Pyramids (Triangles), Gummie Bears and Learning about Ancient Egypt
This piece came about because I was thinking about equilateral triangles. One of the recommendations on one of my Gummie pieces was to use equilateral triangles because they are the most "efficient shape". In my quick research on Google (emphasis on quick) I couldn't find the answer to whether equilateral triangles are the most efficient shape (there are a lot of definitions for efficiency), but it got me thinking about triangles and equilateral triangles. :)
Then I thought of some of the most awesome triangles in history: the Pyramids of Ancient Egypt. This piece was made with the gogobox app.
This piece is based on an image from rawpixel.com and is based on an illustration of the Pyramid of Cephrene illustration from the kings tombs in Thebes by Giovanni Battista Belzoni (1778-1823). (Also notable is the beautiful illustration of the Pyramids made by Belzoni in late 1700s/early 1800s. There are a lot of cool images on rawpixel.com :) )
Then, I wondered about how did the Ancient Egyptians build these massive pyramids -- an architectural feat that would be commendable today with our modern technology. And I wondered about what kind of math the Ancient Egyptians knew to build the pyramids.
Here is some info and links I found:
"Pyramid construction is a continuously debated topic. There are no existing records of building plans or discussions of construction methods, so no one knows exactly what happened. Of course, archaeologists and engineers have plenty of ideas -- some sound far-fetched and others seem more reasonable."
These things the ancient Egyptians knew with certainty (in no particular order):
how to manipulate rational numbers (to some extent)
how to bisect an angle
how to construct similar polygons of certain ratios
how to find vertical and horizontal
that a triangle with the sides 3:4:5 was a right triangle
that the length of a year to be 365 days
Additionally they probably knew:
the cardinal points of the compass as we understand them
that the earth was a sphere of immense size
that certain other triangles having integral sides were also right triangles (just as the ancient Babylonians did)
that there existed numbers that could only be approximated, such as Ö2, Ö3 and f (the Golden Ratio).
What these simple lists suggest is that the ancient Egyptians understood relationships between abstract ideas, even though the computational machinery had not yet been developed. As algorithms were invented the Egyptians used them to produce "mathematical handbooks". One example of this is the Rhind Papyrus.
"These facts are more than mere coincidences. It is clear that the Egyptians incorporated their acquired fundamental mathematical knowledge into the design of their pyramids. Further, the incorporated mathematical relationships have share an important characteristic with the Egyptian Pharaoh perception, both are eternal. What better way to recognize the spiritual immortality of a Pharaoh than with immutable enduring mathematical truth?"
This website also has a list of the pyramids and what kind of triangles they are. The Pyramid of Cephrene is not exactly an equilateral triangle, but pretty close!
This website also has information on the Slopes of the Egyptian Pyramids.
The Gummies led me to Ancient Egypt. :)
Give it a try! We are good at this!