Inscribed Polygons

Imagine a circle with a radius of one unit. Inside the circle, inscribe the largest possible equilateral triangle. In the triangle, inscribe a circle. In the circle goes a square ... in the square a circle...in the circle a regular pentagon ... in the pentagon a circle ... etc. Each consecutive polygon has one more side ... alternating with circles. The circles get smaller and smaller.

Can you make a rough guess as to how small the circle will eventually become?

Hexagon In-Out

Imagine a hexagon with a circle inside it. Six points, on the circle, each lie on the center of a different side of the hexagon ... thus it is the largest circle which will fit inside the hexagon. Now imagine another hexagon inside the circle ... each vertex of the hexagon lies on the circle ... making it the largest hexagon which will fit inside the circle.

The inner hexagon has an area of three square units.

What is the area of the outer hexagon?

3D Object

* Draw Square 1 with sides of length x. Draw a smaller square, inside square 1, with sides of length x/2. Align the smaller square such that one of it's sides lies on top of, and in the center of, the lower side of square 1. (lower side of square 1 refers to the side closest to the bottom edge of the paper upon which you are drawing)

* Repeat the above instructions and label the second drawing as Square 2

* Square 1 and Square 2 are identical.

* Square 1 is a plan view (top view) of a 3 dimensional object.

* Square 2 is the elevation (front view) of the same object.

* Draw a 3 dimensional representation of the object.

* DESCRIBE the OBJECT.

-- Zaux