Optimized Pyramids Dec-2019

From the Seven Wonders of the Ancient World, the Great Pyramid of Giza, also known as the Pyramid of Khufu or Cheops (by the Greeks), was the oldest and largest, and it is the only one existing at present. It was built around 2,580 BC, and according to the Greek historian Herodotus (484 BC - 425 BC), it took 10 years of preparation and 20 years of building. The Great Pyramid was the tallest man-made structure in the world for over 3,800 years. Even in our days, with all the technology available, it were very difficult and expensive built such an structure, but the Great Pyramid builders were able to put together about 2,300,000 granite blocks averaging 7 tons each, (plus some other bigger blocks ranging from 9 to 40 tons), raise them to heights above 100 m, and assemble them with incredible precision, at rate of one block every 4.5 minutes!!!

There are hundreds of books (and web pages) containing theories about how the great pyramid was built, and in many of those books there are explanations and interpretations (even hidden symbolism) of its dimensions, orientation, placement, etc. But besides all this, something is true, ancient Egyptians were excellent scientists, mathematicians, and engineers, and the great pyramid was a result of all that knowledge, and the question to answer in this project is: Were the design and dimensions of the Great Pyramid a result of chance? Or there was a special reason for these design?

Students will give an answer to this question. Using Calculus they will answer one of the next questions, Do the dimensions of the Great Pyramid give the minimum lateral surface area to enclose its volume, or give the maximum volume contained by its lateral surface area, in other words, Are the Great Pyramid dimensions the result of a mathematical optimization?

Project's Rubric Link: https://www.sophia.org/tutorials/30-class-notes-and-assignments?playlist=ap-calculus-unit-3-applications-of-differentiation#

Project's References:

• https://www.academia.edu/35507796/THE_GREAT_PYRAMID_OF_GIZA_PI_AND_THE_GOLDEN_RATIO
• https://www.academia.edu/35223106/A_NOTE_ABOUT_THE_CONSTANT_SLANT_OF_OPTIMIZED_RIGHT_PYRAMIDS