Tessellation LbNA #58674

Tessellation is only available during open hours. Detailed hours may be found here under "Branch Libraries". Parking is available at the Virginia Avenue Garage, Lot CG17 and along Hitt Street. More information concerning parking on campus may be found here.

Patterns, shapes and numbers are common tools for a geocacher or a letterboxer. They help interpret sensory information to extrapolate potential hiding spots or hidden containers. Locating this letterbox / cache should prove quite the workout for those skills.

Tessellation, as defined in mathematics, is a repeating pattern of shapes filling a two-dimensional plane neatly (i.e. no gaps or overlaps). While the posted coordinates lead to the front entrance of the Mathematical Sciences building on the University of Missouri - Columbia campus, such a pattern may be found within Jesse Hall on the first level (up the stairs from the front of the building). Ignore the border patterns and notice the tessellation consisting of two shapes clearly taking up considerable space on the floor. Then solve the following . . .

1) Of the two shapes, count the number of smaller shapes at each vertex*.
2) Then, count the number of larger shapes at each vertex*.
3) Subtract the number of large shapes from the number of small shapes at each vertex*.
4) How many of the shapes are non-equilateral polygons**?
5) Count the number of sides on one of the smaller shapes.
6) How many shapes are at each vertex* in total?

Now, go to room 206 of the Mathematical Sciences building (the posted coordinates). Each of the questions you answered in order provides directions once inside the door to the library. If the answer was . . .

- Odd, go right.
- Even, go left.
- Zero, do nothing.

Follow each direction until you can proceed no further. The container should be easy to spot.

Thanks go out to Judy Maseles, Head of the Science Branch Libraries for permission to place this cache / letterbox. Further thanks to Will McCrary who helped develop the original hide.

* A vertex is a point where the corners of the shapes meet. In a tessellating pattern, each vertex has the exact same shapes meeting.
** A non-equilateral polygon is a shape with sides of irregular length.

Hike length: 1 mile