The Stonecutters

Have you ever wondered who built the pyramids, or how they were built? While there’s no definitive proof, the most widely accepted theory is that the pyramids were constructed by skilled workers and laborers, organized by the ancient Egyptian state and led by pharaohs during the Old and Middle Kingdoms (c. 2686–1650 BCE).

Dr. Zahi Hawass has written extensively about the construction of the pyramids in his various publications. In his book “The Pyramids of Ancient Egypt”, he discusses the various theories about how the pyramids were built, including the use of ramps, sledges, and levers to transport and position the massive stone blocks. He also talks about the organization and management of the construction process, which was likely overseen by the pharaoh and his high officials.

In his book “The Builders of the Pyramids”, Dr. Hawass explores the lives and experiences of the workers who built the pyramids, including their living conditions, diets, and religious beliefs. He also discusses the tools and techniques that the workers likely used to quarry, shape, and transport the stone blocks, and the role that engineering and mathematics played in the construction process.

The ancient Egyptians cut granite using a variety of tools and techniques, many of which were developed over centuries of experimentation and refinement. Some of the main methods used to cut granite include:

1. Chisels and hammers: Simple hand-held chisels and hammers were used to carve and shape granite blocks. This method was labor-intensive and time-consuming, but could be effective for smaller, more detailed work.
2. Copper and bronze tools: More advanced cutting tools made from copper and bronze were developed during the Old Kingdom period. These tools were harder than stone and could be used to cut and shape granite more quickly and efficiently.
3. Abrasive sand: Grinding and shaping granite using abrasive sand was another common technique. The ancient Egyptians would sprinkle sand onto a granite block and then use a copper saw or chisel to cut into the block. The sand acted as an abrasive, helping to wear away the granite more quickly.
4. Diabase balls: Diabase is a hard, dense rock that is similar to granite. The ancient Egyptians discovered that by rubbing diabase balls against granite, they could create deep grooves and channels in the stone. This method was used to cut large blocks of granite and create precise angles and shapes.

Molten Granite

Granite is an igneous rock that is composed mainly of quartz, feldspar, and mica minerals. The melting point of granite varies depending on its composition and the pressure under which it is heated, but it typically ranges from 1215°C to 1260°C (2219°F to 2300°F). This high melting point is due to the fact that granite is a coarse-grained rock that is formed from the slow cooling and solidification of magma deep within the Earth’s crust. At these high temperatures, granite would be in a molten or liquid state.

Undulating surfaces have been observed on some of the granite blocks used in the construction of the pyramids in Egypt. These surfaces appear to be slightly curved and may have been intentionally created to fit together more tightly. Some researchers have suggested that these undulations may have been produced using a type of ancient saw or cutting tool, while others speculate that they could have been created using high heat to soften and reshape the stone. However, there is no definitive answer as to how these undulating surfaces were produced, and the true purpose behind them remains a subject of debate among archaeologists and Egyptologists. There are also examples of molten granite on the Giza Plateau.

Fire-setting Techniques

A paper examines the use of heat as a potential tool for quarrying hard stones in ancient Egypt, particularly granite. The authors suggest that fire-setting techniques, which involve heating the rock and then rapidly cooling it with water, may have been used to weaken the stone and make it easier to quarry and shape. The study presents evidence from the granite quarries at Aswan, including features such as heat-induced cracking and surface pitting, which suggest that fire-setting was indeed used in the quarrying process. The paper does not suggest any particular theories about how the ancient Egyptians heated the rocks in fire-setting techniques.

Reflecting on Mirrors

Mirrors were known to exist in ancient Egypt and were typically made of highly polished metal, such as copper or bronze. These mirrors were often used in funerary contexts, as they were believed to possess magical and protective properties that could aid the deceased in their journey through the afterlife. Mirrors were also used for cosmetic and grooming purposes, and there are depictions of women holding mirrors in tomb paintings and reliefs.

One of the most famous examples of a mirror from ancient Egypt is the “Narcissus Mirror,” which dates back to the New Kingdom period and is now housed in the British Museum. This mirror is made of copper and features a handle in the shape of a naked woman with outstretched arms. It is believed to have been used for both cosmetic and religious purposes and may have been associated with the goddess Hathor, who was often depicted holding a mirror.

Mirrors in ancient Egypt also had symbolic and religious significance, and were often associated with the concept of ma’at, which represented the cosmic order and balance in the universe

Parabolas

The concept of a parabola and its geometric properties were known to ancient Greek mathematicians, including Apollonius of Perga, who lived in the 3rd century BCE. Apollonius wrote extensively about conic sections, which includes the study of parabolas, ellipses, and hyperbolas.

Apollonius was also influenced by the work of earlier Greek mathematicians, including Euclid and Archimedes, who had made important contributions to the study of geometry and mechanics. In fact, Apollonius is often referred to as the “Great Geometer” because of his groundbreaking work on conic sections, which laid the foundation for much of the modern study of geometry.

Euclid was a Greek mathematician who lived in Alexandria, Egypt, around 300 BCE. He is often referred to as the “father of geometry” because of his influential work, “Elements”, which is considered one of the most important works in the history of mathematics.

Rhind Mathematical Papyrus

Pythagoras is credited with the formulation of the Pythagorean theorem in the 6th century BCE. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. However, evidence of the application of the theory has been discovered on the Rhind Mathematical Papyrus.

The Rhind Mathematical Papyrus is an ancient Egyptian mathematical text that dates back to around 1650 BCE during the Second Intermediate Period of ancient Egypt. It is written in hieratic script and contains a collection of mathematical problems and solutions covering a wide range of topics, including arithmetic, geometry, and algebra.

One section of the Rhind Mathematical Papyrus contains a list of 84 problems related to the calculation of the area of a rectangular field. These problems involve variations in the dimensions of the field and the use of different methods to find its area. Problem 50 of this section is known as the “Ahmes-Streckeisen problem” and relates to the calculation of a diagonal of a rectangle with sides of 9 and 40 units.

The solution to the Ahmes-Streckeisen problem is presented in terms of a Pythagorean triple, specifically the triple (9, 40, 41). This is a set of three positive integers that satisfy the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In the case of the Ahmes-Streckeisen problem, the side lengths of 9 and 40 units form the two shorter sides of a right-angled triangle, and the length of the diagonal (the hypotenuse) is 41 units.

The Rhind Mathematical Papyrus contains a total of six Pythagorean triples, including the (3, 4, 5) triple, which is the most well-known Pythagorean triple. The inclusion of these Pythagorean triples in the papyrus suggests that the ancient Egyptians were aware of the Pythagorean theorem and its applications in geometry.

The Parabolic Mirror

It surpasses all wonders that a day goes by wherein the whole world is not consumed in flame. For concave mirrors turned toward the sun ignite more easily by its rays than does any other fire. — C. Plinii Secundi, Naturalis Historia

Diocles was an ancient Greek mathematician and physicist who lived in the 3rd century BCE. He is best known for his work on optics, including his investigations into the properties of curved mirrors and lenses.

Diocles is credited with discovering the properties of parabolic mirrors, which are mirrors that are shaped like a paraboloid of revolution. In his treatise “On Burning Mirrors,” Diocles described how parabolic mirrors could be used to focus light and create intense heat, which could be used for a variety of practical purposes, such as igniting fires or melting metals.

Diocles’ work on burning mirrors was highly influential and paved the way for later developments in optics and astronomy. His treatise was widely read and referenced by later scientists, including the ancient Greek mathematician and physicist Archimedes, who also wrote about the properties of curved mirrors and their potential uses in warfare.

Greek historian Plutarch, who lived from approximately 46 AD to 120 AD. In his work “Moralia,” Plutarch describes an experiment in which Archimedes used a “burning mirror” made of bronze to focus sunlight. Archimedes is said to have used parabolic mirrors for defensive purposes during the Siege of Syracuse in 212 BCE. According to historical accounts, he designed a system of mirrors that could reflect the sun’s rays onto Roman ships, setting them on fire and causing them to sink. Roman author Lucian’s account, written in the 2nd century AD, includes a detailed description of how Archimedes constructed a large parabolic mirror made of bronze or copper to focus sunlight and set fire to enemy ships.

Hot Enough to Melt Granite

The temperature that a parabolic mirror can reach depends on several factors, including the size of the mirror, the quality of the reflective material, and the intensity of the light source. In theory, a parabolic mirror can focus sunlight to a temperature as high as the melting point of the reflective material, which can be several thousand degrees Celsius.

The Odeillo solar furnace is a large-scale parabolic mirror located in the Pyrenees mountains of France. It is one of the largest solar furnaces in the world, measuring 54 meters in diameter, and is capable of focusing sunlight to temperatures as high as 3,500 degrees Celsius (6,332 degrees Fahrenheit). The mirror is made of 9,000 individual hexagonal mirrors that are motorized and can be moved independently to adjust the direction of the reflected sunlight.

The Egyptians had access to the following metals. Included are the melting point temperatures which indicate the relative temperatures that could be potentially generated.

• Gold: 1064°C (1947°F)
• Silver: 961°C (1761°F)
• Copper: 1085°C (1985°F)
• Bronze: 950–1000°C (1742–1832°F)
• Iron: 1538°C (2800°F)
• Electrum: 700-900°C (1292°F and 1652°F).

The melting point of Granite sits between 1215°C to 1260°C, a parabolic mirror made of Iron would have the capability of reaching the necessary temperature.

Senetjer

“The History of the Telescope” is a book by Henry C. King that explores the evolution of telescopes from the earliest discoveries of optics in ancient Egypt and Greece to modern astronomical instruments used today.

According to King, Senetjer was a type of rock crystal that was used as a lens in ancient Egypt. The crystal was carved into a convex shape and used as a magnifying glass to help with the engraving of inscriptions and other small-scale artistic works.

King’s theory was based on his examination of a number of ancient Egyptian artifacts, including a small magnifying glass that was found in a tomb dating back to the 5th Dynasty of Egypt (approximately 2500 BCE). This magnifying glass was made of rock crystal and had a convex shape, similar to the Senetjer lenses described in King’s work.

The Nimrud Lens

The Nimrud lens is an ancient Assyrian artifact that was discovered in Nimrud, Iraq in 1850. The lens is made of rock crystal and measures approximately 3 inches in diameter and 1.5 inches in thickness. It has a convex shape on one side and a concave shape on the other.

The precise function of the Nimrud lens is unknown, but some scholars believe that it may have been used as a magnifying glass or to start fires by focusing the sun’s rays. Others have suggested that it may have been used in astronomy or as part of a decorative object.

The Nimrud lens is notable for its advanced optical properties, which suggest that the ancient Assyrians had a sophisticated understanding of optics and lens-making. The lens is believed to date back to the 7th century BC, making it one of the oldest lenses known to exist.

The King then rises, takes the sacred glass,
And holds it in the sun before the mass
Of waiting fuel on the altar piled.
The centring rays — the fuel glowing gild
With a round spot of fire and quickly. spring
Above the altar curling, while they sing!

— CORONATION OF IZDUBAR

Accurate and Efficient Stone Cutting

Did the ancient Egyptians possess parabolic mirrors? Did they apply this technology to cut or melt granite and other stones? They had access to the underlying geometry and metallurgy. Could they have further used a glass lens to achieve same? This could explain the anomalous and advanced examples of highly precise methods of stone cutting from the ancient world.