Resources

Combinatorial Bracelets

This is another wonderful visual demonstration from Jason Davies:  a combinatorial bracelet generator.

http://www.jasondavies.com/necklaces/

Combinatorics is the mathematics of counting things, and one of the classic “advanced” counting problems is this:  given a certain number of beads of various colors, how many different bracelets can you make?

The problem may seem easy enough, but it becomes quite difficult when you start to understand what “different” really means.

For example, if you turn one bracelet into another by rotating it, then those two bracelets aren’t different.  Even more complicating is that if you can obtain one bracelet from another by flipping it over, then they are also the same!

This visualization can really help develop a sense of the complicated symmetries at work here.

Click here to see more in Representation.

www.MrHonner.com

By patrick honner, ago

Mathematics Awareness Month

April is Mathematics Awareness Month.  Sponsored by professional and educational organizations like the American Mathematical Society, the Mathematical Association of America, the American Statistical Association,  and the Society for Industrial and Applied Mathematicians, Mathematics Awareness Month aims to increase awareness and promote the utility of mathematics through activities, contests, and public discourse.

This year’s theme is Mathematics, Statistics, and the Data Deluge.  The application of statistics is playing an ever-increasing role in both theory and practice, and the overwhelming amount of data available to us now is dramatically changing what we can do and how we do it.

There are a number of linked resources to this year’s theme at the Math Awareness Month website.  And this story from Stephen Wolfram offers an interesting tale about the unexpected application of personal data.

In addition, there are plenty of resources to previous MAMs here, like “Mathematics and Sports” and “Mathematics and the Internet” here:  http://www.mathaware.org/about.mam.html#previous.

How will you be celebrating Mathematics Awareness Month?

By patrick honner, ago

Math Lesson: Filling Out Tax Forms

Here is a math lesson I put together for the New York Times Learning Network that is built around parsing income information and properly filling out tax forms.

https://learning.blogs.nytimes.com/2011/04/11/no-taxation-without-calculation-filling-out-tax-returns/

This lesson supplies students with cost-of-living scenarios and mocked-up W2 and 1099-INT forms and challenges them to work their way through Federal Form 1040EZ.

A few older students might like to try this, too!

By patrick honner, ago

Portrait of John Conway

This is a short and engaging portrait of John Conway, one of the world’s most recognized mathematicians.

http://www.dailyprincetonian.com/2012/03/01/30161/

Conway is decidedly eccentric, which is not uncommon in the world of mathematics.  He loves magic, juggling, and games, and has something of a a reputation as an odd chap.   But his mathematical contributions are numerous and substantial:  Conway’s Game of Life in and of itself is a remarkable mathematical construction, but he is also credited with inventing (or discovering?) surreal numbers.  Conway has also contributed to the theory of sphere packing.

The article above, from the Daily Princetonian, is a quick and lively read, a fun portrait of a brilliant and curious man.

By patrick honner, ago

Surface Gallery

This is a nice visual gallery of algebraic surfaces.

Gallery of Algebraic Surfaces

An algebraic surface is essentially a surface whose equation is a polynomial in three variables (typically  x, y, and z).

Judging from Zeppelinand Zweiloch, our curator must be German.  My favorites are the Dromedar and the Wigwam.   Clicking on an image gives you a better look.

It’s interesting that Mobius, Wendel, and Croissant have no corresponding equation listed.  Are these not algebraic surfaces?

By patrick honner, ago
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