C:\TEACH\HISTORY\Egypt.DVI

[Audio] Good morning. Egyptian mathematics was a unique mix of applying the concepts and principles of arithmetic to practical problems. Unlike today, there was a lack of symbolism in their writing which meant much of their computing was communicated through examples rather than the written method. This can be seen in the grand pyramids of Giza, which are a testament to the advanced mathematical and engineering techniques used in ancient Egypt. Facts regarding this ancient civilization tell us that hieroglyphic writing was abundant but undecipherable due to its complexity until the discovery of the Rosetta Stone in Alexandria. This tablet of black basalt was discovered to be about three feet in size, and its discovery opened the doors to understanding the language of the ancient Egyptians..

[Audio] The Rosetta Stone is a significant artifact discovered in 1799 near the town of Rosetta (Rashid). It is a piece of black basalt measuring around 9 inches by 2 feet 4 inches and is inscribed with three different writing systems, namely hieroglyphics, its cursive form demotic script, and Greek. This provided a key to deciphering hieroglyphic writing. Thomas Young and Jean-Francois Champollion, pioneers in Egyptology, worked tirelessly to translate the hieroglyphic text and ascertain that it was a translation from Greek. Moreover, they established that it can be alphabetic, syllabic, or determinative. Their success has given us greater understanding of the ancient Egyptian culture and language, including mathematics..

[Audio] Egyptian mathematics is an extraordinary example of the power of the human mind to and codify knowledge. From the orientation of hieroglyphs to the intricate details of its calendar, Egypt provides an insight into a culture that valued mathematics and its application to everyday life. The Rosetta Stone was a fundamental piece of understanding the past, unlocking hieroglyphs for modern scholars. The papyrus collections not only highlighted the application of mathematics for construction projects, but also showcased the complexity of understanding mensuration, algebra and computation for the Egyptians. This is just one example of the breadth and depth of mathematics in early civilisations..

[Audio] Ancient Egypt is known to have communicated mathematical problems through examples, as preserved in the Rhind Mathematical Papyrus and the Moscow Mathematical Papyrus, written more than 3,500 years ago. These documents contain numerous mathematical problems with their corresponding solutions. Papyrus, the writing material used by Ancient Egyptians, was created from thin strips of the inner pith of the plant, which were pressed together to form papery sheets for writing on. Thanks to these ancient documents, we can get an understanding of the mathematics which was practiced by Ancient Egyptians..

[Audio] Egypt is a historically renowned nation renowned for its advanced mathematics. Much of their mathematics was communicated through examples and hieroglyphics, and has been known to overwhelm researchers to this day. The Egyptian counting system was decimal-based and utilized symbols for specific numbers, although it could not deal with large numbers. Addition was achieved through regrouping, while multiplication and division made use of binary multiples - fractions, of course, were commonplace but only unit fractions were accepted, save for a few exceptions. Geometry was limited to areas, volumes, and similarity, with volume measures for fractional parts expressed differently. Algebraically, simple equations were solvable, and two-dimensional problem sets were also solvable. A remarkable accomplishment for the time..

[Audio] Ancient Egyptians used symbolic notation to document their mathematical understanding. A single stroke represented the number one, while a heel bone represented ten. A snare symbol denoted a hundred, and a lotus flower symbolized one thousand. For ten thousand, a bent finger was used, a burbot fish for one hundred thousand, and a kneeling figure for one million. There is some debate about the exact hieroglyphic symbols used to represent these numbers, but it is known that Egyptians created them by grouping symbols together..

[Audio] Good morning. In ancient Egypt, mathematics was mostly communicated through examples. Examples of addition include grouping different numerical elements together, while alternate forms were also used to represent numbers. As for multiplication, a binary method similar to what we use today was employed. As an example, multiplying 47 by 24 goes as follows: 47 doubled becomes 94, then 188, then 376 and finally 752, which when added together with 16 gives us 24, our answer. Dividing also follows this same process. To illustrate, let us take the example of 329 divided by 12..

[Audio] The Ancient Egyptians were renowned for their invention of hieroglyphs, but it wasn't until the Rosetta Stone was found in 1799 that these symbols could be deciphered. They were also advanced mathematicians, using hieroglyphics to convey their mathematical understanding. The Egyptian system of maths was based on illustrations and the distributive law, which holds that the product of a sum is the same as the sum of the products. This was exemplified in their fractions, which usually only had up to two exceptions and needed to be expressed in unit fractions. Thanks to the discovery of the Rosetta Stone, we can now gain insight into the complexity and precision of the Ancient Egyptians' mathematical achievements..

[Audio] Egyptian mathematics was a blend of intuitive techniques, trial and error and problem-solving tactics such as the application of 'unit fractions' to depict non-unit fractions. Ahmes, an old Egyptian scribe, created a chart of unit fractions which was employed to demonstrate the decomposition of fractions having a numerator of two. This formula was used to determine the precise decomposition of fractions into a sum of unit fractions, however, the exact algorithm for this is still mysterious today. While the Egyptians did favor particular fractions when achievable, the decompositions were not necessarily distinct. This old practice of problem solving with fractions is still used today, as research continues to improve our understanding of the decomposition of fractions into a sum of unit fractions..

[Audio] Between 2000BC and 1800BC, the Egyptians were able to solve complex mathematical problems, as evidenced by ancient texts such as the Ahmes Papyrus. These exercises included problems with fractions, notation, arithmetic, algebra, geometry and mensuration. One example of this was the problem of determining how many loaves of strength 45 were equivalent to 100 loaves of strength 10. The Egyptians solved this type of problem using their practical mathematical tools..

[Audio] Egyptians were highly skilled in mathematics. They were capable of applying the rule of three and other methods of proportion and deduction to solve even complex equations. For instance, they used the rule of three to determine that 450 loaves were needed according to the problem. The solution also showcases their mastery of algorithm, working out the proportions without stating any underlying principles. This problem and solution are just a single example of the capabilities of their mathematical aptitude..

[Audio] Ancient Egyptians demonstrated remarkable proficiency in mathematics, exemplified by the complex problem posed here. To solve it, they utilized a method of false position which is still in use today. This method proved successful not only in resolving this particular mathematical puzzle but also other linear algebra equations of modern format. This evidence shows the great progress the ancient Egyptians had made in mathematics and their capacity to use its principles to solve real-world issues..

[Audio] Ancient Egypt was renowned for its mathematical achievements, particularly in the field of geometry and mensuration. The Ahmes Papyrus contains many challenges pertaining to areas of Isosceles triangles, Trapezoids, Frustums, and Curvilinear Areas, one of which is regarding the area of a quadrilateral. This was presented with the equation A = (b1 + b2/2)(h1 + h2/2). Although it is not precise for all shapes of a quadrilateral, it is accurate for almost rectangular ones..

[Audio] Ancient Egyptians developed powerful methods for solving problems of engineering and commerce already more than three thousand years ago. They used notation for fractions and other mathematical symbols that are still used these days. It was the Rosetta Stone that allowed us to understand that hieroglyphics weren't merely decorative, but they contained formulas for divisibility by two and three, area of triangles, quadrilaterals and other complex problems. The discovery of the Rosetta Stone enabled us to decipher the records of historical mathematicians and to explore the fundamentals of modern mathematics..

[Audio] Without greetings, beginning with 'Today', or thanks, the text reads: As I was going to St Ives, I met a man with seven wives; Every wife had seven sacks, Every sack had seven cats, Every cat had seven kits. This nursery rhyme, an example of a geometric progression, provides insight into the Egyptian Mathematics. Problem 50 of the Egyptian Papyrus Rhind, which dates back to 1650 BC, asked for a sum of all and illustrates knowledge and application of geometric progressions. Problem 48 gives a hint of constructing the formula. It states that a circular field of diameter nine has the same area as a square with side eight, giving an effective pi of 3.16. By trisecting each side and removing the corner triangles, an octagonal figure results that approximates the circle. The area of this figure is 9 times 9 minus four times half times three times three, which gives an approximate value of 63 or 64 which is equal to 8 squared. This is an example of knowledge and application of geometric progressions that the Egyptian mathematics had..

[Audio] Ancient Egypt was highly advanced in its use of mathematics, as evidenced by examples and hieroglyphics found in the Rhind Papyrus. Problem 56 of the Rhind Papyrus showcases the understanding of geometry at this time with its discussion on the ratio of rise and run. It was also used to compute cotangent, which was essential in constructing the pyramids. Another equation within the text, dealing with the octagonal figure, resulted in a surprisingly accurate approximation of pi. Ancient Egyptians truly excelled in their understanding of mathematics, despite lacking the tools and technology that we possess today..

[Audio] Ancient Egypt is known for its impressive mathematics, which was largely communicated through examples and hieroglyphics that were indecipherable until the discovery of the Rosetta Stone in Alexandria in 1799. One of the most notable examples of this is the Moscow Papyrus. It dates back to 1700 BC, measuring 15 feet long and 3 inches wide. Information from the papyrus has provided mathematicians with valuable insight into the mathematics of ancient Egypt and how it was used by its people. The origin of the Moscow Papyrus is unknown, but it was purchased by V. S. Golenishchev in the early 1900s and sold to the Moscow Museum of Fine Art..

[Audio] The ancient Egyptians were great mathematicians, as proven by the Moscow Papyrus, an ancient mathematical document discovered in Egypt. It contains a problem dealing with the volume of a frustum. The scribe in the Papyrus directs the student to apply certain operations to two numbers, which then have to be multiplied by one third of six. The result of these operations is 56 - as the scribe states - demonstrating the accurate math done by the scribe. This example is just one proof of the advanced mathematics knowledge of the Ancient Egyptians, expressed through examples and hieroglyphics..

[Audio] Ancient Egyptians were known for their expertise in mathematics, as evidenced by the discovery of the formula for a 'frustum' written in hieroglyphics. A frustum is a metric form between two similar objects, such as a pyramid with its top cut off. This discovery is an impressive showcase of the Ancient Egyptians' creativity and intelligence, as deriving the formula for a frustum requires methods of modern calculus which were not available to them during their time. This goes to show the immense capability of the Ancient Egyptians to come up with such a sophisticated formula for a metric shape without the use of modern technology and mathematics..

[Audio] Egyptian mathematics was an extremely advanced field for its day. Its practicality enabled the production of prominent monuments, such as the pyramids and the Great Wall of China. Problem 10 of the Egyptian mathematics revolved around the estimation of curvilinear area, in the form of the Quonset hut roof. Whilst not making any theoretical contributions, their formulas were as precise as they were advanced, resulting in the construction of the monuments of that era. It was not until the finding of the Rosetta Stone in 1799 that hieroglyphics were deciphered, and the history of Egyptian mathematics could be studied..

[Audio] Ancient Egypt had a significant influence on the development of mathematics. Through hieroglyphics that were largely indecipherable until the Rosetta Stone was discovered in Alexandria in 1799, examples were used to demonstrate mathematical procedures. The papyrus found in Egypt in the 19th century did not provide much detail about the exact and approximate methods used in their mathematics, but it can be assumed there were more elements to this mathematics than what was written down. What was known of Ancient Egyptian mathematics was integrated into Greek mathematics, however, this knowledge may have been lost when the Library of Alexandria was destroyed around 400 CE. Despite the fact that it is likely we will never be able to fully explore the mathematical understanding of Ancient Egypt, its importance can not be overstated..