|Ornamental wall at gated, front entrance of an estate. Built with a mix of fieldstone and quarrystone from northeastern, Connecticut.
Introduction - Math - Investigating Walls
Pinhead, or expanded tip of the wall. Acadia National Park, ME.
Stone walls are rich objects from a mathematical perspective. There are three dominant scales at which these perspectives change.
- Map & Field: If you are examing a map of stone walls or a view from the field or yard, the dominant aspect of a stone wall is that of a line running in one direction. Of course, these lines intersect to form segments, which junction with one another to form angles.
- Wall: Each wall is a three dimensional object. Let X be the length of the wall, Z be its width, and Z the vertical direction. Most well-built walls will have the same shape in cross section (Y,Z). The face of a wall contains a collection of stones.
- Stone: Each stone in the face of a wall has a size and shape. Consider them to be a collection of objects with different traits: size, shape, composition, etc.
- Geometry: The trace of a wall in map & field view is a vector, consisting of direction and length. These walls intersect at various angles. When a field has walls on all sides, it becomes a polygon. The shape of the wall and the shape of the stone are geometric objects as well.
- Statistical properties: Consider the wall as a collection of stones. The statistical properties of this collection can be easily measured and described. The same is true for other aspects of walls in the local area (i.e. how many walls, rather than how many stones).
- Measurement: Any length or perimeter can be measured by individual student teams. Their results can be compared and interpreted.
- Estimation: An actual count of the number of stones in a wall's face can be compared with an estimate made from a small section.
- pre-Algebra: The slope of a wall, expressed as rise over run, can be used to help introduce the idea of variables, factors, and elementary trigonometry.
Back to Investigation.