June 7, 2012

Model of Ancient Egyptian Pyramid Construction

Model Pyramid Construction
If you are interested in performing your own experiments and would like to build a pyramid to your own specifications, rather than purchasing a commercially prefabricated one, we offer herewith detailed instructions for three different methods of pyramid construction.

Ancient Egyptian Pyramids
Apparently the exact geometric construction of the pyramid is based on mathematics involving two irrational numbers. Irrational numbers are the result of fractions in decimal form which go on to infinity without repeating any set of numbers. The two irrational numbers are Pi and Phi, where Pi (M) = 3.1415 and Phi (") = 1.618 Phi is the number known as the Golden Section of the pyramid and is determined by the proportions incorporated by the pyramid. The pyramid base is a square, and the four sides are isoceles triangles. If we assign the value of 1.0 to half of the triangle base, the slant height (apothem) is Phi and the exact perpendicular height from the apex to the base is the square root of Phi. Therefore, Phi is an actuality equal to the area of each base. We leave the actual proof of this equation to those strongly knowledgeable in mathematics. Phi and Pi are related to each, other by the approximate equation, It is important to note here that each face of the pyramid slants towards the apex at an angle of 51 degrees, 52 minutes and 10 seconds.

Choice of material seems to be very important in the construction of a model pyramid for experimental purposes. The construction materials should be homogeneous throughout. For example, compressed cardboard and not corrugated cardboard, solid wood as opposed to plywood, styrene plastic instead of styrofoam.

Method 1
If your mechanical ability is somewhat limited due to inaccessibility of drafting tools, you may construct a pyramid by taking four sheets of cardboard. Using a ruler and a pencil, scribe out on the cardboard an isoceles triangle whose equal sides, S, are in the ratio to the base, B, of 1.051 to 1.0.

For example, if you wish to construct a pyramid approximately 8 inches high, you would need four pieces of cardboard 12 inches square. Place a ruler at each comer and draw in the lines where each ruler touches the other at 11 Vi inches (see Fig. 31).

An alternative method would be to use a large pair of compasses, with an opening of at least 12 inches. Set the compass to 11 Vz inches and scribe an arc from the two bottom comers of the cardboard. The intersection represents the apex of the triangle. Draw the sides from this intersection marking to the bottom corners. Cut the triangles from the cardboard sheets and tape them together to form your pyramid.

For intermediate or larger sized pyramids, use the following table:

Base Sides
3 inches 2.85 inches
6 inches 5.70 inches
9 inches 8.55 inches"

1. Determine the desired height of the pyramid you wish to build.
2. Choose a number which, when multiplied by one of the numbers in the third column, will equal the desired height of the pyramid. For example, say you want your pyramid to be 8 inches high. Four inches when multiplied by two equals eight inches. Therefore, use the middle line of the table, the one in which the approximate height is 4 inches. Your multiplier is 2.
3. Now multiply each of the numbers in columns one and two (6 inches and 5.70 inches) by 2.
4. You know that a pyramid approximately 8 inches tall must have a base of 12 inches and sides of approximately 11 Vi inches (see Fig. 32).

Method II
To construct a pyramid in one piece, take a pair of compasses and referring to the diagram, draw a circle 5% inches in radius.
Draw a line from the center to the outer point (a) and set the compass to 6 inches. From point (a) mark off one 6 inch length on the circle (b). From point (b) mark off another 6 inch point on the circle (c). Then from point (c) mark off another 6 inch length (d). Finally, from point (d) mark off the remaining 6 inches to point (e).

Approximate
With a ruler, connect points (a) to (b), (b) to (c), (c) to (d), (d) to (e) and (e) to the center. Score a line with a dull knife, from b, c, d to the center (see Fig. 33).

Cut along the pencil lines, fold on the scored lines and tape the edges together. This construction will yield a pyramid approximately 4 inches high, with a 6 inch square base.

If you want to make a circle several feet in diameter, you can construct a wooden trammel from a yardstick or a narow slat slightly longer than the desired radius of the circle. At each end of the stick, drill a hole. The distance between the two holes should be equal to the radius of the circle. Insert a pencil in one hole, a nail in the other. Use the nail as the radius center, or pivot point. To scribe the circle, use the trammel as you would a compass.

Method III
Accdrately trace the following template (Fig. 34).
Extend the sides, S, of the template to whatever size pyramid you desire. Triplicating this process will yield four triangles identical to the first method. The four triangular pieces will have to be taped together.

If you wish to be even more accurate, obtain a very precise protractor. Set the protractor to 61 de grees and draw the angles, extending the lines to whatever size you wish your pyramid to be.

Once you have constructed the pyramid, keep in mind the fact that your construction is not an accurate one; that the exact proportion or ratio will not be perfect and may affect the results of your experiments.

As an adequate control for having your pyramid slightly out of proportion, we suggest that you place a mark towards the base on one of the faces, and keep this dot oriented to a cardinal point during the experiment.

At this point, you may wish to construct a base to support the pyramid and allow for easy relocation.

Simply cut a square piece of cardboard 4 inches bigger than the base of the pyramid. For example, if you have constructed a pyramid with a 6 inch base, cut a piece of cardboard 10 inches square.

Most experiments can be carried out with a specimen placed directly on the base, but not necessarily in the center. Apparently, experimental results are enhanced by elevating the specimen Vz the height of the pyramid from the base. If you wish, you can construct your own platform from any material you prefer.

Worldwide experiments suggest that the forces responsible for the unusual properties are focused upon a point exactly at the Vi level. Small or very thin specimens should be elevated on a platform to bring them as close to this level as possible. However, the total height of the platform plus the specimen should not go beyond the Vz level.

Finally, each of the four faces should point in the direction of the four cardinal points; north, east, south and west. True north should be used for orientation purposes. However, magnetic north appears to work as well, and is more easily found. To determine magnetic north, a good quality compass, not the dime store variety, should be used. True north differs from magnetic north by several degrees of declination, depending on the latitude where you live. You can determine the declination in your area by consulting your local almanac.

When placing the specimen in the pyramid, orient it so that the longest axis is in the direction of the north-south poles. In the case of specimens which are nearly round, simply place them in the center of the pyramid so that they are directly below the apex.

One good way to ascertain if your pyramid is aligned properly is to place ordinary honey in a shallow rectangular dish and align the longest axis of the dish in a north-south direction. After a maximum of five days, if the pyramid is properly aligned, the honey should start to solidify and become tacky to the touch. When the pyramid is shifted slightly from proper alignment, the honey will, within twenty- four hours, once again become fluid. If, however, after the maximum five day period, the honey is still fluid, you will know that either the pyramid itself, or the honey container, or both, are slightly misaligned.

Of course the pyramid should be situated so that it will not be disturbed during your experiment. Also, the surrounding environment should be relatively constant in temperature and humidity. Since the process is theoretically based on cosmic, magnetic and other natural radiation energies, your experiment should not be conducted too closely to radios, television sets, or other high frequency or high voltage-producing devices.

It cannot be stressed too strongly that the primary factors required for successful pyramid experimentation are patience, precision, and scientific detachment. If your early experiments should prove unsuccessful, carefully analyze what you have done. Check to make sure that your pyramidal measurements are correct, that you have properly aligned both the pyramid and the object inside it, kept your specimen inside the pyramid for the specified minimum length of time and have observed the proper controls. Even if you have ascertained that you have complied with all of these requirements, do not give up. Repeat the experiment. There may be other factors at play which you, or we, have not considered and which, given time, can be alleviated or dispelled. In fact, should you be able to pinpoint a negative factor not previously noted by pyramid researchers, you may actually have discovered something of great importance to the science of pyramidology. "

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