The Shape of the Moon’s Orbit

This is a short and readable exploration of the question “What is the shape of the Moon’s orbit around the Sun?”

http://www.math.nus.edu.sg/aslaksen/teaching/convex.html

The Moon makes circles (ellipses, really) around the Earth while the Earth makes circles around the Sun, so what does the path of the Moon look like?

It’s a fun problem to think about, and I encourage you to do just that before you click through and see the discussion.

This simply posed problem touches on polar and parametric curves, 3-dimensional geometry, and of course, astronomy.  And naturally there are lots of extensions, like “What if something were orbiting the Moon?”

By patrick honner, ago

More Quantitative Confusion

I’m pretty sure printer ink is a huge scam to begin with, and stuff like this doesn’t help.

I went to purchase some ink and looking to minimize my time spent in office supplies stores, I thought I’d buy a two-pack.  “We’re out of the two-pack,” the helpful employee said, “but this is the XL.  It’s the same price as the two-pack, and it has 3 times as much ink as the single cartridge.”

So after my purchase, I felt compelled to perform a side-by-side comparison.

I’d estimate the XL cartridge to be about 120% the size of the original.  But its ink capacity is 350% of the original?  That doesn’t seem to add up.

By patrick honner, ago

Who Employs Mathematicians?

Here is a great resource from mathscareers.org:  a collection of links to the Careers pages of various companies that employ mathematicians.

http://goo.gl/m5mIt

It’s easy to envision using math in fields such as Accounting, Education, and Academic Research, but there are also links to Automotive companies, the Food and Drink industry, and Pharmaceuticals.  What a great place for a young mathematics students to get a feel for some of their options!

And here’s another great resource from the same organization:  a set of excellent video interviews about the importance of mathematics skills in industry.

By patrick honner, ago

Street Fighting Mathematics

Sanjay Mahajan’s Street Fighting Mathematics is a short, dense, and engaging book that explores some mathematical problem-solving techniques not typically taught in math class.

These techniques, favored by engineers and scientists who are usually more interested in the answer to a question than in the mathematical theory that gets them there, can turn seemingly intractable problems into simple ones, often just by a change in perspective.

For example, the book offers a short treatment of Feynman’s differentiating-under-the-integral approach, one of the more famous “back of the napkin” techniques.  Mahajan even “guesses” the definite integral that yields the area under the bell curve, using dimensional analysis the likes of which I’ve never seen.

A “Street Fighting Mathematics” course is offered through MIT’s OpenCourseWare, which includes lectures, notes and problem sets.  In addition, Mahajan has made the book available for free in PDF format.

By patrick honner, ago
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