## The Great Pyramid of Egypt closely embodies Golden Ratio proportions.

There is debate as to the geometry used in the design of the Great Pyramid of Giza in Egypt. Built around 2560 BC, its once flat, smooth outer shell is gone and all that remains is the roughly-shaped inner core, so it is difficult to know with absolute certainty. The outer shell remains though at the cone, so this does help to establish the original dimensions.

There is evidence, however, that the design of the pyramid may embody these foundations of mathematics and geometry:

- Phi, the Golden Ratio that appears throughout nature.
- Pi, the circumference of a circle in relation to its diameter.
- The Pythagorean Theorem – Credited by tradition to mathematician Pythagoras (about 570 – 495 BC), which can be expressed as a² + b² = c².

So how might the Great Pyramid have embodied these concepts? There are a number of theories to explore.

**Update:** See also the article on golden ratios in the site design of the Giza Pyramid complex.

## A pyramid based on Phi varies by only 0.025% from the Great Pyramid’s estimated dimensions

Phi is the only number which has the mathematical property of its square being one more than itself:

Φ + 1 = Φ²

or

1.618… + 1 = 2.618…

By applying the above Pythagorean equation to this, we can construct a right triangle, of sides a, b and c, or in this case a Golden Triangle of sides √Φ, 1 and Φ, which looks like this:

This creates a pyramid with a base width of 2 (i.e., two triangles above placed back-to-back) and a height of the square root of Phi, 1.272. The ratio of the height to the base is 0.636.

According to Wikipedia, the Great Pyramid has a base of 230.4 meters (755.9 feet) and an estimated original height of 146.5 meters (480.6 feet). This also creates a height to base ratio of 0.636, which indicates it is indeed a Golden Triangles, at least to within three significant decimal places of accuracy. If the base is indeed exactly 230.4 meters then a perfect golden ratio would have a height of 146.5367. This varies from the estimated actual dimensions of the Great Pyramid by only 0.0367 meters (1.4 inches) or 0.025%, which could be just a measurement or rounding difference.

A pyramid based on golden triangle would have other interesting properties. The surface area of the four sides would be a golden ratio of the surface area of the base. The area of each trianglular side is the base x height / 2, or 2 x Φ/2 or Φ. The surface area of the base is 2 x 2, or 4. So four sides is 4 x Φ / 4, or Φ for the ratio of sides to base.

## A pyramid based on Pi varies by only 0.1% from the Great Pyramid’s estimated dimensions

There is another interesting aspect of this pyramid. Construct a circle with a circumference of 8, the same as the perimeter of this pyramid with its base width of 2. Then fold the arc of the semi-circle at a right angle, as illustrated below in “Revelation of the Pyramids”. The height of the semi-circle will be the radius of the circle, which is 8/pi/2 or 1.273.

This is only 1/10th of a percent different than the height of 1.272 computed above using the Golden Triangle. Applying this to the 146.5 meter height of the pyramid would result in a difference in height between the two methods of only 0.14 meters (5.5 inches).

## A pyramid based on areas is identical in geometry to one based on Phi

In addition to the relationships of the pyramid’s geometry to phi and pi, it’s also possible that the pyramid was constructed using a completely different approach that simply produced the phi relationship. The writings of Herodotus make a vague and debated reference to a relationship between the area of the surface of the face of the pyramid to that of the area of a square formed by its height. If that’s the case, this is expressed as follows:

Area of the Face = Area of the Square formed by the Height (h)

(2r × s) / 2 = h²

We also know by the Pythagorean Theorem that r² + h² = s² , which is equal to s² – r² = h², so

r × s = s² – r²

Let the base r equal 1 to express the other dimensions in relation to it:

s = s² – 1

Solve for zero:

s² – s – 1 = 0

Using the quadratic formula, the only positive solution is where s = Phi, 1.618…..

This same relationship is shown on the Mathematics of Phi article, where we how Phi is calculated based on dividing a line so that the ratio of the line to the larger section is the same as the ratio of the larger section to the smaller section. If the height area to side area was the basis for the dimensions of the Great Pyramid, it would be in a perfect Phi relationship, whether or not that was intended by its designers. If so, it would demonstrate another of the many geometric constructions which embody Phi.

## A pyramid based on a constant gradient varies by 0.8% from the Great Pyramid’s estimated dimensions

Yet another possibility is that the Great Pyramid is based on another method, known as the seked. The seked is a measure of slope or gradient. It is based on the Egyptian system of measure in which 1 cubit = 7 palms and 1 palm = 4 digits. The theory is that the Great Pyramid is based on the application of a gradient of 5.5 sekeds. This measure means that for a pyramid height of 1 cubit, which is 7 palms, its base would be 5.5 palms. The ratio of height to base then is 7 divided by 5.5, which is 1.2727. This is very close to the square root of Phi, which is 1.27202. The slope of a pyramid created with sekeds would be 51.84°, while that of a pyramid based on phi is 51.83°. The seked method was known to be used for the construction of some pyramids, but not all. If used on the Great Pyramid it should have resulted in a height of 146.618 meters on a base of 230.4 meters. This is 0.118 meters (4.7 inches) greater than the actual estimated height of the Great Pyramid. This variance of 0.8% thus does not match the geometry of the Great Pyramid as closely as the geometries based on phi or pi. This result is very close to the dimensions of the Great Pyramid. The question remains though as to why 5.5 would be chosen over some other number for the gradient. What was more appealing about 5.5 rather than simply using a gradient based on 5 or 6? Even without a mathematical knowledge of Phi, a simple awareness of the golden ratio observed in nature might have led choosing this proportion.

Illustration of the Seked method (Image credit to David Furlong):

## Its near perfect alignment to due north shows that little was left to chance

One thing that is clear is that the dimensions and geometries were did not happen by chance. Would a civilization with the technological skill and knowledge to align the pyramid to within 1/15th of a degree to true north leave the dimensions of the pyramid to chance? If they did not intend the geometry that resulted in a rather precise angle like 51.83 degrees, why would they have not used another simpler angle found in divisions of a circle such as 30, 45, 54 or 60 degrees? Only one other Egyptian pyramid used this geometry or angle of incline, the Meidum pyramid, and it’s a step pyramid with three tiers. Given that there are several ways based in simple geometry by which the Great Pyramid could have ended up with this precise angle, it seems unreasonable to suggest that none of them apply, until another equally plausible and accurate theory can be presented.

## Other possibilities for Phi and Pi relationships

If the Egyptians were using numbers that they understood to be the circumference of the circle to its diameter or the golden ratio that appeared in nature, it’s difficult to assume that they truly understood the actual decimal representations of pi and phi as we understand them now. Since references to phi don’t appear in the historical record until the time of the Greeks hundreds of years later, some contend that the Egyptians did not have this knowledge and instead used integer approximations that achieved the same relationships and results in the design.

A rather amazing mathematical fact is that pi and the square root of phi can be approximated with a high degree of accuracy using simple integers. Pi can be approximated as 22/7, resulting in a repeating decimal number 3.142857142857… which is different from Pi by only 4/100’s of a percent. The square root of Phi can be approximately by 14/11, resulting in a repeating decimal number 1.2727…, which is different from Phi by less than 6/100’s of a percent. That means that Phi can be approximated as 196/121.

The Great Pyramid could thus have been based on 22/7 or 14/11, which is the same as 7/5.5, in the geometries shown above. Even if the Egyptians only understood pi and/or phi through their integer approximations, the fact that the pyramid uses them shows that there was likely some understanding and intent of their mathematical importance in their application. It’s possible though that the pyramid dimensions could have been intended to represent only one of these numbers, either pi or phi, and the mathematics would have included the other automatically.

We really don’t know with certainty how the pyramid was designed as this knowledge could have existed and then been lost. The builders of such incredible architecture may have had far greater knowledge and sophistication than we may know, and it’s possible that pi , phi or both, as we understand them today, could have been the factors in the design of the pyramid. It could be that they chose other approaches that resulted in almost identical geometries.

A detail of the geomatries and calculations is below:

Pyramid | Base in Meters | Height in Meters | Base/2 in Meters | Ratio of Height / (Base/2) | Angle Radians using (ATAN) | Convert Angle to Degrees | Variance from Actual in Meters | % Variance from Actual |

Great Pyramid of Giza | 230.4 | 146.50000 | 115.20 | 1.271701 | 0.90443531 | 51.82033 | ||

Phi Geometry | 2.0 | 1.27202 | 1.00 | 1.272020 | 0.90455689 | 51.82729 | ||

Phi to Scale | 230.4 | 146.53666 | 115.20 | 1.272020 | 0.90455689 | 51.82729 | 0.0367 | 0.025% |

Pi Geometry (8/pi/2) | 2.0 | 1.27324 | 1.00 | 1.273240 | 0.90502258 | 51.85397 | ||

Pi to Scale | 230.4 | 146.67720 | 115.20 | 1.273240 | 0.90502258 | 51.85397 | 0.1772 | 0.121% |

5.5 Seked | 230.4 | 146.61818 | 115.20 | 1.272727 | 0.90482709 | 51.84277 | 0.1182 | 0.081% |

## One fact and one interesting question remains

The fact is that whatever method was used in its design, the end result represents the geometry of a phi-based triangle with a high degree of accuracy.

The interesting question is “why did they choose this specific shape geometry and configuration of three pyramids for the Great Pyramid?” It’s different than the rest and was clearly done with intent. Was it because it appeared more beautiful, more aligned with nature? If not that, what other reasons did they have that captured this one number associated with nature and beauty?

## Construct your own pyramid to the same proportions as the Great Pyramid

Use the template below in gif or pdf format:

Thanks go to Jacques Grimault for these insights, and for other fascinating facts and speculations presented about ancient pyramids in the movie on “The Revelations of the Pyramids.”

**References:**

http://en.wikipedia.org/wiki/Great_Pyramid_of_Giza

http://en.wikipedia.org/wiki/Ancient_Egyptian_units_of_measurement

http://www.kch42.dial.pipex.com/sekes0.htm

http://earthmatrix.com/great/pyramid.htm

Great Pyramid Giza Site Complex Golden Ratios

Nico says

The base of the great pyramid could be equal to b=c/π/(sqrt(2)-1) which is in my calculations somewhere close to 230.380924 meters using:

b=base, c=lightspeed (current best estimate) = 299792458 m/s, π=3.141592653589793238462643383279 (some “signigficant” number of decimals:-),

sqrt(2)-1=0.414213562 which also happens to be a nice number since 1/(sqrt(2)-1)=2.414213562 (which is exactly 2 higher)

also,

If you do some calculations on the height it turns out to be b=1/2*π*h to come exactly to the golden ratios for the surfaces. (b=base,h=height)

Caroline P Timmis says

The mathematical argument concerning the discrepancies observed are meaningless. The dimensions of Khufu will have been perfect upon construction. Movement, over time will have resulted in said discrepancies. Enoch Pray

Limok says

https://youtu.be/HiQ8l7Vbgic

Robert O. Pritchard says

Subsequent settling as well as temperature variations based on sun exposure to the smooth versus rugged surfaces of today –all would seem to allow adjusting minute variations between calculated and physical measurements. Robert O. Pritchard Cheboygan MI 5.13.16

Edward Gary Wick says

If the base was 440 cubits, 440/2= 220. Draw a horizontal line 220 cubits long, now off the two end points draw two vertical lines. One of the two lines at (220 * 1.62) 356.4 follow that radius to where it intersects the other vertical line. From the horizontal line to the intersection it is 280.3943 cubits.

You can do this with a square. PHI and a piece of string.

Panagiotis Stefanides says

http://www.stefanides.gr/pdf/2012_Oct/PHOTO_12.pdf

p.stefanides

kerry says

I find it quite interesting that there have been no plans or blueprints found of the great pyramid as the Egyptians were meticulous when it come to writing. surely they had plans in which to work from?

Beto says

Maybe it wasn’t the Egyptians who planned and built it.

Johnny says

I think you are correct.I don’t think the ancient Egyptians build the Great Pyramid or the Sphinx.I think they were build by some advanced civilization either living on Earth or from another place in the Universe.

Mark Windsor says

The civilisation that existed in Noah’s day (before the Great Flood) was INCREDIBLY advanced. It is doubtful they were as advanced as us, but they had knowledge of earth science, physics, and metallurgy that still confounds our scientists of today. For example, in the current study of the remains of Noah’s Ark, researchers discovered metal studs used in the construction that are made of steel, platinum, and aluminum. The latter of which is not even found in nature. Also, in an dated story that made the newspapers in the early 20th Century, someone living in Chicago found a hand bell encrusted in a lump of coal. It dated back to the same Antediluvian Period of history, and not only did the bell still ring perfectly, its composition was of two metals that metallurgists today say they cannot be combined. Yet the pre-Flood civilisation was able to do it. Incidentally, the length of Noah’s Ark is the same exact number of cubits as the height of the Great Pyramid. The slope angle of the Great Pyramid is related to the speed of light (not Einstein’s calculation but the perfected speed of light mathematically discovered in the early 1970’s). Just those two pieces of information are too coincidental to be dismissed as accidental. And then there is all the modern research that has shown how the Great Pyramid is actually some kind of machine to generate power. Thanks to the inventions of aeroplanes and modern navigation instruments, a number of pyramids have been uncovered in the last 80 years. One underwater off the coast of the Bahamas, and another underground just east of Anchorage, Alaska, to name a few. After all these millennia, still generating power and emitting an electromagnetic field that made magnetic navigation instruments go wonky. Scientists, unable to understand how exactly the pyramids worked, were at least able to disable them (so no more planes and boats getting lost at sea). Whatever that pre-flood civilisation was, one can only speculate what other technology those people had (flying craft? genetic experimentation?). In any case, regarding the question of “who built the Great Pyramid”, my money is on them. To generate wireless electricity and/or generate a worldwide A440 harmonic resonance, who knows. It just really stinks that all this information and research and knowledge has been surfacing since 1900 and yet we STILL cannot purchase a Powermid Mark III for our homes. No working replica of the Great Pyramid has ever been attempted, nor has any corporation tried to develop the technology. It is a bit odd. >:\

Franc says

Metal studs from Noah’s Ark? You must be referring to Ron Wyatt’s “find”. Or didn’t you know the ark was “discovered” AGAIN 3 decades later in another location. Sorry, Mark, but Noah’s Ark has not been found, and Ron Wyatt’s discovery has been disproven. You might find the following Web site helpful: http://www.tentmaker.org/WAR/

All that aside, yes I agree the Great Pyramid is one heckuva piece of engineering and a mystery. Besides the possibility of it having been built by an ante-deluvian race, there is even a theory that says a pre-Adamite (pre-Adamic?) race built the pyramids (plural meaning the Great Pyramid and the now-underwater ones). There are quite a few fascinating books on this subject, as you probably know.

kirazeek says

simply we are not alone

Gage says

They probably just got rid of them so robbers wouldn’t be able to get into the tomb that held the pharaoh and his treasure.

Franc says

Ahh,… the tomb was empty.

D. says

There are Egyptian figures all through the region…of course they built it. Romans and Greeks learned mathematics, religion, “government” agriculture, and self-defense from them. The tradition of learning was mostly oral and done by doing, not necessary by writing everything down.

The Egyptian culture was well advanced hundreds of years before anyone else “discovered” the Pyramids and Egyptian culture.

Franc says

It was very different from the other “Egyptian figures all through the region” in that it did not have any hieroglyphics or drawings of any kind, and its tomb was empty — no mummified remains, not even treasure was found. In that sense it was not Egyptian. The only thing Egyptian about it is that it is located in Egypt.

eric says

i think aliens built them

Elton says

There are three possible culprits for the design and construction of the Great Pyramid. They are:

Father Abraham who came out of Ur and brought with him the secrets of Astronomy.

Joseph, who was sold into Egypt who was trained by Jacob/Israel in how to read Hieroglyphs.

And someone so bizarre that it’s unthinkable to the Archaeologist’s mind. A far out, far away, lost Civilization that had mapped the Earth’s longitudes with the same precision that we have. We used time, they used the Precession of the Equinox.

mothergoddess says

Eldon, I truly do believe, after a great deal of research, that ancient people in Europe had a hi order of mathematics and geometry as far back as 25,000 BC or even from Africa ( Blombos cave, ochre stone) and also had “signs” as a very basic language, that are found in ancient cultures around the world ( waves, circles, dots, swastika, etc). If we can have genius’ then they could have too. Many hi IQ people today have Schizophrenia, Aspergers, etc and a few exceptional people who are mentally healthy- In other words people who see the world from a different perspective. The ancients could have had a few that passed on their knowledge and eventually became a nomadic priesthood (astrologers) that left monuments (pyramids, circles, etc) everywhere. About 3500-4000 BC S at Skara Brea there were found 5 types of small carved balls that represented the 5 Platonic Solids ( all matter in the universe can be made from these basic shapes). These were made about 3,000 years before Plato. They could have come into Europe from anywhere, but possible thru Spain around LGM.

Digby says

i think Enoch the shepherd king built the great pyramid of giza

Anand says

Pyramid architecture is surprisingly advanced, but modern science tells what man is able to accomplish, so it may have been our world civilization building these amazing structures of advanced knowledge. The site at http://1008anand108.page.tl shows some of the mathematical perfection by the reorganisation of the ancient yantra mandala as pyramid architecture, closest to sun pyramid in Bosnia perhaps. However, when and who was building it we do not know, because later clues may be just showing one period of time. We plan to build by pyramid architecture a climate ship as Pyramid Architecture Universitas Academy, and welcomes people wanting to form the Academy to join in.

greg says

I also notice the ratio in courses to width in the grand gallery. 22 steps, at 7 ft of width.

I discussed this in respect to resonance with Christopher Dunn in Glenview Il in 1999.

I never heard back on that.

Dave Lightbody says

Interesting to see this article repeat the same (and understandable) erroneous conclusion drawn by many previous works regarding the Great Pyramid and the supposed deliberate occurrence of Phi in its dimensions. In fact, the occurrence of Phi was an inadvertent by-product of the deliberate use of circular proportions in the structure, by its Old Kingdom Egyptian architects. The circular proportions (which explain why Pi is observable) were thought to bestow encircling ritual protection on the monuments, and this was included deliberately there and on other pyramids and tombs, and in the proportions of the Great Pyramid’s tomb chamber. Egyptology Professor Petrie, Verner, Edwards and myself (background in archaeology and engineering and studied this for 10 years) all concur on this point. It was circular proportions that determined the shape of the pyramid at Giza for Khufu, not Phi or any Golden Ratio, which were culturally unknown and even irrelevant for the Ancient Egyptians whose life was based on practical, functional geometry and basic symbolic systems.

SEE HERE FOR a website that discusses some research I carried out on the Great Pyramid with the National Museum of Scotland recently:

http://arkysite.wordpress.com/2013/05/07/the-edinburgh-casing-stone-a-piece-of-giza-at-the-national-museum-of-scotland/

Dr Dave Lightbody.

Gary Meisner says

Actually, the article concludes with this: “It’s possible though that the pyramid dimensions could have been intended to represent only one of these numbers, either pi or phi, and the mathematics would have included the other automatically. We really don’t know with certainty how the pyramid was designed as this knowledge could have existed and then been lost.” There’s still much we don’t know about the pyramids, and there are those who disagree with the traditional beliefs held about them. I respect your work and viewpoint, but think there is merit in presenting viable alternatives for the reader.

mark worrell says

Dr.lightbody…..I am sure your a busy man but I truely need to discuss some very important issues that I think I have answers that I just came across the last couple months…your article here is part of it and I think you may understand me on this one….I look forward to speaking with you if you choose so..take care Mark…..markd.worrell@gmail.com

Scott Tucker says

You state that “phi is the only number which has the mathematical property of its square being one more than itself.” This is not true. If you solve the equation x^2 – x – 1 = 0, you get 2 solutions, one of which is phi. The other number is negative and would be irrelevant in constructing something. But to be accurate, you should probably change your assertion to “phi is the only *positive* number….”

Gary Meisner says

That is partially correct. There are indeed two solutions. One is 1.618…, which is known as Phi with an upper case. The other is the -0.618, and 0.618 is the reciprocal of Phi, also often known as phi with a lower case. So both of these numbers are known as “phi”, with one of the solutions being its negative version.

Paul Hansen says

Isaiah 19:19+20 In ancient Hebrew letters also had numerical value. If you use the measurements that were used at the time, the pyramid inch then the numerical value of the words in these 2 verses in Isaiah add up to be the height of the Giza Pyramid. The pyramid inch was derived by taking distance from north pole to south pole thru the core of the earth and dividing that distance by 500,000,000. The pyramid inch was also used in Solomon’s Temple and the arch of the covenant which is also the same exact measurements of the stone arc found inside the King’s Chamber in the Great Pyramid.

Edward Gary Wick says

The Hebrew’s were in Egypt for how many years before Moses? I don’t see them changing their unit of measurement on their own. Heck, we can’t even go metric.

Study “The Battle of Kadish”. Canaan was part of Egypt at the time of Moses. Thutmose III fought a battle at Tel Megiddo (Armageddon) to secure or take back this land from the upstart Amorities. This land and lands much further north were Egyptian territory up to and past the time of Ramses II. The wilderness that Moses wondered were just outside of Egyptian territory. When Moses died the Hebrew’s reentered Egyptian territory. If the Egyptian army would have won the “Battle of Kadish” the Hebrew’s would most likely have been the occupying force. Moses never was “un-banished” from Egypt.

Abdu says

phi is mentioned as 256/121 the true figure is 196/121

Gary B Meisner says

The text above has been revised. Thank you for the correction.

Sean says

They used a wheel to measure the dimensions of the base. They unknowingly introduced pi.

Gary Meisner says

And perhaps they unknowingly aligned the pyramid to within 1/15th of a degree to true north too? Doesn’t the evidence more readily suggest a high degree of sophistication in their knowledge?

Binkley says

True north is not difficult for anyone who observes Polaris – which from Egypt gives a nice line on true north – or, for that matter establishes East and West at the solstice. I prefer a simpler solution that using wheels for measurement accidentally included the Golden Mean.

For that matter using ‘palms’ and ‘cubits’ could accidentally include the golden mean – our skeletons include the ratio also.

Rajwade Sunil Chintamani says

I am doing search work on music theorapy. I would like to construct a pyramid based on golden ratio. Size of the pyramid around 4 or 6 feet base. What should be height. Kindly guide me. also I would like to small pyramid about 4 inch what should be height.

Gary Meisner says

Use the Golden Triangle above to make such calculations. It’s base is shown as 1, so the full base for a pyramid is 2. If you want a 4 foot base, you multiply the dimensions by 2. The base is then 4. The height is 2 times the square root of Phi, which is 2.544. The hypotenuse is 2 times Phi, which is 3.236.

hack_nug says

Didn’t they say the great pyramid had 8 sides?

Here’s a link with some facts about it (number 12 is the one I mention): http://www.ancient-code.com/25-facts-about-the-great-pyramid-of-giza/

art c says

Simple experimenting will show that for a rectangle with given perimeter, maximum area is obtained if it is a square, and for a triangle the maximum area is obtained if it is equilateral. For a pyramid maximum volume is obtained if base is square and sides are equilateral triangles with sides same base side.

lupsaman says

it’s almost funny how people in charge who have this information can hide it from the controlable masses and rewrite hystory, and supress knowlwdge…. but we are about to wake up.

art says

A rectangle of given perimeter will have maximum area if it is a square.

A triangle of given perimeter will have maximum area if it is equilateral.

A pyramid will have maximum volume if it base is a square and its sides are

equilateral triangles.

This requires only simple math to arrive at.

No pi or phi needed.

Gary Meisner says

That may be, but then the sides of the Great Pyramid are not equilateral triangles. The triangles on each side of the pyramid have a base with a relative length of 2, and the two other sides have a length of 1.618 (Phi). If they could have maximized the volume or surface area by using equilateral triangles, especially given the high cost of construction, then why didn’t they do so?

jacob says

Do you guys make pyramids to these exact dimensions or know someone who does?

Raymond says

I’ve heard that the Great Pyramid is also 8 sided to signify the equinoxes. I saw a documentary that included some history, but mostly about the Pyramid its’ self. In it, there was a photo of the Pyramid taken from a plane a few years after the second World War, during the equinox, and it clearly showed that half of each of the two of the sides facing away from the sun shadowed on one half and (sort of) light up on the other, and that this can not be seen during the rest of the year. Do you have more information about this? I can not seem to find that documentary again.

Indy says

Think of the Pyramids as Foundations of Palaces, Human timeline of 10,000 years people!

mousa sadighi says

Primary concerns of mankind was,is and always will be are Ownership and Orientation that leads to counting,calculation, navigation and astronomy to start with mankind knowledge.Signs for counting(numbers)lead phonetic signs(alphabet)through out the History.

Early use of pen and paper as well as tools goes back to civilizations in Asia and Africa because of easy access to natural facilities like minerals,texture of soil,open skies and so on.

Historical documents are not quiet referable.

We should not be surprised if Chinese,Egyptians,Indians,Babylonians or Persians knew about Square roots or Divine proportions as leading nations, since when a curious person starts measuring shadows as natural time peace in different times of days and seasons and makes breaks for constructions and studies it’s diagonal proportion he will come up with,not so miraculous.

shogun says

The fact that the pyramid faces true north and during the spring and fall equinoxes the pyramid shows 8 sides from the sky is enough to baffle anyone with any sense of wonder. forget the fact of the impossible feat of its construction, its mathematical and symbolic properties is enough for one to realize this is the work of something divine.

PANAGIOTIS STEFANIDES says

COMPARE:

http://www.stefanides.gr/pdf/2012_Oct/PHOTO_11.pdf

WITH

http://www.stefanides.gr/pdf/2012_Oct/PHOTO_12.pdf

Regards from Athens,

Panagiotis Stefanides

Robert Riggs says

Can anyone help me with the ratio of base to ridge dimensions of the Cheops pyramid, please?

Thank you!

Gary Meisner says

Those dimensions are presented on this page. The Great Pyramid of Giza is also known as the Pyramid of Khufu or the Pyramid of Cheops. See http://en.wikipedia.org/wiki/Great_pyramid_of_giza.

Robert Riggs says

Thank you, Gary. That is a good reference. What I am looking for is the base to ridge ratio, i.e.,base equals I, ridge equals X. I see lots of references to height, but haven’t found the ridge length.

Gary Meisner says

This simplest solution is likely to use the Pythagorean theorem to calculate it: Ridge = the square root of (base squared plus height squared.)

Bob Riggs says

Oh, right! Thank you Gary!

I’m building a 10 foot pyramid on a four foot wall to house my astronomy gear and observe from. It’s a fun project, and will be real cozy this winter.

Best regards…Bob

John Morgan says

I wonder if a combination of these schemes was used.

Such a coincidence otherwise..

https://drive.google.com/file/d/0B637hKjsUvvMVnVHdms5OVR4UTg/edit?usp=sharing

thabiso maseko says

its intersting to see that some of the things that we just grew up knowing that they are there,actually have an origin………….

John Morgan says

Have added a pyramid calculation using phi pi and e. Hope its interesting.. let me know..

https://drive.google.com/file/d/0B637hKjsUvvMaDZKXzNMRTUzbGs/view?usp=sharing

Thanks.

Jason Li says

In my opinion, great pyramid of khufu means low golden section transform which is a class of orthogonal transform in mathematics, see my ppt 🙂 http://www.slideshare.net/jasonli1880/great-pyramid-of-giza-and-golden-section-transform-preview

Ashraf says

The actual dimension of great pyramid Giza is in Holy Quran.The verse 28:38 is the main verse regarding pyramid. The verse is in sura 28, verse no 38, total word 27 ,letters 103 and gematrical value is 6157. Add the nos.28+38+27+103=196. Now 6157=3.14×280.11×7. Here 280 is the hight of great pyramid in royal cubits.Again please devide 6157 by 7 it becomes 879.57 which is twice the base of pyramid length. If 6157 is devided by 196 , it becomes 31.4132…..which is 10x 3.1413… Please compare this value from international survey.

Arthur says

The angle of slope 51.8272923730° is acos(phi) –> cos(51.8272923730) = phi = sin(51.8272923730)^2.

according to http://milan.milanovic.org/math/english/golden/golden3.html

after calculations …

“The Great Pyramid turns out to have the same perimeter length when measured in a horizontal plane, as a square, and in a vertical plane, as a circle.”

In your example (pdf) :

Perimeter as a square = 4*2

Perimeter as circle = 2*pi*sqrt(Phi)

Means pi = 4/sqrt(Phi) = 3.1446055110296931442782343433718357180924882313508929506596078804047281904892436548476515566340325422

In Figu forum for example you can find the same result http://forum.figu.org/us/messages/863/8884.html?1205193138#POST31322

Giza Height : 152.9553357

Elements in the universe * Giza Height * 7 = Speed of light

280 * 152.9553357 * 7 = 299792.457972

http://www.futureofmankind.co.uk/Billy_Meier/Contact_Report_127

As Jain said there is a fight between the west and the east about Pi.

http://www.jainmathemagics.com/page/10/default.asp

here is an interesting article about “The Mathematics of the Great Pyramid:”

http://greatpyramidmath.weebly.com/25.html

Gary Meisner says

The pyramid relationship does not necessarily have to mean that pi is defined as 4/sqrt(Phi), or 3.1446055… It can also just mean that the pyramid embodies the actual value of pi, 3.14159…, with a high degree of accuracy.

Arthur says

There are 2 claims about phi and pi in the pyramid.

1 – “The perimeter of the base of the Great Pyramid equals the circumference of a circle whose radius equal to the height of the pyramid.”

So : 4 * 2 = 2 * pi * sqrt(phi) –> pi = 4/ sqrt(phi) –> 3.144 605 511 …

2 – “The area of that same circle, with radius equal to the pyramid height equals that of a rectangle whose length is twice the pyramid height (sqrt(phi)) and whose width is the width (2) of the pyramid.”

Area of rectangle = 2 *sqrt(phi) * 2 = 5.088

Area of circle of radius sqrt(phi) = Pi *r^2 = 5.088

So : Pi * r^2 = 2 * sqrt(phi) * 2 –> Pi = 4* sqrt(phi)/ Phi = 3.144 605 511 …

Which means if (i repeat IF) those 2 claims are right pi is not 3.14159 but 4 / sqrt(phi) = 3.144 605 511

https://www.dartmouth.edu/~matc/math5.geometry/unit2/unit2.html

Gary Meisner says

There are dozens of methods to calculate Pi to as many digits as you want, as shown at http://en.wikipedia.org/wiki/Pi. They’re all based on mathematically sound concepts, and all produce the same value for Pi. The pyramid’s approximate relationship to both pi and phi is very interesting, but the absence of its limestone skin make its dimensions subject to estimation. Why would anyone assume that unproven claims about the pyramid would unveil a more accurate value for Pi than numerous mathematical methodologies that all confirm a different value? Alternatively, can anyone prove that all the other methods of calculating Pi are wrong?

Arthur says

> Alternatively, can anyone prove that all the other methods of calculating Pi are wrong?

Yes.

You can let a comment after this demonstration that pi = 4/sqrt(phi) here :

http://www.veteranstoday.com/2015/02/05/pi/

“Please pass this article along and help us challenge the academics to adopt the correct value of pi”

Or prove the demonstration is wrong.

Kristian Factora says

Try to contact me because when i had created my book(never been publish yet) just last year before i graduate college i was 19 when i first started now i’m 21 and studying mathematics just by myself…I had created a consciousness book related towards my experience and now that i read this site I was SHOCKED! about my findings that this Pyramid of Giza is created upon a mathematical perfection!…Upon my discovery that the Giza has never been finished on its top portion and I had the answer already and this 51 degrees related also towards my findings is very accurate and related towards everything beyond the cosmos…Wew this is Epic!!!

Isaac W. Ofosu says

I think the great pyramid and the sphinx as well as the other artefact dotted around the world such as the one in Peru and Easter Islands were built by an advanced civilization who once inhabited the earth. The Egyptians I think , dicovered the pyramid. They did not know who built it. That is why they don’t have any records.

vikhnesh says

i find it very interesting but my doubt is that how is it related astronomically.

Benjamin says

Hello everyone! 🙂

I made a video about the Great Pyramid, the number Pi and Phi…

The link : http://www.youtube.com/watch?v=dp31oVdIfek

Goodbye! 🙂

ak says

The ‘pi-theory’ is supported by people who argue that the Earth’s radius divided by 432 gives the pyramid height (ignoring some zeros). They claim further that 432 is a very “significant number’. One can agree that, as it is the double of 216, it has some interesting properties but that is another story, probably.

Annd says

The ancient yantra or perhaps also David star, see my homepage; http://www.1008-108.webs.com, I have perfectionated and possible this is lost pyramid architecture. Is phi and golden values found here, too, after al the perfection was found by the relationship between circle and square? Please send answeres also as mail.

cheers Anand

MJ says

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MJ FAN says

OMG everyone its MJ holy moly SICK

Jesus says

A triangle with 2 equal heights and minimum perimeter gives two equal angles whose cosine is 0.6180339887 51.8272923729º is Phi – 1 proportions that we find the Great Pyramid.

http://triancal.esy.es/?y=345.90660621318&z=345.90660621318&p=1151.9349550497

If you click on the “draw” button and marks the notable elements get the approximate position of the secret chambers, perhaps in the orthocenter there is some yet undiscovered.

http://triancal.esy.es/HTML/GG.html?C=0.90455689430235&B=0.90455689430235&a=439.9999999999

kaya-lah says

comment point everything to say the people of the Afrikan Continent did NOT reach such heights..very sad…esp when headed up the great Hapi, u basically find the evolution of pyramid architecture with Giza being the culmination…gasp, cant be…they’re BLACK…smfh aliens only did it because of all the evidence on tv…

Gary B Meisner says

I’ve never heard anyone refer to limitations of our human ability to construct the pyramids to have anything to do with race. Without specific evidence it would be wrong to assume so. The feat of their construction is just beyond what we know any humans to have had at that point in history, and is unexplained today. Race has nothing to do with it.

Richard says

Hi everyone,

What a great debate. I might be jumping in a bit too late, but I was looking for some advise.

I wanted to create a pyramid using the golden ratio number only.

Would be something small, from 10 to 20 or 30cm height, but I wanted to be constructed using the golden ratio numbers.

I need your help to make it as accurate as possible using this method.

I wanted to be perfect all the way, from the angles to the smallest detail.

Can anyone please help me around, providing me the exact measures to be used, in a simplified way, so I can pass it on to the fabric?

Thank you.

Gary B Meisner says

As in the illustration above, the sides of the golden ratio-based pyramid have these relative proportions:

Base – 1

Height – Square root of Phi (1.27201964951…)

Hypotenuse – Phi (1.61803398874…)

If you want a height of 30 cm, just divide that by 1.27201964951 to get the base of 23.585 cm and multiply it by 1.27201964951 to get the hypotenuse of 38.1601 cm. Use the template at http://www.goldennumber.net/wp-content/uploads/2012/08/great-pyramid-golden-triangle-template.pdf to create a pattern that will fold to create the pyramid.

Richard says

Thank you Gary.

antonio says

What kind of beauty hidden dimensions impossible to see if you don’t know “The secret letter” of the ancient builders. Pharaohs were putting their names in the dimensions of the pyramid and thus were given the development of immortality. Nobody can delete the “names” of dimensions.

One of the reasons why there is no text in the Pyramid, the texts are put in the dimensions.

They used Pi to these values: root8 * (10/9) = 3,142696805….

Why? Archimedes said Pi is between this value 223/7 > Pi < 22/7. Between these two values we have an infinite number of values, but only one value can be geometrically constructed "with a divider and a ruler unmarked" this is number 3,142696805…..

Each pyramid is a unique work of art, which carries your message.

Andras Goczey says

first, : “Khufu pyramid size” on youtube

I have been working on Egypt and Giza for the past 8-9 years. Based on my research I have concluded some new and interesting facts that will make the real purpose of the existence of the pyramids clear.

This week I have put a film about Giza, and the time of Giza on youtube in English. I believe it should be interesting for You.

https://www.youtube.com/watch?v=FmHFBgfl7G0

I would greatly appreciate if you would take time to watch the 40 minute long film and perchance reflect on it.

the others:

Khufu’s calendar on youtube

Giza the time machine-World Mysteries Blog on youtube

Sincerely András Gőczey Architect from Hungary

Edward Gary Wick says

I cannot find your video.

What I am seeing here is the Bible code.

I think if you want to know how the pyramids where built and have greater then math 85 skills you should consider yourself unqualified. The reason the sides of the pyramid line up with the north star is, at night someone stood at the center of the base and with a plum line marked the center of the north face, ran a string line from that point to the center plum line and the same distance to the center of the south face. Then took the same distances at 90 degrees for the center of the east and west walls. Now with the Great Pyramid there is no Pythagorean theorem used to find the corners (3, 4, 5). For every two units of measure to each face center use 3 to each corner. Now if you do this for each layer as you go up you will stay true. All you have to do is keep your center point.

I have worked in the stone business for 20 years. It is my understanding that the reason that the Golden Ratio shows up so often is it just looks right to the eye. I try to incorporate it in my creations, not because of some cosmetic connectivity but because it draws the eye for just a bit longer.

Now the building blocks of the Great Pyramid are laid with different thicknesses to the courses because each ledge of stone is different as it sits in the ground. What I put to you is, with the casing stones what height at 51_52 degrees need to be to maintain the same unit of measure so the 2 to edges and 3 to corners without changing the unit of measurement.

The key to the Great Pyramid is they used the K. I. S. S. Principal.

Leon says

All this about the EXTERIOR of the GP and the layout of the plateau. Please look at some of the INTERIOR dimensions, mainly the Kings Chamber which also is built to a ‘rule’.

Newton was concerned with GP measures to try to help him straighten out the true shape of the globe and also a unit of measure.

And ONE other exterior point. The Apothem of the GP is about 185meters. This is an exactly fraction of a minute of arc AT THE PYRAMID.

SsJK says

I read half of the comments here and i have an interesting question for you guys.

We are arguing on how the egyptians the builders of these pyramids knew or didnt know phi?

The question is … hmm how can i put this? So many writings and symbols or any writing system they had.. were there any numerical carvings paintnings or whatever archieologists find due date tells us how did they count things? Cz using about 2.3 million stones to build a pyramid jeezz definitely they knew mathematics and i bet even phi and u know secrecy those days .. they had knowledge and only the ones with power got educated and kept for themselves for centuries.. the city of Iskandaroon the library which held all the records was burned .. well someone till now holds these secrets and as we all know nthng has changed from ancient times till now .. and that’s human nature with his good and evil intentions…

Im just asking it is impossible for one super genious geek to do this work… a system a unit who is well taught and organized could accomplish this kind of achievement so maybe we are looking from the wrong angle and not asking the right questions?

Looking at the pyramid and examining it ..we see that it is almost perfectly build with minor errors of mathematically calculations and alignments with earth and sky… so?? Earth and skyy … earth and upp upp to the sky pointing towards to the sky stars and they are the thombs for the pharoas? Hmm why they want to go up? Preserve their bodies? Magnetic field … and earth is ringing like a bell .. i think they knew mooore about pretty much of everything than what we know and learn 2day …