patrick honner

Math teacher in Brooklyn, New York

2011 AIME A #8: Triangular Tables

Foam Table 1I was inspired to have some more fun with folding by a question from this year’s American Invitational Mathematics Examination (AIME) that turned triangles into tables and asked “How high can the table go?”.  (You can find the question here).

Investigating the problem seemed like more fun than solving it, so I cut out a triangle from some foam board and scored lines near the vertices.

Foam Triangle 2

Then I folded the corners and made the following table with an irregular hexagonal top!

Foam Fold

I made a few, to see what kinds of heights I could get.

Foam Tables

There are so many fun questions to explore here!  What comes to mind?

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By patrick honner, ago

Math Quiz: NYT Learning Network

go-greenThrough Math for America, I am part of an on-going collaboration with the New York Times Learning Network.  My latest contribution, a Test Yourself quiz-question, can be found here:

http://learning.blogs.nytimes.com/2011/05/4/test-yourself-math-may-4-2011/

This question is based on a recent article about the dwindling consumer support for “Green” products.  Just how much does it cost us to “Go Green”?

By patrick honner, ago

Weather Forecast Accuracy Statistics

weatherThis website aims to evaluate the accuracy of various weather-prediction services while providing its own forecast:

http://forecastadvisor.com/

Using composite indices and statistical methods, data from sites like Accuweather and Weather.com  is analyzed and rated.

This is a good resource for an interesting group or individual project in statistics:  how accurate are the various services?  What is a “good” prediction?  How valuable is this information?  How can we use statistics to evaluate these questions?

Several years ago I read this post from the Freakonomics blog:  it details an informal study conducted by a man and his daughter who looked at seven months of TV weather forecasts in Kansas City and evaluated their accuracy.  The entire article is interesting, but the bottom line is best summed up in a quote from someone from one of the TV stations:  ““We have no idea what’s going to happen [in the weather] beyond three days out.”

By patrick honner, ago

CDs, Prisms, and Parallelepipeds

I’ve had some fun playing around with old CDs and CD cases recently.

In addition to demonstrating Cavalieri’s principle both with discs and their cases, I’ve found some other mathematical uses for these objects.

Here I’ve used a stack of cases to demonstrate the difference between some geometric solids.

cd-collage

On the left, we have a right rectangular prism.  Give that prism a slight push in a direction perpendicular to a side and you get an oblique rectangular prism.

And if you give that original prism a push along a diagonal of the base, you’ll get one of my favorite geometric objects, a parallelepiped.  It may not be the perfect parallelepiped, but I’ll take it!

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By patrick honner, ago
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