# 3-D Drawing and Geometry

### by Cathi Sanders

#### A Math Forum Summer Institute Project

1998 Summer Institute || Participant Projects || List of Participants || Sum98 Staff || Agenda

## The Geometry of 3-D drawing

When we draw any object, we have the choice of drawing it "flat" (two-dimensionally) or as a "solid" (three-dimensionally). A floor plan is an example of a two-dimensional representation of a house. Architects often draw 3-D drawings of houses, so their clients can more clearly understand what the house will look like when it is built.

In these pages, you will be studying three-dimensional geometric objects such as cubes, cylinders and pyramids, and learning how to draw them so that they appear to be 3-D. Below are some examples of the 3-D solids you will be studying:

Once you know how to draw these solids, you can combine them to draw all sorts of three-dimensional objects such as furniture, houses, and even castles! The beautiful photograph below from Castles on the Web archive is of a castle called Laussel, at Marquay, in the Perigord region of France.

This and many other castles are made up of geometric solids. Can you find prisms, pyramids, cones and cylinders in the photograph? You can draw castles using a combination of these geometric solids. An example of a simple castle, drawn in oblique using Adobe SuperPaint computer software, is shown below:

The castle below was drawn in isometric, using the isometric grid in the Geometer's Sketchpad software:

Here's another example of a castle. This one was constructed in perspective, using the Geometer's Sketchpad:

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