The Mathematics of Pyramids.

  The cool things about pyramids is that they are not found only in Egypt anymore.  You find them in Las Vegas, and other places around the world.  The even cooler thing about this topic is that you can use Google to bring up actual pictures to give students a better feel for the actual size.

Photographs are nice but they are usually taken from a distance so you get the whole picture but when viewed using google, you get a much better feel for its size.

As you know, a pyramid is basically a square with four triangular sides also known as a square pyramids.  The most famous one is the Pyramid at Giza but others include The Nima Sand Museum in Japan which is a cluster of 6 different pyramids, the tallest of which is over 69 feet tall with a 56 foot base.  The tallest one was built to house the worlds most functional sand timer measuring a year span and is flipped every year at midnight of the last day of the year.

In addition, the Louvre has three pyramids, the tallest of which is 71 feet tall with a 115 foot base.  It opened in 1991 and provides an interesting juxtaposition to the older architectural style of the Louvre itself. Long Beach University has its Walter Pyramid, a monument to athletics as its 18 stories has seating for 4,500 but can hold up to 7,000.  In addition, there are two other pyramids in Russia, one designed for a religious gathering while the other is for entertainment.

We all know the the formula for the volume  of a pyramid is 1/3 x base x height where as the formula for the surface area of a pyramid with regular sides is base area + 1/2 x perimeter x slant length.  In regard to the Pyramid at Giza has some fascinating math associated with it. 

First is the golden ratio (Phi) which is the the only mathematical number whose square is one more than its original number.  Its the number found in nature, its ratio being pleasant to the human eye.  Apply the Pythagorean theorem to these numbers and you get the values which are similar to the golden triangle.

Another idea is that the pyramid could have been based on Pi because the theoretical numbers are within 0.1% different from the Great Pyramid.  Either way the mathematics involved in these claims is fascinating.

Just think with a little work, students could design a Google Tour focusing on these and other pyramid shaped buildings including their volume, surface area and other pieces of information.  They could include a map with pins for each site.  So many possibilities.  In February, I'll be giving a talk on integrating Google into the math classroom, so this would be perfect as an example.

When I get this project done over Christmas break, I'll share it with you .  Have a great day and let me know what you think.