A nice proof without words
Here's a very cool proof without words by Burkard and Marty.

Can you figure out what this proof without words illustrates?
Math Pickle live and interactive talk 7/27
There's a live talk tonight by Gordon Hamilton of Math Pickle, which is one of my very favorite Math sites.
Math Pickle: Million-dollar problems with grades 7 to 12.
During the event, Gordon Hamilton will talk about solving real million-dollar problems with middle and high school students.
The recording will be at
http://mathfuture.wikispaces.com/MathPickleGrades7to12
All events in the Math 2.0 weekly series:
http://mathfuture.wikispaces.com/events
The perfect formula for toast
From the BBC:
Food scientists at the UK's University of Leeds have developed a formula for making the perfect piece of toast.
The equation - which details butter and toast temperature - took three months and cost £10,000 to develop.
Researchers' found that people think the perfect piece of toast should have partly melted butter patches on it, improving its taste and texture.
For this to work, the butter should be applied at fridge temperature of five degrees Celsius, the equation shows.
The formula was developed following research commissioned by the butter brand Lurpak made by Leeds-based Arla Foods. More.
Engaging summer Math activities at CTK Insights
Alexander Bogomolny has a number of outstanding "Cut-the-knot" sites that educate and inspire Math teacher and students. One of his sites, CTK Insights, has a great twelve part series of engaging Math activities for the summer break.
Here are the introductory paragraphs for the first three activities. To find the other nine just go to the day 3 activity and follow the link at the bottom of that article to get to day 4, follow the day 4 forward link to day 5 and so on.
Day 1
Mathematics is certainly not (only) about counting, graphing and solving equations. I do not believe that every child can reach beyond those. I do not believe that a child who does not show an inclination to dig deeper into math mysteries lacks in intellect or creativity. I do think that it is worth trying to find out. I child who gets excited on a discovery of uncommon patterns will have enriched his/her life experiences. [ Full article ]
Day 2
An engaging activity has been described by Martin Gardner in his Mathematical Games column in Scientific American, v 201, No 6, Dec 1959 and later included in one of his collections, New Mathematical Diversions. Rather recently, an upgraded variant has emerged as the Japanese ladders game. Amazingly, neither Gardner has mentioned the Japanese sources in 1959, nor half a century later his article has been referred to in the latest development. [ Full article ]
Day 3
Counting a group of objects can be done in many different ways. The most fundamental idea is that counting is at all possible in the sense that, regardless of the manner in which it is performed, the result is always the same. For example, place random numbers in a rectangular array and then compute separately the column and row sums. Then adding the column sums gives the same total as adding up the row sums. For little children the array and the numbers inside should be small. Letting all the numbers be 0 or 1 not only makes the activity more accessible to younger children but also adds a twist with a mathematical flavor. [ Full article ]
Find me on LinkedIn
I'm about to make a big change in my life to have my work be aligned with my deep love of Math. Part of that change is going to be about having richer connections with other people who love Math. If you and I have made a nice connection through this blog and if you are a Math person, especially someone who is working to popularize Math, I'd love to be connected with you on LinkedIn. Just click on this link and request that I add you to my network. You can use the email sol dot lederman at gmail dot com. I find LinkedIn to be a great way to connect with people even when they move or change jobs so it's a great way to make connections and to keep them.
Oh, and I'm not closing down this blog.
13 surprising Fibonacci appearances
One of my great Math heroes, James Tanton, has written a great essay that provides thirteen examples of the Fibonacci sequence appearing in strange and unexpected places.
"I have YouTube videos presenting some surprising appearances of the Fibonacci numbers and I’ve been tweeting little puzzlers about the Fibonacci numbers for some time. Here, at long last, is my list of Fibonacci results, and a clever way to prove them all. Some of these puzzlers are classic, some are new to the world."

Tanton tantalizes with an Euler gem
James Tanton has produced another great video, this one on a very intriguing partitioning problem with a very clever solution.
There are four ways to break the number 6 down into a sum of distinct numbers: 6 = 5+1 = 4+2 = 3+2+1. There are four ways to break the number of 6 down into odd numbers: 5+1 = 3+3 = 3+1+1=1 = 1+1+1+1+1+1. It is no coincidence that the count of ways are the same. In 1740 Euler proved it will always be so! His proof is ingenious and here it is! I've also added a challenge at the end to discover other bizarre results like this one. (I bet you can do it!)
I thoroughly enjoy Tanton's ability to find interesting problems and make them accessible to those of us who aren't professional mathematicians. In fact, all of Tanton's videos are accessible to motivated high school students.
I was delighted to see Mr. Tanton included in Math Pickle's page of inspired people.
A MathPickle guy to the core - James Tanton is a fully fledged mathematician with a fantastic web site that offers videos for school teachers and first year university lecturers. Visit his web site here.
Geometry at the Royal Ballet
I received an email asking me to promote a ballet at the Royal Opera House that is rich in geometry. Here's the email.
Dear Sol,
The Royal Opera House is currently preparing to stage a triple bill ballet programme opening this Saturday, 28th May, featuring Frederick Ashton’s Scènes de ballet. This exceptional production introduces an intriguing complexity around geometrics with dancing movements creating a geometrical pattern.
We are very interested in attracting both old and new audiences, and particularly interesting is the geometricity of the ballet, which we would love audiences to experience.
We think this could be of an interest to your readers. You can find more information about the production on our website.
Would it be possible for us to leave a comment on your blog inviting audiences to these shows, or could you cover the upcoming production yourself?
Kind regards,
Anastasia
Calling all Math bloggers who tweet
[ Update 5/25/11 ] I've deleted the Mathtweet group for several reasons which I may or may not blog about sometime.
I notice that my new Playing With Mathematica blog gets a fair amount of traffic from twitter. I'd like more of that traffic so I've come up with an idea and a plan that will serve all of us.
How about if those of us who are Math bloggers tweet each other's blog articles? Friendfeed makes it easy to create a private (invitation only) group where we can post our latest Math blog articles so I've created such a group.
The commitment for anyone in the group is to tweet a large percentage (or all) of the links members post. If you don't like an article then don't tweet it. If you don't like most of what people post then this group isn't for you. While the commitment is for all of us to post to twitter, you are also welcome and encouraged to post to other social networks. Friendfeed is free (say that three times fast) and makes it very easy to post to a handful of social networks.
I'm the owner of the group so you need to email me at sol dot lederman at gmail dot com to receive an invitation. Please include your twitter id so that I can verify that you're active on twitter. If I don't know your blog then please send me a link to that as well so I can check it out. If your blog is heavy on commercial and light on content then I won't send you an invite. I want to have members with content that people feel good about promoting. And, if I discover that some members are receiving benefits but aren't tweeting very much then I'll drop them from the group.
Send me an email if you'd like an invite or if you have any questions.
Food scientists at the UK's University of Leeds have developed a formula for making the perfect piece of toast.