Exploring the Mystery of the Pyramids Through Units of Measurement Across Eras and Civilizations
Diverse Perspectives on the “Mystery of the Pyramids”
Napoleon and the Egyptian Campaign
y the 19th century, Europe’s dominance in science and technology was firmly established, and many Europeans began to view their continent as the epitome of progress—while labeling Egypt and Asia as undeveloped and primitive. Ancient Egyptian traditions such as magic, astrology, secret rituals, alchemy, numerology, and superstition were increasingly cast as opponents of science, and myths and legends were dismissed as unscientific.
In 1798, the hero of the French Revolution, Napoleon Bonaparte, launched his Egyptian campaign. Armed with modern weaponry such as cannons, the French army decisively defeated the Islamic forces. Napoleon brought with him a large team of 175 specialists, including painters, scientists, and mathematicians, to study the pyramids and other ancient sites. The detailed illustrations produced during this expedition would later become invaluable resources in the development of Egyptology. During the campaign, measurements of the Great Pyramid’s orientation and dimensions were also conducted.
One of the key members of the expedition was the surveyor Edme-François Jomard. He was particularly interested in testing the legend that the ancient Egyptians had known the true circumference of the Earth. Jomard hired a team of 150 Turkish laborers to clear away the debris from the base of the Great Pyramid. Thanks to their efforts, he succeeded in measuring the base length more precisely than anyone before him.
However, despite this remarkable achievement, Jomard withheld his findings for nearly 30 years. By the time he finally published two volumes in 1829, Europe’s fascination with Egypt had faded, giving way once again to the resurgence of Greek idealization. As a result, his work received little attention.
John Taylor and the Proposal of the Pi Mystery
When did the “Pi Mystery” of the pyramids first emerge? According to existing literature, the earliest reference appears to come from a man named John Taylor (sometimes spelled “Tayler”). Taylor began studying the Great Pyramid after reading the work of John Greaves, sometime after turning fifty. Though he never visited Egypt, he dedicated years to his research and eventually published a book titled
“The Great Pyramid: Who Built It and When?” in 1859, at the age of eighty.
In this book, Taylor made a striking claim:
“If you divide the perimeter of the base of the Great Pyramid by twice its height, you get 3.144, a value astonishingly close to the mathematical constant π (pi).”
He argued that the builders of the pyramid possessed advanced mathematical knowledge, and that they must have known an extremely accurate value of pi. In doing so, Taylor praised the ingenuity of the pyramid’s architects.
What makes Taylor’s perspective particularly intriguing is the historical context in which it was written. By the mid-19th century, European views toward Egypt and Asia had grown increasingly dismissive, often labeling them as inferior or primitive compared to Europe. Why, then, would Taylor—a 19th-century Englishman—credit the ancient Egyptians with such sophisticated knowledge?
John Taylor was a devout Christian.
According to the Old Testament, the people of Israel, descendants of Abraham, once lived and labored in Egypt. Many are familiar with the famous biblical story of Moses leading the Israelites out of Egypt, a narrative that has been widely depicted in books and films.
Taylor claimed that the builders of the Great Pyramid were descendants of Abraham, and that one of the prominent tribes among them had migrated to Britain. Therefore, he argued, the British people were direct descendants of Abraham.
As “evidence,” he pointed out that the ancient Egyptian unit of length—the cubit—measured 25 British inches, as Newton had once suggested. According to Taylor, this showed that the British system of measurement was a direct inheritance from ancient Egypt.
However, this value of 25 inches (≈ 63.5 cm) is significantly longer than the actual ancient Egyptian royal cubit, which is now known to be about 20.63 inches (≈ 52.4 cm). In fact, 25 inches would be unusually long for a human forearm, even by generous standards.
Taylor insisted that his proposed measurement—1 cubit = 25 inches—was a “sacred cubit” that had been divinely revealed, much like how Noah received instructions from God. He claimed that God had designed this sacred cubit based on the radius of the Earth.
Despite his passionate assertions, most of his contemporaries dismissed his ideas. The Royal Society of London, one of the most prestigious academic institutions in Britain, politely declined his request to give a lecture on his pyramid theories.
Measurement Errors, Uncertainty in Ancient Units, and the Mystery of the Pyramid
n the previous section, “1-3. Those Captivated by the Mystery of the Pyramid,” we mentioned that the so-called “Herodotus Document” is frequently cited in discussions about the mysteries of the Great Pyramid. It appears that the origin of this citation may be traced back to John Taylor.
The ancient Greek historian Herodotus, in his monumental work Histories, made the following remarks regarding the Great Pyramid:
“Its base is square, each side measuring eight plethra, and its height is the same.”
（– Herodotus, Histories）
Taylor translated Herodotus’s statement as follows:
“Its base is square, each side is 800 feet long, and its height is the same.”
Here, the unit plethron is a measure of length, and Taylor assumed 1 plethron = 100 feet.
While this conversion may not be entirely accurate, it is not an especially serious error in itself.
The more significant issue lies in the original statement by Herodotus, which describes the pyramid as having a base side equal to its height.
This is clearly incorrect. If the height truly equaled the length of one side, then—as Taylor himself claimed—dividing the perimeter by twice the height would yield 4, not a value close to π.
Today, the widely accepted estimate is 1 plethron ≈ 29.6 meters.
Let’s try calculating using that figure instead.
8 plethra = 8 × 29.6 meters = 236.8 meters (1)
The value 236.8 meters, calculated in (1), is quite far off from the actual measured height of the Great Pyramid, which is 146.6 meters, as mentioned earlier in “1-1. What Is the Mystery of the Pyramid?”
However, this figure closely matches the length of one side of the base.
In this sense, Herodotus was fairly accurate in describing the base, but when it comes to the height, it seems likely that he merely assumed it was about the same.
While the length of the base can be measured directly, determining the height requires mathematical knowledge and calculation.
Moreover, Herodotus was writing a travel account, not a scientific report, and likely did not feel compelled to provide precise figures.
Let’s try dividing the number from equation (1), 236.8, by the golden ratio φ = 1.618:
236.8 ÷ 1.618 = 146.35 (2)
Isn’t this almost identical to the actual measured height of the Great Pyramid, 146.6 meters?
In fact, the value 236.8 from (1) does not perfectly match the real base length of the pyramid, which is 230.37 meters.
So this is likely just a coincidence caused by a measurement error, and not a true reflection of any “golden ratio mystery.”
As we’ve seen, when dealing with the “Mystery of the Pyramid,” we must be cautious:
- measurement errors,
- inconsistencies in the lengths of ancient units, and
- modifications or misinterpretations of ancient texts
can all play a role. When we conveniently choose values that “fit the theory,” we often end up with such “mysterious coincidences”—but they may not mean anything at all.
Piazzi Smyth’s Survey of the Great Pyramid and His Interpretations
One of the individuals influenced by John Taylor’s writings on the Great Pyramid was Piazzi Smyth, an astronomer and mathematician from the Royal Observatory of Scotland.
Smyth began corresponding with Taylor, who was nearing the end of his life, and after Taylor’s death, he resolved to travel to Egypt himself to investigate the pyramid firsthand.
In 1864—more than 200 years after John Greaves’s measurements—Smyth set out for Egypt, accompanied by his wife. Like Greaves, he brought the most advanced surveying instruments available at the time, and carried out a detailed examination of the Great Pyramid.
His measurements were even more precise than those of his predecessors. However, the conclusions remained largely unchanged.
Upon returning to Britain, Smyth published three volumes of work documenting his research. In these, he stated the following:
“In ancient Egypt, remarkably precise structures were built as early as 1,500 years before the rise of Greek civilization. This suggests that an astonishingly advanced understanding of astrophysics and geophysics already existed at that time.”
Of course, Smyth set out to verify Taylor’s hypothesis, confirming that the ratio between the height of the Great Pyramid and the perimeter of its base was designed to match the ratio of a circle’s radius to its circumference.
Remarkably, the value Smyth obtained was even closer to π than Taylor’s 3.144.
Smyth fully embraced Taylor’s theory and proposed that the Great Pyramid was a scaled-down model of the Earth.
He also asserted that the perimeter of its base corresponded to the number of days in a solar year.
For this research, he was awarded a gold medal by the Royal Society of Edinburgh.
However, not long after, doubts began to surface about these claims.
By the time Smyth published his findings in book form, his work had become the target of dismissive mockery and quiet disregard, despite the lack of clear rebuttals or solid counterarguments.
The Pyramid Viewed Through the Lens of Ancient Egyptian Units
Today, most people likely take the meter as an absolute and unquestionable unit of length.
But have you ever truly considered: “What is length?”
The truth is, we rarely think about things that we don’t need to question.
In ancient Egypt, there was no need for such reflection.
The cubit, a unit defined by the Pharaoh, was sufficient for all practical purposes.
Although the length of a cubit changed slightly from era to era, it remained consistent across all of Egypt during any given period.
Therefore, there was no need to use the pyramid itself as a standard of measurement.
This does not mean that the ancient Egyptians lacked the ability to measure the Earth’s circumference—only that they had no practical reason to do so using the pyramid.
Systems of Length Measurement and the Pyramid
In contrast, Europe had long been home to a diverse mix of ethnic groups, and there was no unified system of weights and measures.
In France, in particular, there were said to be over 800 different unit names, and their actual sizes varied from town to town and village to village.
For length alone, there were reportedly tens of thousands of different units.
It wasn’t until the 19th century that France officially adopted and enforced the metric system, and even then, the process involved many complications and setbacks.
Long before that, there had been proposals to use the Earth’s circumference as the basis for a standard unit of length.
In fact, in the 18th century, members of the French Academy of Sciences cited this idea, claiming that:
“In ancient times, the standard of length was based on the Earth’s circumference, and this idea traces back to the Greek philosopher Aristotle.”
As mentioned earlier, Piazzi Smyth published a series of books on the Great Pyramid in the late 1860s.
This was not coincidental—he was deeply opposed to Britain adopting the metric system, and his works can be seen as part of his effort to stop that movement.
Piazzi Smyth claimed:
“The British inch is a venerable unit, divinely ordained by the very God who designed the Great Pyramid. It is unquestionably superior to the atheistic metric system, devised by the most barbaric and bloodthirsty revolutionary government the world has ever seen—France.”
Britain and France have always been in opposition. Even today, in the United Kingdom and the United States, units other than the metric system are commonly used in everyday life.
While the ancient Egyptians likely had no motivation to use the Earth’s circumference as a basis for measurement, there was a strong impetus for this in Britain and France. In these countries, the Great Pyramid frequently appears in discussions concerning the establishment of the metric system. Let’s take a closer look at what this entails.
Since the data obtained with the measurement techniques of those times were inconsistent, we will use modern data. The data used is as follows:
- Earth’s circumference = 40,000 km
- One side of the Great Pyramid = 230.56 m (3)
- 1 inch = 2.54 cm
- 1 arm’s-length cubit = 52.4 cm (4)
This is a straightforward calculation exercise, so everyone is encouraged to use a calculator.
The Views of Herschel
Let us begin with the view of Herschel, who was considered the foremost British mathematician of his time.
The Ordnance Survey of the United Kingdom had estimated the Earth’s diameter to be approximately 500,500,000 inches.
Let’s examine this claim.
Assuming the Earth’s circumference is 40,000,000 meters, then:
πR = 40,000,000 → R = 40,000,000 / π ≈ 12,732,395.45 meters (5)
Since 1 meter = 100 cm = 100 / 2.54 inches, we get:
R in inches = 12,732,395.45 × (100 / 2.54) ≈ 501,275,411.3 ≈ 500,500,000 inches (6)
The approximation (≒) at the end is a bit of a stretch, but still, for its time, the British survey result claiming a 500-million-inch diameter was remarkably accurate.
Herschel suggested that by making the current inch just one-thousandth longer, the Earth’s diameter would become exactly 500 million inches.
In reality, the necessary adjustment is 1/500, not 1/1000, but such a small increase would have virtually no practical effect.
In other words, if the inch were stretched by 1/500, the Earth’s diameter would round perfectly to 500 million inches.
Based on this, Herschel proposed new definitions for the yard and cubit:
1 yard = 50 inches
1 cubit = 1/2 yard = 25 inches (7)
These newly defined units reflect the idea of a “sacred cubit” measuring 25 inches, aligning with the theory that the cubit used in the construction of the Egyptian pyramids was 25 inches long.
However, this idea is based on incorrect data.
In reality, the royal cubit of ancient Egypt was about 20.63 inches.
Thus, this revised definition of the cubit was artificially chosen to make the “Earth-scaling” theory appear to work.
The British estimate of 500 million inches for the Earth’s diameter may be mathematically neat, but it carries no deeper meaning.
After all, the inch is a bodily unit, derived from the width of a human finger, and has no inherent relationship to the size of the Earth.
Moreover, while this theory replaces the Earth’s circumference with its diameter, such substitutions fail to add scientific credibility, even if the resulting numbers seem to “fit” nicely.
The Viewpoint of Edme-François Jomard
Next, let us examine the theory proposed by Jomard, the surveyor who accompanied Napoleon on his expedition to Egypt.
Jomard’s idea is remarkably simple:
“The length of one side of the Great Pyramid is 1/480 of one degree of latitude.”
This is the same theory mentioned in “1-1. What Is the Mystery of the Pyramid?”
Notably, this theory is independent of any unit of measurement, such as meters or inches—it is purely mathematical.
Since one degree of latitude is 1/360 of the Earth’s circumference, the formula becomes:
1 degree / 480 = (1/480) × (Earth’s circumference / 360)
= 40,000,000 ÷ (480 × 360) = 231.481 meters (8)
This result, 231.48 meters, is fairly close to the actual measured side length of the Great Pyramid, which is 230.56 meters.
Jomard’s theory therefore appears numerically plausible.
However, there are several critical questions we must consider:
- Did the ancient Egyptians know that a circle contains 360 degrees?
- Did they understand that the Earth was a sphere?
- Did they possess a concept of latitude?
Moreover, why divide by 480 specifically?
Why not choose a rounder number like 500?
These questions highlight that, while the numbers seem to work, the theoretical foundations remain uncertain.
Taylor’s Perspective
Finally, let us consider the theory proposed by John Taylor, who was particularly focused on the British inch as a unit of measurement.
The data Taylor relied on (which was, in fact, incorrect) came from Newton’s estimate:
1 royal cubit ≈ 63 cm ≈ 25 inches (9)
Based on this assumption, Taylor concluded the following:
Length of one side of the base = 366 royal cubits
Perimeter of the base = 366 × 100 inches (10)
Here, the number 366 is meant to represent the number of days in a year, rounded up from the more precise 365.2422 days.
Let’s test this calculation:
230.56 ÷ 0.63 ≈ 365.968 ≈ 366 (11)
366 × 4 cubits ≈ 366 × 100 inches (12)
If one assigns symbolic meaning to the number 366, these formulas indeed appear elegant.
However, since the foundational assumption—1 royal cubit = 63 cm—is incorrect, the entire line of reasoning loses credibility and cannot be taken seriously as a valid argument.
Conclusion
Let us summarize the findings of this section.
In the modern era, several theories emerged claiming that the Great Pyramid was designed based on the Earth’s circumference.
However, none of these theories provided compelling evidence to support such a claim.
Notably, names such as Pythagoras and Aristotle often appear in these accounts,
but Eratosthenes, who was historically the first to calculate the Earth’s circumference, is nowhere to be found in the narrative.
Similarly, the so-called mysteries of π (pi) and the golden ratio also appear to be concepts that only gained attention in more recent times.
The claims concerning these two “mysteries” merely point to certain numerical relationships in the Great Pyramid of King Khufu,
without offering any deeper theoretical framework or explanation.
Of course, coincidences can occur, even in the most unlikely places.
And yet, legends and traditions sometimes contain a kernel of truth.
We will return to these mysteries in more detail in Chapter 5.