math & pyramids
The geometry of the pyramids
The spectacular pyramids are one of the world’s greatest architectural wonders.
The spectacular pyramids are one of the world’s greatest architectural wonders.
The main pyramid calculation performed by the ancient Egyptians is the calculation of the seked. The seked of a pyramid is a measure of gradient or the inclination of any one of its four triangular faces to the horizontal plane of its base () The seked was the ancient Egyptian method for measuring the slope of an inclined surface.
The seked was based on the royal cubit. This ancient unit of length was based on the length of the forearm from the elbow to the tip of the middle finger (originally the forearm length of the Pharoah).
1 Royal Cubit = 7 palms = 28 fingers (1 cubit was approximately 0.52 meters)
The seked of a pyramid was calculated as the ratio of half of the base divided by the height.
Seked = ½ base ÷ height (equivalent to the cotangent of an angle)
The ancient Egyptians would express height and base in cubits and express the seked in palms for pyramid mathematics.
For example: Find the seked of a pyramid whose base is 360 cubits and whose height is 250 cubits?
Seked = ½ base ÷ height
½ base = 360/2 = 180
seked = 180 ÷ 250 = 0.72 cubits
Expressed in palms where 1 cubit = 7 palms: seked = 0.72 cubits X 7 = 5.04 palms
The seked was based on the royal cubit. This ancient unit of length was based on the length of the forearm from the elbow to the tip of the middle finger (originally the forearm length of the Pharoah).
1 Royal Cubit = 7 palms = 28 fingers (1 cubit was approximately 0.52 meters)
The seked of a pyramid was calculated as the ratio of half of the base divided by the height.
Seked = ½ base ÷ height (equivalent to the cotangent of an angle)
The ancient Egyptians would express height and base in cubits and express the seked in palms for pyramid mathematics.
For example: Find the seked of a pyramid whose base is 360 cubits and whose height is 250 cubits?
Seked = ½ base ÷ height
½ base = 360/2 = 180
seked = 180 ÷ 250 = 0.72 cubits
Expressed in palms where 1 cubit = 7 palms: seked = 0.72 cubits X 7 = 5.04 palms
Why did the ancient Egyptians use 7 as a measurement of length? The number 7 is a prime number and cannot be divided evenly by any other number. In other measurement systems length can be divided by 2, 4, 8, etc. to make it easier to divide things up into halves or thirds. Well, we can represent the value of pi as 22/7 by using whole numbers.
Area of a circle = pi*r^2 = (22/7)*r^2
Circumference of a circle = 2pi*r = 2(22/7)*r = (44/7)*r
Therefore, a circle with radius of 7 cubits = 7*(44/7) = 44 cubits circumference. From this we can see that a circle with radius 1 cubit has a circumference of 44 palms. Therefore, it is easy to calculate the circumference of any circle with any number of cubits radius and giving an answer in palms.
The distance around the base of a pyramid exactly equals the circumference of a circle whose radius is the height of the pyramid.
Say the length of the base of a pyramid is equal to 440 cubits and its height is equal to 280 cubits (these are the measurements of the Great Pyramid of Giza).
The distance around the base = 440 X 4 = 1760
Circumference of a circle = 2*pi*r = 2*pi*height = 2*(22/7)*280 = 1760
Area of a circle = pi*r^2 = (22/7)*r^2
Circumference of a circle = 2pi*r = 2(22/7)*r = (44/7)*r
Therefore, a circle with radius of 7 cubits = 7*(44/7) = 44 cubits circumference. From this we can see that a circle with radius 1 cubit has a circumference of 44 palms. Therefore, it is easy to calculate the circumference of any circle with any number of cubits radius and giving an answer in palms.
The distance around the base of a pyramid exactly equals the circumference of a circle whose radius is the height of the pyramid.
Say the length of the base of a pyramid is equal to 440 cubits and its height is equal to 280 cubits (these are the measurements of the Great Pyramid of Giza).
The distance around the base = 440 X 4 = 1760
Circumference of a circle = 2*pi*r = 2*pi*height = 2*(22/7)*280 = 1760
References
Skinner, S. (2006). Sacred geometry: Deciphering the code. Toronto, ON: Sterling Publishing.
African Creation Energy. (2011, November, 17). Pyramid Mathematics: Calculating the Seked. Retrieved from https://www.youtube.com/watch?v=FIzKgA0Ol9M
Skinner, S. (2006). Sacred geometry: Deciphering the code. Toronto, ON: Sterling Publishing.
African Creation Energy. (2011, November, 17). Pyramid Mathematics: Calculating the Seked. Retrieved from https://www.youtube.com/watch?v=FIzKgA0Ol9M