# Mystify with the Mathematics of Ancient Egypt

## Hieroglyphics, surveying, and the pyramids may all be explored with mathematics.

The ancient Egyptians used math for just about everything. They measured time, surveyed land, calculated the level of the Nile flooding, created a monetary system, and even collected taxes. Integrating mathematics and mythology, they were one of the first civilizations to estimate the number of days in a year and create a calendar. Architecturally, ancient Egyptians used math to create their spectacular pyramids, tombs, and other monuments.

Students might begin a unit on ancient Egyptian mathematics by researching the history of this ancient culture’s achievement in math and science. Yet another avenue of great interest to students might be how the Egyptians used hieroglyphics as representations of numbers. The Egyptians also employed original multiplying, dividing, and fraction techniques. For instance, the ancient Egyptians only multiplied by 2. So if they wanted to find some quantity, say “x” multiplied by 5, they would turn that into x*2+x*2+x. Regarding division, 13/2 would be done by 4*2+4=12, 13-12=1, and so the answer was 3 ¼. When the ancient Egyptians wrote whole numbers, like 32, they would have to write 10+10+10+1+1+1 because those were the symbols they had created in hieroglyphics. One tool that the ancient Egyptians are hypothesized to first use was a rope knotted into 12 sections stretched out to form a 3-4-5 right triangle, thus utilizing the Pythagorean Theorem prior to the ancient Greeks.

Students could also pretend they are going on an excavation and research the dimensions of the ancient Egyptian pyramids. For instance, the Great Pyramid of Giza (also called the Pyramid of Khufu and the Pyramid of Cheops) is a mathematical wonder.  Students might speculate how, for instance, the 2,300,000 giant stone blocks in the pyramid were placed so close together that even a knife blade could not be inserted between them. Analyzing the margin of error of the square base (less than 1/14,000) or of the right angles (less than 1/27,000) is yet another avenue for contemplation.

Students will certainly be intrigued to investigate the “secrets” the ancient Egyptians are said to have built into the Great Pyramid as well.  A couple of mathematical secrets explored by professor of mathematics and working artist Paul Calter is the fact that the Great Pyramid contains the Golden Ratio and that it also “squares the circle.”  In exploring the Golden Ratio of the Great Pyramid, Calter used the dimensions found (on various excavations) of height=146.515 m and the base=230.363 m. He then determined the length of the pyramids slant height using the Pythagorean theorem, and finally compares the slant height to half of the base to arrive at 1.61804 “which differs from phi (1.61803) by only one unit in the fifth decimal place,” according to Calter.

Here are some more ancient Egyptian lessons to intrigue and mystify students:

## Ancient Egyptian Lessons and Activities:

Pyramid Building

Students calculate the slope of a line. They determine how the slope of a ramp impacts the amount off force needed to move an object up the ramp. They apply their knowledge of slopes to real world examples.

Discovering Math Rational Number Concepts

Students research Egyptian hieroglyphics using print and Internet resources. They discuss Egyptian achievements in mathematics. Students explore how the ancient Egyptians used hieroglyphics to write numerals. They multiply and divide numbers using the Egyptian doubling and addition method.

Scaling Down the Pyramids

Students construct three-dimensional models of the three pyramids at Giza. They research the building of the pyramids, recording the height, base and angle.

Students investigate Egyptian number symbols. They conduct Internet research, create an equation representing a parabola in Egyptian number symbols, and create a class paper quilt.