3D Geometry
Geometry is the mathematical study of shapes, figures and positions in space. Geo refers to the earth and ometry refers to measure. From ancient times, people used geometry to determine and mark locations on land and in the cosmos.
All geometry begins with the point. The point is the smallest unit of geometry. It takes three points to make a line: a beginning, a middle and an end. Lines form shapes and shapes exist in planes. Shapes are in planes and have length (x) and height (y).
A triangle has three sides, a cube is foursided and a circle is all points in a plane at a fixed distance (radius) from a center point. Add the dimension width (z) to these shapes and you have a volume. Triangles become pyramids, squares become cubes and circles become spheres. Geometry locates positions in space (x, y, z) with points, lines, and angles. Make the invisible visible! Take measure of the earth!
Activity 1 Skyline Geometry
Choose one of the city skylines or photograph your own hometown. Find and outline at least one example of each two dimensional shapes and three dimensional volumes of the following:
 triangle
 rectangle
 square
 circle
 regular polygon
 irregular polygon
 concave shape
 pyramid
 cube
 sphere
 point
 line
 plane
Shape your city!
Activity 2 Polygon and Volume Power
Examine geometry around your home. Find examples of two dimensional geometry: triangles, rectangles and pentagons anywhere you can. Then, find examples of three dimensional geometry: spheres, pyramids, cylinders and cubes.
Look at the floor tile, the design of a door knob or even your soccer ball. Photograph or sketch what you find, then copy them, label them and paste the shapes in your journal. Think about how to fold a 3dimensional shape from a flat piece of paper. Is it even possible? Start with a square shape and draw all six sides on a flat sheet of construction paper. Cut and fold your design into a cube. Then work with a triangle to make a pyramid. Finally, be brave! Try to draw and fold more complex shapes into regular solids.
Activity 3 Volume Power In Your Neighborhood
Take activity 2 out into your neighborhood. This time, look for threedimensional volumes. Find examples of pyramids, cubes, and spheres anywhere you can. Look closely; they are everywhere around you. A light pole or a mailbox, or look into the eave of your house; almost everything is a 3dimensional shape. Sketch and photograph your discoveries. Next, paste them in your journal to make a map of your neighborhood. See if your friends can guess where you found each shape.
There is a language in shape!
Activity 4 Digital 3D!
Using GoogleSketchUp start drawing 3 dimensional geometry!
Plot a circle; pull up a cylinder!
Review

How are the dimensions of a cube described?

How many sides can a pyramid have?

What is the strongest shape?

The Earth is a perfect sphere:

Is a dome 3dimensional or 2dimensional?
Explore
 Geometry of the Circle
 Elements of Geometry
 Geometric Shapes
 3D Geometry From the Land of the Incas
 3D Geometry in Your Home
 Seeing Geometry
 Shape Gallery
 Paper Models
 Virtual Shapes
 Measuring Angles
 Sacred Geometry
 Geometric Solids
 British Metric Interactive for 3D Shapes
 3D Geometry Annenberg Learners
 Buildings by Tadao Ando
 Exploring Other Dimensions:TEDed
 New Geometries at MIT
 Illuminations Geometric Solids Interactive (Uses Java)