Wolfram Computation Meets Knowledge

Date Archive: 2010 August

Education & Academic

Tetrahedra Packing

Back in 325 BC, Aristotle talked about which polyhedra can fill space, and noted that regular tetrahedra could fill space. Around 1470 AD, Regiomontanus showed that Aristotle was wrong. He also found the spot where a statue on a pedestal appears the largest, as shown in the Demonstration “The Statue of Regiomontanus”. In 1896, Minkowski tried to solve the problem of how well tetrahedra could pack. He failed. But he did introduce many valuable tools to math, such as “The Minkowski Sum of Two Triangles”. In 1900, Hilbert tried the problem of tetrahedra packing and included it as a part of problem 18 in his list of unsolved problems. Hilbert is also famous for the Hilbert curve and “The Hilbert Hotel”.
Education & Academic

A Call to STEM Teachers: What’s Your Plan for Back to School?

It's back-to-school time in the U.S., and we're starting our trips to meet with educators ranging from the high school to post-graduate level. Many schools will be hearing about Mathematica for the first time, while others have requested specialized training to expand Mathematica usage in their work and in the classroom. Several schools are taking advantage of a program created in response to a recent domestic focus on science, technology, engineering, and mathematics (STEM) education called the STEM Education Initiative.
Best of Blog

25 Best Hangman Words

A simple question from a six-year-old about hangman turned into another analysis obsession that made me play 15 million games of hangman recently. Back in 2007, I wrote a game of hangman for a human guesser on the train journey from Oxford to London. I spent the time on the London Underground thinking about optimal strategies for playing it, and wrote the version for the computer doing the guessing on the return journey. It successfully guessed my test words and I was satisfied, so I submitted both to the Wolfram Demonstrations Project. Now, three years later, my daughter is old enough to play, but the Demonstration annoys her, as it can always guess her words. She asked the obvious question that never occurred to me at the time: "What are the hardest words I can choose, so that I can beat it?"

Nine Cool Points on the Complex Plane

Pick some points at random. What can be said about them? What curves go through them? What polygons and polynomials can be made from them? Deep mathematics lurks behind these questions, but the answers can be explored just by moving points around within some Wolfram Demonstrations. Simply by moving points you can see deep mathematics in action. For example, "Five Points Determine a Conic Section" (Ed Pegg Jr and Paul Abbott) uses a matrix determinant on five points to produce an equation going through all five points.