Wild About Math! Making Math fun and accessible

From “God Plays Dice,” an interesting geometry problem

A clever geometry problem:

Here's a cute problem (from Robert M. Young, Excursions in Calculus, p. 244): "What is the average straight line distance between two points on a sphere of radius 1?"

(Answer to follow.)

Note the number of comments with different answers.

"Excursions in Calculus," from what I could see at Google Books, looks like it has many interesting problems.

New math book makes its debut on Fibonacci Day

Today is 11/23, which some call Fibonacci Day. I received an email a few days ago from a Mr. Tony Gonzalez who has translated a very popular Japanese math book into English. I did receive a PDF review copy and liked what I saw but will wait to receive a printed copy before reading and reviewing. Here's Tony's email and press release. Tony, I wish you much success.

---

Hi, Sol.

My name is Tony Gonzalez. I'm a former math teacher (which is how I came to know your blog), but I'm now working mainly as a translator and publisher. I'm writing to let you know about a book that I translated and my company will be publishing next week, "Math Girls". We will be releasing the book on 11/23, "Fibonacci Day", perhaps making it a good topic for a blog post on that day?

I'm taking the liberty of sending you a press release announcing the publication (below). That should give you the rough details, but if you have any questions do please feel free to contact me by email, or you can get more information about the book at our website, bentobooks.com.

Thank you!

―Tony

_______________________________________

Press release
--- For immediate release ---

Another clever exploration by James Tanton

I really enjoy James Tanton's Math explorations because they tend to be easy to describe and rich in exploration value. Here's such an exploration:

The problem statement is very simple. Is there a way in which we can say that there are more triangular numbers than square numbers? If so, how do we compare the sizes of the two sets? Can we compute the ratio of triangular to square numbers where both T(n) and S(n) are less than an arbitrary constant? Can we generalize what we find for other polygonal numbers?

This is a great exploration!

A great triangle exploration

Mr. Honner has a great exploration at his blog. It starts with a simple question, that has subtlety and depth to it: How do you determine the "equilateralness" of a triangle? Can you compare two triangles and determine which is more equilateral than the other?

The post introducing the investigation is here. I encourage you to do your own exploring before reading the 28 comments which are rich in ideas. Once you've played around with the ideas yourself then take a look at what Mr. Honner came up with in Part II.

I love this kind of exploration for a number of reasons:

1. The question is simple to understand.
2. Just like in the real world there are multiple approaches.
3. It's not clear that there is a right solution but some are better than others.
4. Students get to think about properties of triangles in new and different ways.
5. Students get to think deeply about the notion of "metric."
6. This problem is more interesting than many other geometry problems I've seen.

Nice!

Seeking interesting math factoids about the number 11

I'll be doing a brief talk at a conference next month, on 11/11/11 at 11:11AM, about the number 11. If you know interesting factoids about 11 (or about 1111...) that I could include in the talk I'd greatly appreciate it.

One factoid is that 1/(1+(1/(1+1/(1+... converges to the golden ratio.

Another is that if a number is divisible by 11, reversing its digits will result in another multiple of 11.

Other ideas?

Thanks.

A practical math test

From xkcd.

Hat tip to Jon McLoone.

Stephen Wolfram on Steve Jobs and his influence on Mathematica

Stephen Wolfram wrote a nice article on his personal blog: Steve Jobs: A Few Memories.

Real-world math activities at yummymath.com

[ Editor's note: Brian at Yummymath contacted me on twitter to introduce me to his web-site. I hadn't heard about it so I went to check it out. I liked what I saw and I offered to promote the site if he wrote a guest article. Here's the guest article. ]

Making Math Meaningful to Students: www.yummymath.com

Have you ever heard math students ask “Why do we need to learn this?” or “When am I ever going to use this?” There is a relatively new website, www.yummymath.com whose purpose is to help educators answer those exact questions. The website provides authentic and timely math activities that relate to real life happenings. Math activities are written
about current events that are of interest to students, including sports, technology, movies,
big news stories and holidays. While the activities are written about topics that kids can
relate to, the activities focus on number sense reasoning, problem solving and conceptual
development of math concepts.

Yummymath activities incorporate real life data. For example, a recent activity was
written about the NFL to coincide with the start of the NFL season. The activity was
centered on actual NFL team values, something that is relevant to many students. The
activity represented actual NFL franchise values in bar graph form and focused on
visualizing the concept of the mean. Other notable recent activities include an analysis of
the Harry Potter movie franchise, which coincided with the final Harry Potter movie, and
a “hurricane math” activity that coincided with Hurricane Irene.

Two new videos by James Tanton

After a hiatus of several months Dr. Tanton is making videos again. Here are two new ones.

Lulu has two children. You are told that at least one of her children is a boy who was born on a Tuesday. What is the probability that her other child is also a boy?

The answer will surprise you!

Here is a cute geometry puzzle: Imagine you are an archeologist and have come across just a small section of a rim of an ancient wheel. What size wheel did it come from?

This is a great puzzle to give to geometry students too. Hand out a picture of an arc of a circle and ask if is possible to find the measure of that arc using only basic tools - and them have students actually do it.

An infinite number of mathematicians walk into a bar …

From Instapundit

Math joke from Anna, the bartender and civil engineering student: an infinite number of mathematicians walk into a bar. The first one tells the bartender he wants a beer. The second one says he wants half a beer. The third one says he wants a fourth of a beer. The bartender puts two beers on the bar and says “You guys need to learn your limits.”

Hat tip to Algut Runeman at MathFuture.