A project about Pyramids...and Mathematics. (Source: )

Transcription

1 A project about Pyramids...and Mathematics. (Source: ) How Tall? At m (481 ft) high, the Great Pyramid stood as the tallest structure in the world for more than 4,000 years. Today it stands at 137 m (449.5 ft) high, having lost 9.5 m (31 ft) from the top. Here's how the Great Pyramid compares to some modern structures. Task 1 Draw this pyramid on a separate piece of paper according to the measurements given in the outline following in Task 2, you drawing must look like the one in Task 2 but accurately measured (e.g. the square s sides must be exactly 7.7cm long etc. ) This outline in Task 2 shows the Great Pyramid's actual dimensions scaled down using the scale of 1 cm = 30 m. Scale: 1 cm = 30 m

2 Task 2 1. Take the outline you created in Task 1, and cut it out along the solid lines. 2. Fold each triangle side along the dotted lines towards the centre of the square base. 3. Align the sides of any two triangles and tape into place. Repeat until the pyramid is complete.

3 Task 3: Do in your Maths book Once you have assembled your scaled-down model of the Great Pyramid, draw the following table in your Maths book. Then work out the missing numbers and fill in the missing numbers: Object Actual Height Scale Height (1 cm = 30 m) Object to represent scaled-down height Great Pyramid m 4.9 cm paper pyramid Statue of Liberty 92 m? cm small paper clip Sears Building 443 m? cm ball-point pen Average person 1.7 m.05 cm (.5 mm) grain of salt Eiffel Tower 300 m?? Leaning Tower of Pisa 55 m?? Big Ben Task 4: Do in your Maths book How Heavy? More than 2,300,000 limestone and granite blocks were pushed, pulled, and dragged into place on the Great Pyramid. The average weight of a block is about 2.3 metric tons (2.5 tons). How much do all the blocks weigh together? Find out how much a Boeing 747 weigh...how many Boeing 747 s make up the weight of the Great Pyramid? (Do in your Maths book) Task 5: Do these questions in your Maths book a. What is the area of one triangle that makes the Great Pyramid? First work it out in square centimetres. Now times your answer by four to get the total area of all four triangles in square centimetres. b. What are the dimensions of the base, height and side edges of the pyramid in metres? (You need to times the centimetres by 30 to get it into metres.) Now use your answers to work out the total area of the four triangles in square metres.

4 c. What is the total area of the square that makes the base, in square metres? Show all your working out. d. How many Melbourne Cricket grounds (MCG s) would fit into this base area? Task 6: Do in your Maths book How Deep? The descending passageway that leads to the Unfinished Chamber is long, narrow, steep and, without any windows, very dark! When you arrive at the burial chamber, you'll be 20 m (66 ft) beneath the foundation with over 6 million tons of stone piled above you! If the Unfinished Chamber is 20 straight down from the foundation, and the chamber sits right in the middle of the Great Pyramid about 115 metres from the sides, how long is the passage? (This is a tricky question! You may have to use Pythagoras Theorem to solve it...) Take a virtual tour of this passage way here: Task 7: Do in your Maths book How Steep? Each side of the Great Pyramid rises at an angle of 51.5 degrees to the top. Not only that, each of the sides are aligned almost exactly with true north, south, east, and west. For a pyramid to look like a pyramid, each of the four triangular-shaped sides must slope up and towards each other at the same angle so that they meet at a point at the top. The builders constructed the pyramid layer by layer, starting at the bottom. They had to check their work often, for even a tiny error at the bottom could grow into a very large error by the time the workers reached the top! If the bottom two angles in a triangle is 51.5 degrees each, how big is the angle at the top of the triangle? (Please show your working out.)

5 Task 8: Do in your Maths book Perimeter? The base of the Great Pyramid is a square with each side measuring 230 m (756 ft) and covering an area of 5.3 hectares (13 acres). If you were to walk around the base, about how far would you walk? Task 9: Do in your Maths book The most enigmatic of sculptures, the Sphinx was carved from a single block of limestone left over in the quarry used to build the Pyramids. Scholars believe it was sculpted about 4,600 years ago by the pharaoh Khafre, whose Pyramid rises directly behind it and whose face may be that represented on the Sphinx. The Sphinx from the rear, gazing down on Cairo. Half human, half lion, the Sphinx is 240 feet long and 66 feet high. What are these dimensions in metres? Task 10: Do in your Maths book I have scaled down the Great Pyramid for you. Now it's up to you to see if you can create scale models (use a scale of your own choice, but write the scale onto each of your models) of the other two pyramids on the Giza Plateau, Khafre and Menkaure. Here are their actual dimensions: Khafre Base: m (704 ft) on each side Height: m (471 ft) tall Angle of Incline: 53 degrees 7' 48" Menkaure Base: 110 m (345.5 ft) on each side Height: 68.8 m (216 ft) tall Angle of Incline: 51.3 degrees

6 Task 11: If you do on netbooks, put product in dropbox as your name Egypt Use Excel or poster paper to create a timeline of the following information: Timeline of New Kingdom Pharaohs Dynasty Pharaoh Reigned(dates in B.C.) 18th Dynasty Ahmose Amenhotep I Tuthmosis I Tuthmosis II Tuthmosis III Hatshepsut Amenhotep II Tuthmosis IV Amenhotep III Amenhotep IV (Akhenaten) Smenkhkare 1334 Tutankhamen Ay Horemheb th Dynasty Ramses I Seti I Ramses II Merenptah Amunmesses Seti II Siptah Twosret th Dynasty Setnakhte Ramses III Ramses IV Ramses V Ramses VI Ramses VII Ramses VIII 1126 Ramses IX Ramses X Ramses XI

7 Task 12: Do in your Maths book. For all the problems, write the problem into normal Maths first, then do the problem and show all your working out. Problem 1a Queen Hatshepsut has ordered her Nubian general, Nehsi, to sail to the Land of Punt and obtain planks of the finest cut cedar wood for the gates and doors of her new temple. Each ship can carry planks of wood so how many ships will Nehsi have to take with him to transport all the wood back to Egypt? Problem 1b. If pyramids have bricks

8 How many bricks are needed to build pyramids? Problem 2. If bucket of food feeds camels for days. How many buckets are needed to feed camels for day? Problem 3. The kings of Megiddo and Kadesh are preparing to invade Egypt. But pharaoh Thutmose III has decided to cross the Sinai desert and attack his enemies before they are ready. He is taking men with him. It takes him days to cross the desert and each man needs litres of water per day. How much water will he need to take? Problem 4. Before Thuthmose and his army reach Aaruna, at the foot of the hills in which Meggiddo stands, he is going to send reconnoitre a narrow pass. men to The expedition is expected to last days. They are using camels to carry their food and water. Each person needs kilogram of food and litres of water per day, and each camel needs kilograms of food per day (they don't need anything to

9 drink because they're camels, and camels don't get thirsty very often). If each camel can carry kilograms and the rest of the expedition equipment weighs kilograms. How many camels are needed to carry the water, food and equipment? (The density of water in ancient Egypt was kilogram per litre) Problem 5a. An Egyptian wants to build a pyramid in his back garden to bury his favourite cat. His garden is meters wide and meters long. He has goats which each need square metres of land to graze on and camels which each need square meters of land to graze on. If his pyramid has a square base what is the maximum length of one side of the pyramid? (Please draw a little picture to show your thinking). Problem 5b What will the surface area of the pyramid be if the angle of elevation is degrees and the pyramid is smooth? (ignore the base of the pyramid as that is on the ground) Give the answer as a whole number.

10 Problem 5c. The Egyptian wants to paint the pyramid black (his cat was black) and a barrel of tar covers square metres how many barrels of tar will he need to buy? (unfortunately the market only sells full barrels) Task 13: Refer the the numbers given in Task 12 to answer these questions. Do them in your Maths book. Show all your working out. Start by writing each questions in normal maths first. a) A man borrows donkeys to use for transporting goods. To re-pay the loan the man must give the lender deben of copper every month per donkey. The man uses each donkey for days per month for transporting goods and earns deben of copper per donkey per day for this work. How many deben of copper does the man make per month? b) The donkeys take some looking after, though. The man has to spend deben of copper per donkey per day for feed. When the donkeys are working they need twice as much feed as they do when they re resting.

11 How much does the man have to spend per month to keep the donkeys? (There were days in the ancient Egyptian month and the donkeys are working as described in part [a]) c) Occasionally the man has to get the donkey doctor to visit if the donkeys get sick. Over a five-month period the donkey doctor has to visit times the first month, in the second, times in the third, times the fourth and in the fifth month. What is the average number of visits the donkey doctor makes per month? d) The donkey doctor charges deben of copper per visit. Taking into account the amount the man must spend on the loan (part a ) and the feed (part b ), and the amount that the man makes from hiring out the donkeys (part a ), how much does the man get to keep each month?

12 e) If the man needs to earn at least deben of copper per month to support his family then what is the minimum number of whole days he needs each donkey to work to make enough money? (assume the donkey doctor makes the same number of visits per month)? Task 14: Do in your Maths book by first writing the numbers into normal numbers first, then finding the missing number. Task 15 Create a PowerPoint containing at least 15 slides, about Egyptian Mathematics. The first slide must contain your Name, the title Egyptian Mathematics, and your year level. The last slide must have the Bibliography with all the websites you used, or all the books you used. The other 13 slides must contain images and information relating to Egyptian Mathematics, e.g. Egyptian number system, Maths relating to the pyramids, Maths relating to their money, the Nile river, the way they did business, how they worked out time, how they worked out angles, weight etc. When you have finished your Power Point, you must save it as Your Names Egyptian Maths PowerPoint, in your home drive or on a USB or your netbook, then drag it to my drop box and put it into 7T6 Mathematics folder. Thank you!