I got a bit bored on a recent trip to IKEA, so I started looking for mathematical things to play around with. I quickly found this octagon.
There were plenty available, so I started tiling the plane.
Unfortunately, I didn’t have time to finish.
Challenge Numbers
02/12/2012 — Another Permutation Day!
Today we celebrate our second Permutation Day of the year! I call days like today permutation days because the digits of the day and month can be rearranged to form the year.
We enjoyed our first permutation day of 2012 just 21 days ago. Exactly three weeks apart! That seems unusual. I also wonder “How close could two permutation days be?”
Celebrate Permutation Day by mixing things up! Try doing things in a different order today. Just remember, for some operations, order definitely matters!
Representation Technology
GIF Animations of Simple Machines
World of Technology has several great GIF animations demonstrating some fundamental mechanics:
http://mytechnologyworld9.blogspot.com/2010/08/complicated-mechanisms-explained-in.html
Seen at right is the radial engine. The constant velocity joint is my favorite, but it’s also great to learn how a sewing machine really works!
Some great visualizations of interesting and intricate 3D geometry and engineering.
Resources
Career Advice for the Mathematics Student
There is a great set of videos from MathsCareers.org.uk that focus on mathematics in industry. The videos speak to strong math students who have questions about finding careers that utilize their mathematical abilities.
The speakers are employers and recent graduates working in technical fields, and they offer a lot of clear, thoughtful advice.
The “Why are ‘Soft Skills’ Important?” segment is particularly great to see: the speakers all stress how communcation, writing, presenting, and teamwork skills are crucial to success in technical fields. In addition, the “Why are Maths Graduates Sought After?” segment really highlights what is fundamentally important in mathematics: problem solving skills, thinking creatively, and the ability to break complex ideas down into simpler ones. These skills are prized in every field and industry.
The best advice I saw throughout the videos is to start thinking early about what really interests you and explore all the options you can. There’s more to math than just teaching and banking!
Appreciation Geometry
Torus Games
Ever wonder what it would be like to play chess on a donut? Well, wonder no further: here’s a free set of simple games all redesigned to be played on a torus.
http://www.geometrygames.org/TorusGames/
A torus is a geometric surface that is basically equivalent to a donut (the surface of the donut; not the interior). One way to [theoretically] construct a torus is to take a flat piece of paper, roll it into a cylinder by gluing the two opposite edges together, and then curling the cylinder into circle and gluing the two circular ends of the cylinder together.
So how do you play pool on a torus? As the image to the right suggests, if you shoot the ball toward the top edge of the table, it will wrap around and come out the bottom. The sides similarly wrap around, too.
This strange geometry definitely creates new strategic options in Chess and Tic-Tac-Toe, and this free set of games also include Word Search and Crossword.
A simple, thought-provoking idea. And free and fun to boot!