Math Encounters: Craig Kaplan on Math and Art

Craig Kaplan’s Math Encounters talk, “Revolution and Evolution in Math and Design,” was a whirlwind tour of the design space that lies at the intersection of computer science, mathematics, technology, and art.   Kaplan, a professor of computer science at Waterloo university, is an innovative software engineer, an accomplished artist, and a passionate and engaging speaker.  His talk wove together the mathematical and cultural history of Islamic art, tilings of the plane, non-Euclidean geometries, and the mathematics of aesthetics.

The Math Encounters series, sponsored by the Museum of Mathematics, strives to bring mathematics to the public through dynamic speakers, meaningful topics, and engaging interactivity.  In that spirit, after the talk Kaplan and George Hart led a fun, collaborative workshop where the audience teamed up to create a work of art themselves!

Using some tape, some scissors, and some clever mathematics, each group turned their table into a “tile” using the techniques Kaplan covered in his talk.

And as each group finished their “tiles”, we started putting them all together!

It was a fun and fitting end to an inspiring and mind-opening evening!  You can learn more about Craig Kaplan and his work at his webpage.

Quadrilateral Challenge — A Solution

Here is one approach to answering the quadrilateral challenge posed earlier.  In summary, the challenge was to prove or disprove the following statement:  A quadrilateral with a pair of congruent opposite sides and a pair of congruent opposite angles is a parallelogram.

I offer this disproof without words.

By starting with an isosceles triangle, cutting it, rotating one of the pieces, and gluing it back together, we have constructed a quadrilateral with one pair of congruent opposite sides and one pair of congruent opposite angles that it is not necessarily a parallelogram!

A Quadrilateral Challenge

Here’s an easy-to-understand, remarkably rich question that arose during a recent Math for America “Bring Your Own Math” workshop.

If a quadrilateral has a pair of opposite, congruent sides and a pair of opposite, congruent angles, is it a parallelogram?

I had a lot of fun thinking about this problem on my own, discussing it with colleagues, and sharing it with students.  At different times throughout the process, I felt strongly about incompatible answers to the question.  For me, that is a characteristic of a good problem.

I encourage you to play around with this.  I was surprised at how many cool ideas came out as I worked my way through this problem, and I look forward to sharing them!

And if you want to see a solution, click here.

Another Equilateral Comparison

The passing of consecutive isosceles triangle days has me once again thinking about the question “Which Triangle is More Equilateral?”

I first considered the question on 10/10/11, comparing the 10-10-11 triangle and the 10-11-11 triangle.  After a spirited discussion, I offered one approach to the question here.  The problem gave me lots to think about, both mathematically and pedagogically, and I reflected on what I liked about this problem here.

But as 12/11/11 and 12/12/11 pass, I thought I’d revisit my strategy for answering the question “Which triangle is more equilateral?”

My basic strategy, outlined in more detail here, is to ultimately to quantify the circleness of each triangle.  To me, being equilateral is all about trying to be as much like a circle as possible.  So I created a measure to determine how close to circlehood a triangle is.  Here are the numbers.

The 11-12-12 triangle’s measure is closer to 1, thus making it the more equilateral triangle.

Related Posts

 

Math Lesson: European Debt Crisis

My latest contribution to the New York Times Learning Network is a Math Lesson designed around exploring loan repayment and risk assessment in the context of the European Debt Crisis.

https://learning.blogs.nytimes.com/2011/11/30/crunching-the-numbers-exploring-the-math-of-the-debt-crisis/

In this lesson, students interact with some cool infographics, collect debt data, run the numbers on possible loan repayment schedules, and explore an elementary notion of “risk” in finance.

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