There is no doubt that the ancient Egyptians were intrigued by the height of the Entrance from the base of the Pyramid. For some reason the value 55.6898 was extremely important to them. It is used throughout the interior. This dimension was very important to the Egyptians, but what does it mean? The person that designed the Pyramid had to be extremely intelligent. He introduced the twelve to one ratio that allows the design to function and he also knew about the qualities of the 1.618033 to 8.618033 ratios that take the pyramid to its peak. He made abundant use of ratios and multiples of the Entrance height. He also used the base to the Entrance dimension throughout the Pyramid interior. He made all the ratios and dimensions work together. Why this was done we may never know, but it was and it worked flawlessly Invoked the 12:1 ratio to create the Pyramid exterior and interior dimensions. Split the height, the base and the slant height into sections using 1.618033 to 8.618033. Used ratios in the interior passageway system. Used the Entrance to base vertical dimension and the Entrance to base angular dimension throughout the interior passageway system. The Great Pyramid of Giza has always been a source of mystery. Experts from all over the world have studied the greatest structure ever built. Many people have claimed to solve the design of the world’s greatest mystery but no one has been successful. It has been connected with the earth, the sun, the moon, the stars, space, and even spacemen. The mathematics involved in the construction has been deemed by experts to be too advanced for modern man to understand. This is not true. The mathematics used in the design of the Pyramid is well within the capabilities of any mathematician, Egyptian or Modern. This will be shown in this article. Everyone, no one excepted, forgot about simplicity. Designing ‘simply’ was what the architect did. His methods in designing the structure were simple but they were wise and ingenious. Note: The key to the Pyramid design is the ratio 12:1. This ratio generates the exterior dimensions, the interior dimensions, and the entrance height of the Pyramid. This is the secret of the Pyramid mathematics. Using this Design the angles of the Descending and Ascending passageways are 26.565º and 26.565ºrespectively, at this stage the bottom of the Great Step is not in the calculations. The Design follows the interior passages to the top of the Great Step. The Design angle of the Slant Sides is 51.776º. Three reference points are used: 1) The Entrance floor height from the base. 2) The Queen’s chamber floor level height from the base. 3) The King’s chamber floor level from the base. The text and prints in this article will show how every measurement in the Pyramid followed an exact plan and how the builders managed to obtain accuracy and remain close to this Design, a design similar to the one that they must have used to accomplish their enormous task. Every dimension has been calculated to eight places after the point and reduced to four in the prints, for the sake of accuracy. Angles are accurate to three places after the point. No dimension had digits ‘put in’ to make things work. The most surprising find in this exercise was the fact that the Entrance floor level height from the base interacts with every vertical and horizontal interior dimension. This is a very important dimension and its value is 55.6898, it generates the interior and exterior dimensions accurately. Inspect a triangle, let’s say 2.5 X 1.25. (Two to one ratio) The dimension 2.5 is a multiple of the Entrance door height 2.5 X 55.7927 = 139.2245. The value 1.25 is also a multiple of the Entrance door height 1.25 X 55.7927 = 69.6122. When you have studied the drawings and you become familiar with the dimensions your perception of the ancient designers will change forever. Please use the information supplied, plot it and enjoy, find out that the Great Pyramid dimensions have finally been solved. Bill McMaster. Copyright © 2012 [William McMaster]. All Rights Reserved. An Exercise to show that the Great Pyramid of Giza was designed using Ratios. The base of the Pyramid in this exercise is 756 (500 cubits X 18.144”). The half base is 378. The Rules as applied to the Pyramid Design 1) The 12:1 ratio generates the height of the Pyramid, the slant height and the entrance floor height. 2) All interior angular and vertical dimensions originate from the Pyramid base. 3) Ratios apply to all interior horizontal and interior angular dimensions. 4) All horizontal and vertical dimensions are multiples of the Entrance floor height 55.6898. Using these rules the Pyramid has a height of 479.94 a slant height of 611.9226 and a half base of 378. If the base is deemed to be incorrect then a 12:1 ratio has to be constructed for the new base. Every dimension ratio will remain in the same proportion. The first very important find is the ratio 12:1 that positions the Entrance height from the base. (668.2776 : 55.6898). The distance from the Entrance floor level height to the South face at the same height is 668.2776, exactly twelve times the door height of 55.6898. Once this ratio was in place all other dimensions can proceed. Since this exercise only uses the north cross section of the Pyramid this ratio will be 334.1388 : 55.5898 a ratio of six to one. Sir Flinders Petrie had the height of the entrance correct, he had 668.2”, very close indeed but he missed the 12:1 connection. Maybe if he had a computer? One more point on the 12:1 ratio. The Ascending passage passes through the half base (6:1) ratio centre of 334.1388 precisely. The base half length in this exercise is taken as 378and the ratio is 6:1. If you have another dimension that you would prefer to use then construct a 12:1 ratio for that length. All other dimensions will of course change but will still be in proportion. Construct the Design using the prints. |

Pyramid height 479.94

Pyramid slant height 610.9226 Angle 51º 46' 34"

Pyramid base length 756

Pyramid base half length 378

When the above dimensions have been put in place the most important measurement is 55.6898 the entrance

height from the base, the KEY to all dimensions. It also builds all interior horizontal and vertical ratios.

King's' Chamber floor height from the pyramid base is 2.5 X 55.6898. (2.5 X the Entrance height from the base)

The King's Chamber floor height from the base is twice the Queen's Chamber floor height from the base.

accomplished. Time, 4500 years, also has to be factored in. There is a mistake in construction in the ascending

passage that changes the angle to today's measurements. Follow the design measurements and question why the

floor meets the bottom of the Great Step. It becomes quite obvious.

from the base is shown in red. It is the most important dimension in the Great Pyramid of Giza.

the base and the King's floor height from the base.

The comparisons between the ancient measurements verified by archaeologists and the design using the 12:1 ratio

are extremely close. The 12:1 design shows how 'it was meant to be'.

It would be almost impossible to construct such an enormous object and keep all the dimensions exactly as it was

designed.

Today's Measurements The 12 : 1 Ratio Results Difference

The Entrance floor 55.6833 55.6898 0.0065

The Queen's Chamber floor 69.5650 69.6122 0.0472

The King's Chamber floor 140.8487 139.2245 1.6242

Pay particular attention to this group of measurements.

Notice how close the ancient lengths are to the modern day lengths.

QUESTIONS TO BE ANSWERED What is the height of the Great Pyramid of Giza What are the Pyramid of Giza entrance dimensions What is the slant height of the Great Pyramid of Giza What is the length of the base of the Great Pyramid of Giza What are the interior dimensions of the Great Pyramid of Giza What are the measurements of the Great Pyramid of Giza What are the dimensions of the Great Pyramid of Giza What is the height of the Great Pyramid entrance What is the angle of the Great Pyramid of Giza How old is the Great Pyramid of Giza The Great Pyramid of Giza |

Entrance

70.8384

43.8615

Pyramid of Giza and gives the height, slant height and entrance height values.

Without these values other dimensions cannot be calculated.

The 12:1 ratio is acceptable mathematics for the time the Pyramid was built.

The ancient Egyptians would have used this ratio.

The Great Pyramid of Giza |

Entrance Height 55.6898

measurements in this design. The reference points are extremely

close.

The King's Chamber difference is 1.642

The Queen's Chamber difference is 0.0473

The Entrance difference is 0.0065

descriptions are different of course but the end result is the same. We describe the Entrance

height as 55.6898. How did the Egyptians describe it? Was it cubits or something else, it would be

nice to know. One thing is certain, this measurement was very important to The Pharaoh and his

designers and builders.

RATIOS Built The Great Pyramid |

The geometrical layout of the Great Pyramid interior was accomplished by manipulating ratios.

Two lengths were used:

1) Derived from the Entrance height from the Pyramid Base. 55.6898

This ratio was used on horizontal and vertical planes only.

2) Derived from the Descending passage from the Entrance to the Pyramid Base. 124.5262

This ratio was used on angular planes only.

Both ratios were connected. The start and end of the vertical meets the start and end of the

horizontal.*Precisely!*

e.g. The Ascending passage angular ratio meets the Base to King's Chamber vertical ratio.

*Precisely!*

This means that the Passageway angles are controlled by the ratio values and establishes the

original desired Passageway angles at 26.565º and 26.565º respectively,

Their is no reason to today to question what the angles were meant to be.

Two lengths were used:

1) Derived from the Entrance height from the Pyramid Base. 55.6898

This ratio was used on horizontal and vertical planes only.

2) Derived from the Descending passage from the Entrance to the Pyramid Base. 124.5262

This ratio was used on angular planes only.

Both ratios were connected. The start and end of the vertical meets the start and end of the

horizontal.

original desired Passageway angles at 26.565º and 26.565º respectively,

Their is no reason to today to question what the angles were meant to be.

Angular ratios derived from the Entrance to the base 124.5262

Vertical and horizontal ratios derived from the Entrance height from the base 55.6898

Was it a cubit? There are many different cubit dimensions out there. Could it be Egyptian inches?

Other than being a part of the 12:1 ratio what does it mean?

Did the ancients use multiples of 1.618 and 8.618?

These dimensions require investigation above all else.

THE RATIOS EXIST.

THEY CANNOT BE DENIED.

The ratios shown constitute the only true mathematical |

system found in the Great Pyramid. |

SIMPLE EFFECTIVE MATHEMATICS.NO pi NO phi NO aliens. ONLY SIMPLICITY, ENGINEERING SKILLS, AND INGENUITY. THE SECRET OF THE GREAT PYRAMID IS THE ENTRANCE HEIGHT. |

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Sir Flinders Petrie (1880) King's Chamber floor height from Base **140.8487**

Sir Flinders Petrie (1880) Queen's Chamber floor height from Base **69.5650**

Sir Flinders Petrie (1880) Entrance Height from Base **55.6916**

If you decide to experiment with the dimensions please draw them in this manner:

This dimension must be entered accurately.

As with the others, it must be entered accurately.

As you enter the lines as described you will find as you go along that the ratios become evident. It is all simple, no higher

mathematics are needed.

The Base, the Queen's Chamber, The King's Chamber, The Passageway Intersection, the Entrance Doorway are all connected

by Ratios. The angular passageways are positioned by using the Descending Passageway length 124.5262.