How Was Math Used In Building The Great Pyramid?

Abstract The Egyptians have had many great wonders. One of these wonders are pyramids. Because this was an ancient wonder, many people believe that the Egyptians didn't use any math but only used logic and reason to build pyramids. If this is true, then how did they build the Great Pyramid? They used simple math to make such a great pyramid. They used the Pythagorean Theorem, trigonometry and simple algebra. They also measured the angle of each direction so that each side of the pyramid was facing exactly north, south, east and west.

(the essay) "In ancient Egypt mathematics was used for measuring time, straight lines, the level of the Nile flooding", calculating areas of land, counting money, working out taxes and cooking. Math was also used in mythology. The Egyptians had figured out the numbers of days in the year with their calendar. They were one of the ancient peoples who came close to the actual year, through their mathematical skills.

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Math was also used for building tombs, pyramids and other architectural marvels. The Egyptian built one of the seven ancient wonders which was the great pyramid. The Great Pyramid of Khufu from the Fourth Dynasty was a mathematical wonder. Not only did it take a long time to build but it involved a lot of math. This essay shows how the pyramids were built using math.(Seawright) "The ancient Egyptians built pyramids as tombs for the pharaohs and their queens.

The pharaohs were buried in pyramids of many different shapes and sizes from before the beginning of the Old Kingdom to the end of the Middle Kingdom.

There are about eighty pyramids known today from ancient Egypt. The three largest and best-preserved of these were built at Giza at the beginning of the Old Kingdom. The most well-known of these pyramids was built for the pharaoh Khufu. It is known as the "Great Pyramid".(Nevin) Khufu the pharaoh began planning his own pyramid as soon as he took the throne. The spot that was chosen for the making of his pyramid was on the west bank of the Nile River. ` "Khufu's architects were wise and experienced men. They knew the importance of building the pharaoh's final resting place so that its sides faced directly north, south, east and west. The architects planned the largest pyramid ever built in ancient Egypt. The outlines of the pyramid were measured and marked in the desert sand. Then they started to build it. Many large blocks of stone were cut from quarries that were nearby. They were dragged by groups of men across the desert to the site of the pyramid and set in place."(Morris) Most of the workers were farmers who worked on building the pyramid during the flood season when their fields were under water.

The flood season was when the Nile River's water began to rise. This day was calculated with math and astronomy. The Egyptians looked for a star called Sirius just before the sunrise. They made this the first day of a new year. This meant that it was time to work on the pyramid. Slaves also worked on this massive pyramid. There is still controversy on how the Egyptians got the stones on higher levels of the pyramid. Some people say that they built ramps of mudbrick, limestone chips and clay. Others say that t they tied trees together and used them as ramps. But the question is where would the Egyptians get trees from? After all there weren't many trees in and around the area that the Egyptians lived. They lived mostly in hot, sandy deserts. After the first levels of blocks were in place, the workers built more ramps on top of the first layer of stones. This helped make carrying tons of stones faster. For about 20 years, hundreds of men worked on building the pyramid. As they built each level, they also built up the ramps around the pyramid. "When the pyramid was almost finished, a special block covered in shining metal was placed on the top of the pyramid.

Then, blocks of white limestone from quarries across the Nile were used to cover the pyramid. The blocks were trimmed to make the outside of the pyramid smooth. Finally, the pyramid was finished. There are about 2,300,000 giant, heavy stone blocks in the pyramid, which are placed so close together that a knife blade can not be inserted between them!"(Joseph) Math has existed from the beginning of time. Egyptians knew addition, subtraction, some division and multiplication. If someone wanted to count to the number sixty six in Hieroglyphic, he would write down six staffs(strokes)and seven yokes(heel) bones. The Egyptians had the number system backward to that of today. They wrote the smaller units on the left of the larger units. If someone added sixty six to 600, they would write seven staffs and seven yokes, and directly underneath it they would write down seven scrolls(hundred place). "The Egyptians only multiplied and divided by two. So if they wanted to find (e x 3)+1/e, they would use e x 2 + e +(sum+1/original number). This was done as 4 x 2 + 4 = 12, 12+1= 13, 13/4 would equal 31/4 and so the answer was 3 ¼.

The Egyptian method of "multiplication" required nothing more than the ability to count, since even the multiplying by two in the second column can be done by just duplicating symbols."(Seawright) Having a system in which you could only multiply or divide by two wasn't very good. This made simple math longer and harder math even longer. Having a system like this was also good because this made more people want to learn it. Also to learn this, people would only have to know simple addition and subtraction. "To get whole numbers like 32, the Egyptians would have to write: 10 + 10 + 10 + 1 + 1."(Seawright) Along with all the math that was used to make the pyramid, there an important scroll that was also used. This is called the Rhind Papyrus. It is a mathematical scroll which shows how the Egyptian engineers calculated the proportions of pyramids. One of the problems in this scroll shows how the pyramids were made.

Problem no. 56 gives an equation to find the angle of the slope of a pyramid's face, which in fact is its cotangent. With a cotangent, one automatically has a tangent by taking the inverse of the cotangent. Also, the architects of Egypt had several times built into their structures right triangles that obeyed the theorem: a2 + b2 = c2, where a and b are the two sides and c is the hypotenuse. The pyramids built by the Egyptians were an amazing construction. The great pyramid of Khufu was one of the biggest and best pyramids that was ever built. The Egyptians had learned a great deal of advanced math by the time of Khufu. Egyptians taught from basic math like adding and subtracting to more advanced math like algebra and geometry. All these mathematical concepts were used to build the pyramids. As you can see that the great pyramid was not only a wonder in the sense that it was huge, but also in the sense of the entire math that was involved in building it.

References

• How Was Math Used In Building The Great Pyramid?
• Ancient Egyptian Pyramids