Pythagoras was a Greek philosopher who is said to have lived around 500
BC, and is credited by most western educational institutions with the
development of what they call the Pythagorean Theorem, the mathematic equation
which expresses the relationship between the sides of a right triangle; where
the square of the hypotenuse of the triangle is equal to the sum of the squares
of the other two sides of the triangle.
The Pythagorean Theorem is also known as the 47th Problem of
Euclid, because Euclid, who is said to have lived several hundred years after
Pythagoras, and is called the “father of Geometry” by western educational
institutions, worked on solving the ratio 3:4:5 Pythagorean triple. If the first 5 numbers 1,2,3,4,5 are
squared to yield 1,4,9,16, and 25, then subtracting each square from the next
yields the sequence 1,3,5,7,9…
However, it has long been suspected that this theorem, and the proof of this theorem, existed thousands of years before Pythagoras is said to have been born.
Evidence that the Babylonians had knowledge of Pythagorean Triples is
available on the artifact known as Plimpton 322, which contains tables
inscribed with Pythagorean Triples.
In his collection of
essays entitled “Moralia Volume 5”,
the Greek essayist Plutarch comments on the Ancient Egyptian’s knowledge of the
3:4:5 Pythagorean triple and its relationship between the sides of a right
triangle expressed in Ancient Egyptian symbolism by saying:
“The
upright, therefore, may be likened to the male, the base to the female, and the
hypotenuse to the child of both, and so Ausar may be regarded as the origin,
Auset as the recipient, and Heru as perfected result. 3 is the first perfect odd number, 4 is a
square whose side is the even number 2, but 5 is in some ways like its father
and in some ways like its mother, being made up of 3 and 2...”
In the book entitled “The
Pythagorean Theorem: The Story of Its Power and Beauty”, by Alfred
Posamentier, he states:
“The Pythagorean Theorem was
known long before Pythagoras, but Pythagoras is attributed as the first to
prove it.”
However, in the book “Stolen
Legacy” by George G.M. James, it is argued that Pythagoras was shown proof
of the theorem by the Ancient Egyptians.
It states:
“Pythagoras travelled to Egypt and was taught geometry by the Egyptian
Priests and made to sacrifice to the Gods, before they showed him the proof of
the theorem of the square on the hypotenuse of a right angled triangle.
Pythagoras did not discover this proof, and it is misleading to name the
theorem after him.”
The book “Stolen Legacy”
also states:
“… we have the statements of Plutarch, Demetrius and Antisthenes that
Pythagoras founded the Science of Mathematics among the Greeks, and that he
sacrificed to the Muses, when the Egyptian Priests explained to him the
properties of the right angled triangle. Pythagoras was also trained in music
by the Egyptian priests.”
The proof attributed to Pythagoras is very simple, and is called a
proof by rearrangement. The two large
squares shown in the figure each contain four identical triangles, and the only
difference between the two large squares is that the triangles are arranged
differently. Therefore, the white space within each of the two large squares
must have equal area. The triangle in figure 1 can be rearranged to create
figure 2, and equating the area of the white space yields the proof attributed
to Pythagoras.
So, is there any evidence that a proof by rearrangement for this
theorem is available in Ancient Egypt? Well,
since we are talking about triangles, let us look to the pyramids of Giza, the
three giant triangular structures built by the Ancient Africans in Egypt 2000
years before Pythagoras was said to have been born. From above, if we rearrange the pyramids of
Giza, we see evidence of the proof of the theorem.
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The base of Menkaure’s Pyramid is 51.7
cubits, the base of Khafre’s pyramid is 107.6 cubits, and the base of Khufu’s
pyramids is 115.2 cubits. Plugging into
the equation, we see that the mathematical result (119.4) is a statistically
significant reasonable approximation, a difference of 4.2 cubits, less than 4%
error (3.5%). Considering that the outer
casing of the Giza pyramids have been removed, and the wear and tear on the
pyramids over the thousands of years, this may account for the
discrepancy.
Given this evidence, it does not seem right to use the term
“Pythagorean Theorem” for a concept which existed thousands of years before
Pythagoras. In the book Stolen Legacy, Dr. George G.M. James
suggests that “The name of Pythagoras…
should be deleted from our mathematical textbooks: in Geometry, where the
theorem of the square on the hypotenuse of a right angled triangle is called
the Pythagorean theorem, because this is not true.”
So what term can we use to replace the term “Pythagorean Theorem”? We can see the civil engineers and architects
of the Giza complex built the proof of the theorem into the design of the
Pyramid complex at Giza. So the term we
use as a replacement for the term “Pythagorean Theorem” should pay homage to
the African Pyramid builders, architects, and engineers. Dr. Kaba Kamene (Dr. Booker T. Coleman)
suggests that the name “Pythagoras” comes from a Greek amalgamation of the names
of African Egyptian deities Ptah and Horus (Heru). Interestingly enough, the deities Ptah and
Horus were patron deities of the Ancient African Pyramid builders, architects,
and engineers. Ptah was a patron deity
of builders and craftsmen, and Horus as Heru-Behutet was a patron deity of
blacksmiths and workers in metal, The Great Chiefs of the Hammer.
Additionally, Ptah and Ausar were combined in Egyptian Mythology, and
both Ptah as Ausar, and Horus are present as the upright and hypotenuse of the
3-4-5 right triangle ratio represented by Ausar, Aset, and Heru
respectively.
Considering the aforementioned phonetic and symbolic relationships of
Ptah and Horus to “Pythagoras”, then the proposition is put forth that the
Pythagorean Theorem should henceforth and forever be known as the Ptah-Horus Theorem.
Q.E.D.