Pigeons

Pigeons can learn higher math!

Yup, those guys.

Check it out at the NY Times.

Measuring Earthquakes

Tsunami Energy Map of the Pacific

The recent earthquake in Japan has motivated me to do some research on earthquakes, particularly on how they are measured. I think most people in general understand that the larger the “size” of the earthquake, the stronger it is, but how many people truly understand what those numbers mean?

For starters, earthquakes are measured using the Richter scale. If you don’t want to get into the mathematics behind the numbers, here’s what they mean and how they are classified:

(above taken from UPSeis)

The Richter magnitudes are based on a logarithmic scale (base 10). So what this means is that for every whole number you increase on the Richter scale, the magnitude of the earthquake gets ten times larger. For example, an earthquake registering 2.0 on the Richter scale is ten times larger than a 1.0 earthquake and an earthquake registering 8.0 is 10,000,000 times larger than the 1.0 earthquake. I’ve attempted to create a visual that helps explain the increase.

(Each circle’s area is ten times larger than the area of the circle before it.)

If that doesn’t help, here’s another way to think about the measurements:

*The above example shows that a 6.0 earthquake is 10,000 times larger/stronger than a 2.0 earthquake.

It is estimated that there are over 500,000 detectable earthquakes in the world each year. For current or recent earthquakes, check out:

USGS’s Earthquake Map

IRIS’s Seismic Monitor

Fibonacci Numbers & the Golden Spiral

If you’re not familiar with the Fibonacci sequence, it’s not too difficult to create on your own. You start with 0, then 1, then start adding the previous two numbers to get the next in the sequence.

0, 1, (0+1)

0, 1, 1, (1+1)

0, 1, 1, 2, (1+2)

0, 1, 1, 2, 3, (2+3)

0, 1, 1, 2, 3, 5, (3+5)

0, 1, 1, 2, 3, 5, 8, … and so it goes.

And so what’s the point? What’s so special about this particular sequence of numbers? The Internet says that Fibonacci numbers are used in the analysis of financial markets; they’re used in computer algorithms; they’re used sometimes to tune musical instruments. In general, people use them for stuff. It’s a rather interesting sequence of numbers that pops up in some other sequences of numbers (math people love finding connections between seemingly random numbers).

Some people like to think that maybe they are useful for explaining parts of nature. It has been said that the Fibonacci numbers can be readily observed in flowers, trees, fruits, vegetables, shells, in the breeding of rabbits, and in the family tree of honeybees. While I believe that people are searching for relevance (and really stretching it), it is interesting to see this particular pattern of numbers in nature.

There are Fibonacci numbers in there somewhere. Consider it a challenge to find them.

There’s also the Golden Spiral, that has to do with the Fibonacci sequence too. The most common natural form is “found” in shells. Perhaps you’ve already heard/seen it?

The Golden spiral can be drawn by increasing the size of the next drawn square to align with one side of the previously drawn squares and moving in a circle (in this instance – counterclockwise).

While not perfectly representative, a lot of people like to say it’s in there so I’ll just go along with it.

Getting artsy with photography and math!

This may be the only one that actually uses the Fibonacci sequence in its spiral. See, math can be art/beautiful!

For more on the Fibonacci numbers and some interesting applications, check out this post. It’ll even show you how to use the sequence to convert from miles to kilometers!

Snowflakes

“Under the microscope, I found that snowflakes were miracles of beauty; and it seemed a shame that this beauty should not be seen and appreciated by others. Every crystal was a masterpiece of design and no one design was ever repeated. When a snowflake melted, that design was forever lost. Just that much beauty was gone, without leaving any record behind.” -Wilson A. Bentley

In 1885, Wilson Bentley was the first person to photograph a single snowflake. He went on to photograph over 5000 snowflakes in his lifetime, never finding any two alike.

Here are just a few of those thousands:

Hyperbolic Coral Reefs

The hyperbolic plane is kind of a big deal in mathematics. It’s a surface in which you can find infinitely many parallel lines to a given line from a given point outside the line. (We’re used to being able to only draw one parallel line that is parallel to a given line through a given point that is outside that line.)

Parallel lines we’re used to

Parallel lines in hyperbolic space

It is possible to crochet a model of hyperbolic space and in fact I’ve played around with these models in a college math course. The great thing about these models is that they also can mimic some of the natural hyperbolic planes around us, like those made by coral.

Check out the Hyperbolic Crochet Coral Reef project by the Institute For Figuring in Los Angeles.

Graphing/Photography

There was an article in Wired Magazine (January 2010) online that showcased a photographer’s art in which she graphed her images. You can also check out Nikki Graziano’s website – which is worth taking a look at even if you don’t like math.

This could be a really engaging project for students in both high and low levels of math. Students in Algebra or Geometry could graph simple lines and curves, while students at more advanced levels could graph more complicated functions and shapes.