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

http://www.pbs.org/wgbh/nova/pyramid/geometry/index.html )

How Tall?

At 146.5 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

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.

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 146.5 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.

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:

http://www.pbs.org/wgbh/nova/pyramid/explore/khufuenter.html

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.)

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.

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: 214.5 m (704 ft) on each side Height: 143.5 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

The Sphinx from the rear, gazing down on Cairo.

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 1570-1546

Amenhotep I 1546-1524

Tuthmosis I 1524-1518

Tuthmosis II 1518-1504

Tuthmosis III 1504-1450

Hatshepsut 1498-1483

Amenhotep II 1450-1419

Tuthmosis IV 1419-1386

Amenhotep III 1386-1349

Amenhotep IV

1349-1334

(Akhenaten)

Smenkhkare 1334

Tutankhamen 1334-1325

Ay 1325-1321

Horemheb 1321-1293

19th Dynasty Ramses I 1293-1291

Seti I 1291-1278

Ramses II 1278-1212

Merenptah 1212-1202

Amunmesses 1202-1199

Seti II 1199-1193

Siptah 1193-1187

Twosret 1187-1185

20th Dynasty Setnakhte 1185-1182

Ramses III 1182-1151

Ramses IV 1151-1145

Ramses V 1145-1141

Ramses VI 1141-1133

Ramses VII 1133-1126

Ramses VIII 1126

Ramses IX 1126-1108

Ramses X 1108-1098

Ramses XI 1098-1070

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

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 men to reconnoitre a narrow pass.

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

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.

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.

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?

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!