The glass is half-full… I think.

This post inspired a classroom activity and corresponding reflections. If you would like to see how this went when it was given to a group of young people, please feel free to check out Mathematical Modeling: The Glass is Half-Full.


I was drinking a glass of water recently. The glass looked like this:

Notice how the glass gets wider as the glass gets taller. This will make the task of drawing horizontal half-way line (that is, the line where half the volume of the glass is above the line and have the volume of the glass is below the line) more difficult.

So, how would you figure out where to draw the horizontal half-way line? Would that method work for finding the quarter lines as well?

A simple sports question

So, it turns out that a basketball is bigger than a baseball. (Those ready to nominate thegeometryteacher for a Nobel Prize may want to use this as my fundamental discovery).

But, I have a simple question. The number of answers that we can discover will illustrate the reason that science, math, and economics require many years of study to master.

So, here’s the question: speaking of a standard baseball and a collegiate men’s basketball: How much bigger is the basketball than the baseball?

Your mind is probably already asking at least 3 clarifying questions (all excellent questions, at that). Normally, clarifying questions are great. They are designed to focus the mind after an unclear task. However, in this post, we don’t want to seek an answer. We want to see just as many possible answers we can.

So, flood the comments with answers. Explain your answers after you state them.

How much bigger is the basketball than the baseball?

Follow-up to Math Rushmore: Crazy Horse, Crazy Math!

Friend of the blog, C. Wright dared (more or less) thegeometryteacher to explore a lesser known, but equally fascinating monument in the Black Hills of South Dakota (in the United States, for you international readers).

A bit of background: Crazy Horse was a warrior from the Lakota tribe that resided in the American Great Plains. Construction of this gigantic monument started in the 1940’s and remains incomplete. It is truly a fascinating story. The story of Crazy Horse is equally fascinating, by the way, especially his connection to General Custer (who was raised in Michigan) and The Battle of The Little Big Horn in 1876.

Here are some photos of the monument.


And a profile shot.

C. Wright’s comment “What math could thegeometryteacher do with this monument?” raises some interesting possibilities. And me, being more of a question-asker than answerer thought of a possibility:

Could Teddy Roosevelt’s Glasses (in Mount Rushmore) fit Crazy Horse (in his monument?)

So, let’s go with that one. Think about what information you would need in order to answer that question. What would the plan be once you had that information?

There may be a video solution in the mix for this problem. Don’t wait for it, though.

Put your thoughts in the comments.