Investigation 2

Fractal Skewed Web

Part 1

Given: Equilateral triangle ABC and AB is equal to 1 unit, find the following:

BC = ______

BD = ______

AD = ______

AD = ______

DQ = ______

BQ = ______

EQ = ______

AQ = ______

Area of triangle ABC = ______

Answer to Part I

Part 2

Given: Regular tetrahedron ABCP with AB = 1 unit, find the following:

Recall:Volume of a pyramid = 1/3 (area of base) x (height).

PQ = ______

Volume of ABCP = ______

Answer to Part II

Part 3

Given: A regular octahedron with AB = 1 unit.

Find:

• AD =
• DC =
• PD =
• DE =
• QE =
• PE =
• PQ =
• Area of ABCD =
• Volume of the square pyramid ABCDP =
• Volume of the regular octahedron =

Answer to Part III

Part IV

Review the results of Investigation 3. Do you see a relationship between the volume of the regular tetrahedron and the volume of the regular octahedron?

What is the relationship if one does exist?

When the fractal Skewed Web is generated, we see that at each step one half of the previous volume is removed. Can you express these steps as an infinite Geometric Seires? The sum of the infinite Geometric Series represents the volume removed from the original figure.

A.What is the total volume which has been removed when the Fractal Skewed Web is completely generated?

B.What is the volume of the Fractal Skewed Web?

Answer to Part IV

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