"Apart from the information in the papyri, what else can we deduce about Ancient Egyptian mathematical knowledge?
"Professor Beatrice Lumpkin, an authority on early African mathematics, points out that there is a demonstrable relationship between an Egyptian cubit and another Egyptian unit of measure called a double remen. A double remen is the square root of two cubits. This is particularly interesting because the square root of two equals 1.4142 etcetera, an irrational number.... Many scholars see the relationship between the cubit and the double remen as convincing evidence that the Ancient Egyptians were familiar with the concept of irrational numbers....
"Robert Bauval and Graham Hancock, co-authors of the impressive 'Keeper of Genesis,' report a figure of 3023.16 feet for the base perimeter of the Great Pyramid of Giza. This is the most famous of Egypt's 90 pyramids and represents the highest achievement of the Egyptian Old Kingdom Period. They also report a figure of 481.3949 feet for the vertical height of this monument. Since the radius of a circle x 2= the diameter of a circle, and the diameter x pi = the circumference of a circle, therefore pi= the circumference divided by the diameter of a circle. Crunching some figures, this means : 481.3949 x 2=962.7879. Therefore pi = 3023.16/962.7879=3.14. Compare this figure with the more accurate modern figure of 3.14159 to five decimal places. Pi is an irrational number. The decimal places keep going on without an end....
"Each of the four sides of the Great Pyramid is approximately 755.5 feet long against a vertical height of 481.3949 feet. This seems like an arbitrary size to choose to build. However, the Egyptians actually reckoned the base as 440 cubits (half the base was 220 cubits), they reckoned the height as 356 cubits. Thus the Egyptians thought of the Great Pyramid's dimensions in round numbers. These round numbers are not arbitrary.
"Let us crunch some figures. If the sloping height of the pyramid is 356 cubits and half of the base is 220, then 356/220=1.1618181. Compare 1.1618181 with phi = 1.1618 to 3 decimal places.
This figure of ...phi is 1.618 to three decimal places, is also called the Golden Section ( the actual figure like pi , is an irrational number of infinite decimal places). Snails' shells are based on this number. Artists and architects have found if they base their designs on this number, the results are often aesthetically pleasing. It has been even claimed that a beautiful human face is also based on this figure."
P. 35-38, "Chapter 5: Egyptian Mathematical Evidence from Non-Documentary Sources," AFRICAN MATHEMATICS: HISTORY TEXTBOOK AND CLASSROOM LESSONS by Robin Walker & John Matthews (2014)
Monday, June 8, 2015
AFRICAN MATHEMATICS: PROOF OF IRRATIONALS, PI AND PHI
"Apart from the information in the papyri, what else can we deduce about Ancient Egyptian mathematical knowledge?
"Professor Beatrice Lumpkin, an authority on early African mathematics, points out that there is a demonstrable relationship between an Egyptian cubit and another Egyptian unit of measure called a double remen. A double remen is the square root of two cubits. This is particularly interesting because the square root of two equals 1.4142 etcetera, an irrational number.... Many scholars see the relationship between the cubit and the double remen as convincing evidence that the Ancient Egyptians were familiar with the concept of irrational numbers....
"Robert Bauval and Graham Hancock, co-authors of the impressive 'Keeper of Genesis,' report a figure of 3023.16 feet for the base perimeter of the Great Pyramid of Giza. This is the most famous of Egypt's 90 pyramids and represents the highest achievement of the Egyptian Old Kingdom Period. They also report a figure of 481.3949 feet for the vertical height of this monument. Since the radius of a circle x 2= the diameter of a circle, and the diameter x pi = the circumference of a circle, therefore pi= the circumference divided by the diameter of a circle. Crunching some figures, this means : 481.3949 x 2=962.7879. Therefore pi = 3023.16/962.7879=3.14. Compare this figure with the more accurate modern figure of 3.14159 to five decimal places. Pi is an irrational number. The decimal places keep going on without an end....
"Each of the four sides of the Great Pyramid is approximately 755.5 feet long against a vertical height of 481.3949 feet. This seems like an arbitrary size to choose to build. However, the Egyptians actually reckoned the base as 440 cubits (half the base was 220 cubits), they reckoned the height as 356 cubits. Thus the Egyptians thought of the Great Pyramid's dimensions in round numbers. These round numbers are not arbitrary.
"Let us crunch some figures. If the sloping height of the pyramid is 356 cubits and half of the base is 220, then 356/220=1.1618181. Compare 1.1618181 with phi = 1.1618 to 3 decimal places.
This figure of ...phi is 1.618 to three decimal places, is also called the Golden Section ( the actual figure like pi , is an irrational number of infinite decimal places). Snails' shells are based on this number. Artists and architects have found if they base their designs on this number, the results are often aesthetically pleasing. It has been even claimed that a beautiful human face is also based on this figure."
P. 35-38, "Chapter 5: Egyptian Mathematical Evidence from Non-Documentary Sources," AFRICAN MATHEMATICS: HISTORY TEXTBOOK AND CLASSROOM LESSONS by Robin Walker & John Matthews (2014)