## Building and Constructing

Problems and tasks from a variety of sources intended to illustrate the way mathematics arises in life and work.

Visualization. Given a drawing of a building from a northwest view, sketch what the building looks like from the east, and from the south.

Energy Efficiency. In planning a new home, a builder wants to design the southern exposure for maximum solar efficiency---to let the winter sun shine through the large windows, while having the summer sun blocked by the roof overhang. Make a scale drawing showing a realistic design for the latitude in which you live--including positions of the summer and winter sun, the roof overhang, and the location of the south-facing window.

Kitchen Shelves. A home owner is planning a built-in shelf unit for a remodeled kitchen. The current plan calls for 1" x 8" oak boards of four different lengths: four to six at 2'10"; three to five at 4'6", seven or eight at 5'9", and two or three at 6'6". The local lumber yard sells oak boards in lengths of 6', 8', 10', 12', and 16', but the shorter lengths are more costly per board foot. The homeowner needs to decide what combination of shelf lengths and purchased boards will yield the most economical shelf unit.

Tiling a Floor. What measurements do you need to take in order to be prepared to tile the floor of a room? Explain how these measurements can help you calculate the number of regular tiles, border tiles, and corner tiles that are needed. What changes if you decide to lay the regular tiles diagonally within a conventional border?

Isometric Drawing. Given an isometric drawing of an object, prepare top, front, and side views, to scale.

Cutting Plywood. An assistant on a construction job needs to cut a number of pieces of plywood of various sizes to fill in around the edges of the roof. Given the dimensions of the desired pieces, figure out how to cut them out of sheets of 4' x 8' plywood with minimal waste.

Laying a Foundation. You are helping your brother-in-law build a garage on gently sloped land next to his house. After leveling the land, you begin locating batter-boards to lay out the foundation. To check that corners are square, you measure the diagonals--but discover that they differ by 3 inches. Is that because the corners may not be perfectly level, or because they are not perfectly square? How can you determine what needs fixing to make sure that you start with a foundation that is both level and square?

Handicapped Access. Modify a simple home floor plan to accommodate a wheelchair--with ramps and doorways of the right size and slope.

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Last Update: 12/28/98