a shame it is that our children see only the dry remains of these people’s passion. By learning math history, our students will see how men and women wrestled with concepts, made mistakes, argued with each other, and gradually developed the knowledge we today take for granted.

In a previous article, I recommended books that you may find at your local library or be able to order through inter-library loan. Now, let me introduce you to the wealth of math history resources on the Internet.

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black-rooster

Hooray for (Math) History

Photo by Benimoto.

John Napier foiled a thief with the aid of logic and a black rooster. For this and other acts of creative problem solving, his servants and neighbors suspected him of witchcraft.

What does this have to do with mathematics?

Math was Napier’s favorite hobby. He invented logarithms to help people handle large numbers easily, and he even created a calculator out of a chessboard. [See how it works: addition, subtraction, multiplication.]

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