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Senior VCAL Numeracy – Design Investigation 3
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FLAGS OF THE
WORLD
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3 DIMENSIONAL DRAWINGS
1. Redraw the following objects on the isometric dot grid.
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2. Draw the front, side and top views of the following objects. An example is
given.
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3. The front, side and top views of several objects are shown below. Draw
these objects on the isometric dot grid. MODERN AND HISTORICAL FLAGS Flags are everywhere. They are so common we barely notice them. Throughout the world they are used as a means of identification and display symbols representing nationality, politics, religion and ideas. The study of flags is called Vexillology. Most modern flags are rectangular in shape but other shapes have been used in the past.
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1. Look at the following flags and answer the following questions:
a. Show all lines of symmetry b. State the order of rotational symmetry, if it exists.
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THE GEOMETRY OF FLAG DESIGN Flags are divided into quarters which are known as cantons. The two cantons nearest the flag pole are called the hoist and the other two are the fly. Constructing a flag is easy when the design is given in geometrical terms. Some of the expressions used to describe a flag’s construction include:
• Top left-‐hand corner or upper hoist • Bottom right-‐hand corer or lower fly • Vertical, horizontal or diagonal stripes • Down the middle • Equal width • Half, or twice, the width • Across the centre
2. Which description matches which flag?
a. Two vertical stripes of equal width with a
crescent in the upper fly.
b. Two horizontal stripes of equal width with a Crescent in the upper hoist.
c. A Greek Cross in the upper joist and two vertical stripes of equal width.
d. A diagonal stripe from the upper hoist to the lower fly with a Star of David in the upper fly.
e. Two vertical stripes where the stripe in the hoist has half the width of the other stripe.
length
width
upper hoist
upper fly
lower hoist
lower fly
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3. Draw a flag to match each of the following descriptions.
a. Two horizontal stripes of equal width with a Star of David in the upper fly.
b. Five horizontal stripes of equal width.
c. Two diagonal lines with a Star of David where the two diagonals
intersect.
d. Three vertical stripes of equal width with a Crescent in the middle.
e. Two vertical stripes of equal width and 2 horizontal stripes of
equal width.
f. In the top left-‐hand corner, a rectangle with length half the length
of the flag and width half the width of the flag.
g. Three horizontal stripes. The top one is half the width of the flag
and the two bottom ones have equal width.
h. Two vertical stripes of equal width with a large circle in the centre
of the flag.
4. Write the instructions you could give someone else to help them draw these flags.
a. b.
THE GEOMETRY OF FLAG DESIGN Most Australians know little of the ideas and symbols behind the design of our national flag, how it came into being or who designed it. The first of January 1901 was a very important day in Australia’s history. It was the day the former six British colonies combined to become a nation. But the flag flying over the new nation was a British Union Jack. Australia did not have a flag of its own. Prior to Federation in 1901, several unofficial flags had been flown around the country. Probably the first Australian designed flag was flown in 1806 by the Bowman family on
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their perspective property near Richmond, New South Wales. Their flag featured the emu and kangaroo which are now an important part of the Australian Coat of Arms. In 1851 the Australasian Anti-‐Transportation League used a flag with five golden stars in the shape of the Southern Cross in its campaign to end the transportation of convicts to Australia and New Zealand.
The Southern Cross design was also incorporated in the Eureka flag flown by the miners in the troubles of Ballarat gold fields in1854.
Just before Australia became a nation, the Review of Reviews journal offered a prize of £50 for the best design for a national flag. In April 1901 the Federal Government launched its own flag competition and accepted all the entries in the Review of Reviews competition. With sponsorship from the Review of Reviews journal, the Havelock Tobacco Company and the Commonwealth Government, £200 was offered as a prize. In 1901, £200 was a lot of money, more than a year’s wage. More than 32 000 entries were received from people all around Australia. The design selected as the winning entry was submitted by five different Australians who were declared equal winners. One of the winners was a 14 year old Melbourne school boy, Ivor Evans. Ivor’s entry was special because he included with his design a description of what each feature of his flag symbolized to him.
For Ivor, the Southern Cross represented Australia’s future position as a leading nation in the Southern Hemisphere. The four prominent stars in the Cross represented the four moral virtues of Justice, Prudence, Temperance and Fortitude. Ivor believed these virtues were what all Australians aimed for. Honouring the flag meant living up to the ideals it represented.
5. Find meanings for the four virtues that Ivor mentioned.
The large six-‐pointed Commonwealth Star represented the joining together of all Australians in the six British colonies to form one nation. In 1908 a seventh point was added to Ivor’s Commonwealth Star to represent Australian Territories.
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Finally Ivor explained the significance of including the Union Jack. To Ivor, the Union Jack not only represented the origin of the original white settlers of Australia, but the basis of modern Australian society: our language, law, democracy, freedom of speech and our system of government. Use the scale diagram of the Australian Flag (on next page) to find out the geometric specifications of the Australian Flag.
6. Measure the length and width of the flag on the scale diagram.
7. What is the length and width of the Union Jack on the scale diagram?
8. What is the relationship of the dimensions of the Union Jack to the
dimensions of the whole flag?
9. What fraction of the area of the Australian Flag is covered by the Union
Jack?
10. Measure the size of the angles α and θ as illustrated to the right on the
Commonwealth Star on the scale diagram.
11. Angles β and γ are two different angles formed in the Crosses of Saint
George and Saint Andrew.
a. Use a protractor to measure the
size of the two angles on the scale diagram.
b. Are the pair of angles
supplementary? Explain your answer.
12. The diagonals of the Union Jack are
shown on the scale diagram of the flag as light
dotted lines.
a. What is the size of the obtuse angles between the diagonals?
b. Measure the acute angle between the diagonals.
c. True or False? ‘The two angles measured in 12a and 12b are
complementary’.
α θ
γ
β
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RATIO AND PROPORTION IN FLAG DESIGN Flags are made in different sizes, from small flags on sticks to giant flags on flagpoles. Even though the size can be different, the proportions of the flag are always the same. When Australian flags are manufactured the length of the flag is always twice the size of the width. The ratio of the length to the width of an Australian flag is always 2:1.
13. Refer back to question 6, was the scale diagram in a ratio of 2:1? Explain.
14. Use the scale drawing of the Eureka Stockade flag to find the ratio of its
length to its width.
15. Matt is going to make a Eureka Stockade flag as part of his History
assignment. He wants to make the flag 15cm long. Using the ratio of the
flag from question 14, calculate how wide the flag will be.
16. The flag of Scotland has a white cross on a blue background.
a. Copy and colour the flag.
b. The flag has been drawn to scale.
Use a ruler to measure its
dimensions and find the ratio of
its length to height.
c. A Scotish flag has a height of 1.5
metres. What is its length?
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17. Copy this scale drawing of the Australian Aboriginal flag and follow these
directions to complete it.
a. The flag has a large yellow circle in the
centre. It also has two horizontal
stripes of equal width. The top stripe is
black and the bottom stripe is red.
b. What do the colours on the flag represent?
c. An aboriginal flag has a length of 6 metres. What is its height?
18. What geometrical shapes can you see in these flags?
a. b.
c. d.
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19. This is scale drawing of the flag of Ecuador.
a. Use your ruler to measure the flag
and find the ratio of its length to
width.
b. The flag has a length of 3.5 metres. What is its height?
c. Your friend wants to know how to draw and colour the flag. Write
how you would explain it over the phone.
20. Here is a scale drawing of the flag of Panama.
a. Describe the design of the flag.
b. What is the ratio of the length to the
width of the flag?
c. The real flag is 70cm wide. How long
is it?
21. Dick Smith flies a giant Australian flag which is 6m long and 3 m high.
a. What is the ratio of its height to length?
b. What is the area of Dick Smith’s flag?
c. 15% of the Australian flag is white. Calculate the
area of white on Dick Smith’s Australian flag.
22. This is a diagram of the Canadian flag.
a. What is the ratio of the length to the width?
b. The red stripes are both 30 cm wide. What shape
and dimensions of the middle white section?
c. The area of the maple leaf is approximately
1600cm2. What percentage of the Canadian flag is red?
120cm
60cm
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23. This is a scale drawing of the NATO shipping signal for ‘P’. What fraction
of the area of the flag is white?
24. The following diagrams represent the National Flags of one of the
countries on the world. Each is in the shape of a rectangle but they have
not been drawn to scale.
Find the size of each angle indicated by a pronumeral.
c. Brazil – South America d. Mozambique – Southern Africa
a. Bhuton – Indian Subcontinent
31°
θ α
80° α β 145°
θ
64° β
α
b. Djibouti – Eastern Africa
α
θ 30°
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25. Using the supplied flags from your teacher, draw accurate scale diagrams for:
a. Canada
b. Saskatchewan.
26. Design a Senior VCAL flag.
a. Make a scale diagram of your flag.
b. Make a real life size flag in any appropriate materials.
Complete either Q27 or Q28.
27. Semaphore Flags
a. What are Semaphore Flags? Explain.
b. Include a diagram to illustrate the flags.
c. Make a set of Semaphore Flags. Compose an appropriate message.
Practice it and then film the message.
e. Grenada – The Caribbean
f. Cuba – The Caribbean
g. Guyana – South America h. Bahamas – The Caribbean
48°
x
x y
θ
Φ
Φ
Φ α
θ 58°
Φ 75°
60°
60°
θ
Φ
β α
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28. International Maritime Signal Flags
a. What are International Maritime Signal Flags? Explain.
b. What is the ratio used to create them?
c. Use this ratio to create a set of flags of either your full name or a
message.
CONCLUSION o What did you learn in this investigation? Be specific.
o Do you think your VCAL flag is appropriate and could be used
realistically?
o Find what you think is the strangest flag in the world. Explain why. (Mine
is the Netherlands so you can’t use this one!)
o Discuss any difficulties you encountered and how you overcame them.
o Any improvements.
Extension
Go back and complete Q27 or Q28!
Fryslan Netherlands
