When working the set, you will realize very quickly that all the answers are the same. You could easily "finish" the problems by copying the same answer in each slot. But that would be totally unsatisfying.

When Anthony worked the problems and got some different answers, he was puzzled. "I know I got it wrong. What am I missing?" I have never seen Anthony work so hard to double-check his work.

Even better, after he got the right answer several times, he felt compelled to understand why it was the same. "I got it, and I see how it is related to seven, but where is the three?" He was really taking a new approach to math.

What you learn from this little problem set goes way beyond combinatorics:

The lesson is that math is not about the answer.

So for the 3d-unaware student I have put together a super-compressed introduction to the basics of middle-school solid geometry, with a high level of challenge for intended for math team middle schoolers who are trying to learn everything they need to know in a week. The packet here has only 4 pages and 27 problems, with an extra 6 pages for solutions to check after you are done. The easy bits are skipped, and in exchange you get to see some common types of tricks as well as a hint of insight beyond basic prisms, pyramids, cones and spheres.

Here it is: Solid Geometry Facts and 3³ Problems and solutions.

Sometimes math team practices are disastrous, and I just want to let all my wild gazelles outside to play in the sun. And yet other times the classroom is exciting and magical and packed with learning, with the kids buzzing about primes or permutations by the end of the hour. It's not just the people in the room: we are the same every week.

But every week is different. What is happening?

Solution:

Real solution:

The real question is, how the heck do you write all that notation in HTML? This problem is the bane of math teachers everywhere. But I did it here in about 5 minutes using a wonderful new tool that was released yesterday. Here is how.

The solution is to use mimeTeX notation via the brand-new version of the Google Chart Server. You can use the mathematical notation editor I have posted here - it will interpolate formulas within $dollar signs$ into HTML, generate the right <img> tags, and help insert css styles based on the image heights to get your vertical-alignment approximately right.

It helps if you know TeX syntax ahead of time, but even if you don't, it's not hard to learn what you need. When you go to davidbau.com/formula, it starts you off with a simple example.

Copy and paste your HTML.   QED.]]> 2010-02-12T14:36:57-05:00 http://davidbau.com/archives/2010/02/09/second_coming_of_wydenbennett.html Republicans, preparing for Obama's Healthcare Summit, clearly want to avoid looking as foolish as they did when hosting Obama at their House issues summit. "Start over," seems to be the new mantra. GOP proposals for preconditions before talks just make... 360@http://davidbau.com/ Republicans, preparing for Obama's Healthcare Summit, clearly want to avoid looking as foolish as they did when hosting Obama at their House issues summit. "Start over," seems to be the new mantra.

GOP proposals for preconditions before talks just make them look like ridiculous Iranian nuclear negotiators; if Republicans continue on this path, they are playing into Democratic strategies and providing political cover for Democrats to pass healthcare by reconciliation next month.

Democrats look serious, and Republicans look like Ahmadinejad. Any good hawk knows that in that situation, stiff and swift sanctions are justified.

Here is an excellent new tool for reading the jQuery source, thanks to James Padolsey.

Food for Thought: International jQuery Use

On going back and looking at the top regions in which 'jquery' is a topic of Google searches, I find it interesting - and maybe worrying for U.S. internet innovators - that none of the top 6 jQuery cities of the world are in the U.S...

Many games that use weak random number generators have been cracked by exploiting their lack of randomness, and recently it has even been shown that it is possible to guess your 'random' Social Security Number given information about the time and location of your birth. To resist this type of attack, you want do better than a linear congruential PRNG seeded with the current time. Explanations below.

A Math.seedrandom Function

This script defines a function Math.seedrandom() that replaces Math.random with a seeded sequence of your choice. You use it by including seedrandom.js and then calling

Math.seedrandom('any string you like');

Next time you call Math.random(), you will get a deterministic sequence of results that can be reproduced at any time on any browser by calling seedrandom with the same string (with the example seed above, you will always get 0.4514661562021821, 0.06749172707294095, 0.8393296727715214, etc).

The code uses RC4 as the pseudorandom number generator, so the randomness is a bit better than what you get from most browsers' built-in Math.random. But since it does all the computation in javascript, it is also is 3-10x slower.

A minified version of seedrandom.js (using the Google Closure Compiler) is about 1K.

The code also supports automatic seeding...

There is a whole world outside China and outside Fox News that is starkly different and a bit closer to reality.

But when you realize that Fox is actually the most trusted news brand in the U.S. today, you can get an appreciation for the success that a censored Chinese media can have inside the world's largest society. The effects of squashing dissent in the name of nationalism are not "very limited"...

But everybody around here is a Democrat!

But it's turning out to be a nailbiter, so she's going to vote after all.

Go vote.

Perhaps torture of lawyers is routine at Microsoft; it is a bit unusual at Google.

Rearrange the letters SEARCH ENGINE to make a phrase representing the displeasure of a nation.

h/t Rachel Grey

As the world's most famous search engine company, supposedly its defense capabilities should also be very strong. If the defense system is really flawed, it is necessary to strengthen preventive measures, while passive withdrawal only shows incompetence, but also contributes to the arrogance of hackers, which is very inconsistent with Google's prominent identity.

Think about that for a moment.

Google caught the electronic equivalent of a Chinese drone attack, using sophisticated weapons and circumnavigating layers of defenses. Imagine if the Chinese People's daily had issued a similar statement about the lack of antiaircraft missiles atop the World Trade Center or lax security of United Airlines.

The Google attack was not merely a picked lock.

As some details come out, it is clear that the attacker must have had access to many resources: the ability to make a custom virus on a previously unknown bug in IE; a familiarity with the architecture of Google's highly protected internal systems; and the knowledge of Chinese dissident private email addresses. An expert has called the attack on gmail "incredibly sophisticated, the kind only seen in the government and defense industrial sector."

What seems increasingly flawed is the premise that it is possible to operate an honest business under the thumb of Chinese authorities.

A Few Thoughts and Lots of Links

Commentators who interpret Google's policy change as a retreat in the face of stiff competition from Baidu miss the point. Despite serious obstacles, Google has steadily gained share after entering China in 2006, and there are a billion financial reasons to stay and compete.