Transcript The Golden Ratio Begin by drawing a square with sides of 10cm 10 cm 10 cm.

The Golden Ratio
Begin by drawing a square with sides of 10cm
10 cm
10 cm
The Golden Ratio
Make a 5 cm mark on the top and bottom of the
square and connect with a line
10 cm
x
10 cm
x
5 cm
The Golden Ratio
Notice that the square has been divided into two
equal rectangles
10 cm
x
10 cm
x
5 cm
The Golden Ratio
Now draw a diagonal in the 2nd rectangle as shown
10 cm
x
10 cm
x
5 cm
The Golden Ratio
Set your compass to the length of this diagonal
10 cm
x
10 cm
x
The Golden Ratio
Use the compass to draw an arc as shown
10 cm
x
10 cm
x
And extend the bottom line
of the square to meet the arc
The Golden Ratio
Carefully measure the line AB
10 cm
x
Write down your
measurement in
centimetres to 1 decimal
place
10 cm
A
x
B
? cm
The Golden Ratio
Now complete the rectangle
Write down the ratio of
long side : short side
10 cm
x
??.? : 10
10 cm
A
x
B
Express this as a fraction
??.?
10
? cm
And convert to a decimal
??.? ÷ 10 =
The Golden Ratio
This decimal is your answer and you should round it
to one decimal place.. this is the ratio of the sides of
the rectangle (long side : short side).
x
10 cm
A
x
B
Your teacher will now
survey the class and collect
all the answers
A class average (mean) can
now be calculated using
the formula
x

m ean
n
The Golden Ratio
Mark the point C on your diagram as shown
And measure the distance
CB to the nearest millimetre
Write down the ratio of
AC : CB
10 cm
A
B
C
? cm
Now convert this ratio into a
decimal in a similar way as
before.
You should arrive at approximately the same answer –
about 1.62
The Golden Ratio
Focus on just the line AB
We have found that the
ratio of
AB : AC
Is the same as
AC : CB
10 cm
A
C
B
These ratios represent the lengths of sides of two
rectangles in the diagram – your teacher will point them out.
The Golden Ratio
So BOTH rectangles….. The BIG one
10 cm
10 cm
A
C
B
The Golden Ratio
So BOTH rectangles…..
and the SMALL one
have
10 cm
long side : short side
10 cm
In the SAME ratio of
about 1.62
A
C
B
And they share a common side
This ratio is very special and is given the symbol Φ (Phi)
It is commonly referred to as The Golden Ratio
The Golden Ratio
Some links to explore
10 cm
A
C
B
http://www.mathsisfun.com/numbers/golden-ratio.html
http://www.bbc.co.uk/learningzone/clips/the-beauty-of-the-golden-ratio/9017.html
K.Rybarczyk 2011