Part One: Important Calculations
The most important measurement we need from the Great Pyramid is the angle of incline, measured to be 51 degrees 52 minutes (51.86); simple trigonometry can be used to determine any model ratios with this angle:
cos 51.86 = 1/2 the length of the base divided by the length from the base to the tip
sin 51.86 = height of the pyramid divided by the length from the base to the tip
tan 51.86 = height of the pyramid divided by 1/2 the length of the base
Part Two: A Paper Model
Supplies you will need: large white board, pencil, ruler, tape, a square, and utility knife.
1. Start by drawing a nine inch square on the white board, marking a center point for each side. This will be the base of the pyramid.
2. At the center point of each side, extend a perpendicular line 7.28 inches. This if the length from the base of the pyramid to the tip along an inclining side.
3. Draw a line connecting the tip of the perpendicular to the corners of the square.
4. Using the knife, cut out the outline of the pyramid pattern.
5. Fold the four sides of the pyramid together and tape. If your white board is thick, you may need to score the board on the inside of the fold for a crisp edge on the outside.
Part 3: A Brick Model
Supplies you will need: String, stakes, a square, bricks (9in x4.5in x2.5in), outdoor grout, tiles (or other mosaic materials).
I have chosen a base length of 22.5 inches to conform to the brick size. Using the trigonometry listed earlier, I can calculate the height of the pyramid to be 14.23 inches.
1. Clear the spot where you will construct your model. Mark the string using four stakes at intervals of 22.5 inches, this will define the base length as you lay out the pyramid. Using the square, push the stakes in at the approximate corners of your pyramids. The diagonals of the square should be equal if all the angles are at 90 degrees, so use this diagonal measurement to adjust the stakes.
3. Continue layering bricks into each course, it will take five layers of bricks to construct the core of the pyramid.
4. To create a facade for your pyramid, collect tiles, pottery shards, or any other materials you wish to mosaic into the model. Mix a portion of the outdoor grout according to the instructions on the bag and put a thin layer over the stack of bricks to secure their location.
5. Cover one side of the pyramid with the grout, being careful not to disturb the placement of the bricks. Begin to place the mosaic pieces at random or from a plan. After one side is finished, move on to the next side; do not cover the pyramid with the grout all at one time, or it will harden before you are able to place all of your mosaic pieces.
6. After all tile pieces have been placed and the grout stiffens, scrub the tile clean.
No pyramid is complete without a sphinx.
