Lining up time
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CANVAS & STRETCHER
Lining up time: how many ways can you arrange the people in a portrait?
Quite a few portraits show several people standing or sitting in a line. You are going to work out how many different ways this could be done - and think why the artist actually chose the particular arrangement that you see in some of the pictures.
by Sir Joshua Reynolds, oil on canvas, exhibited 1773
Here is the portrait of David Garrick and his wife Eva Maria.
The artist only has 2 ways to arrange them:
man | woman
or
woman | man
by John Francis Rigaud, oil on canvas, 1782
Now look at this picture with 3 men, each wearing a different coloured coat. The artist has shown them like this:
but he could have done:
brown | green | red
red | brown | green
Find the other ways he could have done it: |
green |
||
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How many different ways are there to arrange 3 people?
Do you think one man looks more important than the other two or do all three look about equal?
by John Michael Wright, oil on canvas, 1673
This is the Viner family.
Here you have got:
girl | mother | boy | father
the artist could have done
father | girl | mother | boy
now find all other ways:
How many different ways are there to arrange 4 people?
Charles is the smallest person in the picture. Where has the artist put him to make him look important? What else has the artist done to help you notice him?
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by Unknown artist after Sir Anthony Van Dyck, oil on canvas, (1637)
These are the children of King Charles I. Their names are:
Mary | James | Charles | Elizabeth | Anne
Work out some of the other ways they could sit.
Now guess how many different ways they could sit (don't try to work out all of them).
I guess
different ways
Why did the artist choose Charles to be in the middle, do you think?
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Extension
Jonathan Tyers and his family
by Francis Hayman, oil on canvas, 1740
You are now going to look at some portraits with more people in. Don't try to count all the different ways to arrange them as there are hundreds of ways!
For 6 look at the Tyers family.
The Capel Family by Cornelius Johnson (or Jonson), oil on canvas, circa 1640
For 7 look at the Capel family.
The Gunpowder Plot Conspirators, 1605
by Unknown artist, engraving, circa 1605
For 8 look at Guy Fawkes and the Gunpowder Plot conspirators.
There is a way to work out how many ways to arrange a set number of people.
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Fill in this chart using the information you already have:
1 person can be arranged |
1 |
way | |
2 people can be arranged in |
2 |
ways | |
3 people can be arranged in | ways | ||
4 people can be arranged in | ways | ||
5 people can be arranged in |
120 |
ways |
How good was your guess for 5 people?
Can you find a pattern which links the number of people with the number of ways they can be arranged?
(CLUE - it's to do with multiplying, and you always use your last answer in the next sum).
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The pattern you have found is called the factorial for each number and is written !2.
So !5 means 1 x 2 x 3 x 4 x 5 = 120
Now use a calculator (if you need one) and work out the answers for those other portraits
The Tyers family
The Capel family
The Gunpowder Plot
The Tyers family, 6 people, can be arranged in | ways | |
The Capel family, 7 people, can be arranged in | ways | |
The 8 Gunpowder Plot conspirators can be arranged in | ways |
If you arranged all the people in your class in a line, how many different ways could you do it? - you will need a calculator for this!
Now make a portrait of a group of people in your class - how will you arrange them?
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Canvas & Stretcher:
The Capel's garden
William Jones & circles
William Hogarth's self portrait