Technology

Meet the Egg-Bot

This is pretty awesome: an assemble-yourself perhipheral that allows you to draw on spherical/ellipsoidal/other objects: the egg-bot!

http://egg-bot.com/

Plug it in to your USB port, render your drawing in a freeware illustration program, and voila! And it’s open-source: both hardware and software.

There are so many interesting things that could be done with the egg-bot: sketching grid lines on ellipsoids to illustrate parametric surfaces, investigating how projection affects map-making, graphing closed-curves on golf balls, or maybe just creating the greatest Easter Eggs in human history.

By patrick honner, 15 yearsSeptember 18, 2010 ago

3-D Printing

The NYT has an interesting article about the increased use of 3D printers in commercial applications. Nowadays, companies are using the technology to build custom furniture, low-cost prosthetic limbs, and even housing components.

Basically, the geometry of the object is laid-out in software (like Autodesk), and the “printer” then translates the design into reality by extruding layers of hot plastic, one after another, building the object up essentially by printing one cross section at a time.

It seems that the process is becoming more commonplace and less expensive, opening the door for a wider array of commercial uses. I’ve seen students using this technology, and it is a pretty remarkable advance. I believe you can even have a custom-designed plastic guitar built!

By patrick honner, 16 yearsSeptember 15, 2010 ago

Application Technology

Real-Life Transformers

This is an absolutely mind-blowing idea: robotic “paper” that can fold itself into an arbitrary three dimensional object. Be sure to watch the short video accompanying the article.

http://web.mit.edu/newsoffice/2010/programmable-matter-0805.html

Tying (or folding?) all of the physics and engineering together here is the mathematics of origami. How can you fold a square sheet into a boat? A plane? A tetrahedron? A super-intelligent robotic giraffe?

By patrick honner, 16 yearsSeptember 1, 2010 ago

Game Theory Technology

What is the Hardest Word to Guess in Hangman?

In 2007 Jon McLoone used Mathematica to create a Hangman game pitting the computer guesser against the human word-selector. As his daughter became old enough to play against the demonstration, and old enough to get frustrated with the computer guesser always winning, she asked her dad the obvious question: to beat the computer, what are the best words to choose?

Surprised that he had not considered such a good question himself, McLoone set about playing 15 million games of Hangman (automated, I imagine) using every word in the dictionary and arming the computer with a number of different letter-guessing-strategies. The word that the computer failed to guess the most often was somewhat surprising.

So what kinds of strategies make the best guesser? And to counter that, what kinds of strategies should the word-selector employ?

By patrick honner, 16 yearsAugust 30, 2010 ago

Application Technology

P v NP and Collaborative Mathematics

This is a nice article in the NYT about a recently proposed solution to the famously unsolved mathematical question “Does P = NP?”

http://www.nytimes.com/2010/08/17/science/17proof.html

Essentially this question is about how long it takes to solve certain kinds of problems: if a proposed solution to a problem can be checked in some reasonable amount of time, does that mean we can always solve the problem in a reasonable amount of time? [Warning: the definition of reasonable here may seem unreasonable.]

For example, it doesn’t require many operations to determine whether or not 7411 divides 748511; even by hand, you can work it out in a few steps. It requires significantly more operations, however, to find the prime factors of, say, 837751. Essentially, P v NP asks “are problems that can be checked by computers (maybe lots and lots of computers working in parallel) necessarily solvable by computers?” It is still an open question.

Another fascinating aspect of this particular open question is the role that the internet has played in bringing great mathematical minds together. Proposed solutions can be instantly accessed and vetted by those capable of evaluating the arguments. Such a community can work quickly and efficiently, not just to ascertain a proof’s validity, but to improve and refine it together.

By patrick honner, 16 yearsAugust 26, 2010 ago