NOTE: 8/4/13 - New nearby location after original location removed for new construction. If you solved before it was disabled, just double check the math off the new numbers.
Domes
The Wikipedia article on Domes says that a dome is "a structural element of architecture that resembles the hollow upper half of a sphere." [1]
There are a number of different kinds of domes. You've probably seen "Onion Domes" in pictures of Russian cities or on top of the Taj Mahal. You've seen Roman domes in churches and renaissance art. The "Spaceship Earth" building of Epcot at Disney World is a geodesic sphere. And, of course, let's not forget the dome atop the Capitol Building in Washington, D.C.
Today, we will be looking at two of my favorite types of domes: the geodesic [2] dome (as popularized by Buckminster Fuller[3]) and the conoidal dome first created by Donald Grieb. [4] The cache is located near three conoidal domes which make up the Mitchell Park Conservatory.
Most geodesic domes like those used in houses are only partial spheres. You will usually see either a 3/8 or 5/8 sphere. The majority of these are three frequency (or chord factor) domes. [5]
To solve the final coordinates and find the cache, you will need to build a one frequency, full sphere, geodesic dome.
For this project, you will need a number of mini-marshmallows and toothpicks. For reasons that will become clear, I can't tell you how many of each, but if you have a full box of toothpicks and a bag of mini-marshmallows, you will be fine.
Attn. Grown-ups: This can also be done with cocktail supplies such as stirring sticks and olives.
As you can see, this bag has been checked for quality control purposes.
Building the Dome
1. Start by creating a triangle
2. Next add triangles to the two sides creating a line of three triangles.
3. Repeat this process until you have a line of nine triangles.
4. Now, gently stand the line up and bend the ring around
5. Connect the two marshmallows on the top with a toothpick (see below) and combine the toothpicks of the two lower marshmallows into one (also highlighted below)
You should now have a ring of triangles like those below
6. Put toothpicks in each of the top marshmallows forming a point. Cap that point with another marshmallow.
7. Turn the structure so that you can get at the bottom and repeat the toothpick/marshmallow cap with this side
You have now created your full geodesic sphere! Now we need to do some math to find the final coordinates.
Please feel free to take a picture of your dome and post it with your logs for others to see.
The Math
Geometric shapes like this have a number of properties including vertices, edges and faces.
The edges (E) are the toothpicks.
The vertices (V) are the marshmallows.
The faces (F) are the triangles in-between the toothpicks and marshmallows.
Once you have these numbers, do the following math with the starting coordinates:
X = F + V
Y = E + V + F
Finding the Cache
Your final coordinates are:
N 43 01.(479+X) W87 56.(828-Y)
The cache is located at the Mitchell Park Domes. While they have some of the same "feel" as our geodesic dome, these are *not* geodesic. They are conoidal or beehive shaped.
Please take some time to look around this gorgeous place both inside and out.
Also in this listing is a waypoint taking you to a memorial plaque honoring the men and women who have served in our armed forces. I ask you to take a moment and stop by.
I hope you enjoy this cache. I have included some additional reading material about domes, Buckminster Fuller and the Mitchell Park Domes below for your enjoyment.
You can check your answers for this puzzle on GeoChecker.com.
RocketMac
References:
1. http://en.wikipedia.org/wiki/Dome
2. http://en.wikipedia.org/wiki/Geodesic_dome
3. http://www.bfi.org/
4. http://county.milwaukee.gov/ConstructionoftheDom10361.htm
5. http://en.wikipedia.org/wiki/Geodesic_dome#Chord_factors
Additional Reading:
Wikipedia's article on Geodesic Domes [http://en.wikipedia.org/wiki/Geodesic_dome]
Wikipedia's article on Buckmister Fuller [http://en.wikipedia.org/wiki/Buckminster_Fuller]
Wikipedia's article on the Mitchell Park Domes [http://en.wikipedia.org/wiki/Mitchell_Park_Horticultural_Conservatory]
Milwaukee County Parks page on the Mitchell Park Domes [http://county.milwaukee.gov/MitchellParkConserva10116.htm]
Friends of the Domes [http://www.milwaukeedomes.org]
The Buckmister Fuller Institute [http://bfi.org]
Wikipedia's List of Celebrated Domes [http://en.wikipedia.org/wiki/List_of_celebrated_domes]