Aquila peers into the past
HERE’S LOOKING AT
EUCLID
Euclid of Alexandria was an Ancient Greek mathematician who is
sometimes called the ‘Father of Geometry’. He lived around 300 BC (that’s
about 2,317 years ago) in the Egyptian city of Alexandria, where all the big
names in philosophy, mathematics and astronomy hung out. Or did he?
ANCIENT MATHEMATICAL
MAN OF MYSTERY
Here’s the thing… No one really knows
if Euclid of Alexandria ever existed! He is
an ancient mathematical man of
mystery. To unravel it, we have to look
at the evidence.
Evidence for the existence
of Euclid
Clue 1: Over nine major mathematical
works are attributed to Euclid BUT…
Evidence against the
existence of Euclid
Clue 2: No one knows where, when or
to whom he was born (no records).
Clue 3: No one knows when, where or
how he died (no known tomb).
Clue 4: No one knows what he looked
like, or who his family and friends were
(no records).
Clue 5: No one claimed Euclid as a
student or as their teacher (no
contemporary biographies).
Clue 6: Later biographies were written
as much as 800 years after his life
(ooh-err).
Clue 7: The name Euclid comes from
Ancient Greek Εύκλείδης Εύ (Eu),
meaning ‘good’ or ‘well’ and κλεος
(Kleos) ‘glory’ or ‘renown’. Is this a secret
clue or a clever trick? Who was the ‘well
renowned’ man no one claims to have
met?
SO WHAT CAN WE
DEDUCE ABOUT EUCLID?
Theory 1: Documents about Euclid’s life
were destroyed or lost.
Theory 2: Euclid had another name and
just called himself Euclid when he wrote.
Theory 3: Euclid collected work from
other mathematicians and published
the work anonymously.
Theory 4: Euclid was the collective team
name for a group of mathematicians.
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Which theory do you think best fits
the facts?
Whether or not Euclid was an actual
man, there are a whole lot of clever
mathematical ideas attributed to him.
The famous Elements books and the
Golden Ratio, among other works, are
thought to have come from the pen of
Euclid.
THE ELEMENTS
The Elements are a series of thirteen
books containing all the collected
mathematical knowledge of the time,
hailed as a ‘masterpiece of mathematical
logic’. It brought together ideas and
statements about all the things that
could be done in two dimensional space
with a straight line and a compass, plus
some simple facts about lines and
angles. Euclidean Geometry is still
taught in schools today.
Five Euclidean Geometrical
Rules (geometry basics)
1) It is possible to draw a straight line
between two dots.
2) A straight line extends both ways to
infinity.
3) It is possible to draw a circle, given a
centre and a radius.
4) All right angles are equal.
5) Where two straight lines are crossed
by another with an interior angle that
is less than 180, they will eventually
cross (but parallel lines never will).
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THE GOLDEN RATIO
Called the ‘extreme and mean ratio’ by
Euclid, the golden ratio appears in
geometry, art, architecture and nature.
Some people later called it the divine
ratio, its essence is simple:
A straight line divided into two parts,
where the bigger part divided by the
smaller part is the same as the whole line
divided by the longer part.
You can draw the Golden Ratio in a
rectangle:
You will need
ruler
compass
pencil
(the same kit Euclid would have used –
if he existed).
1) Draw a square.
2) Measure halfway along the bottom
side and add a point.
3) Connect the point to an opposite
corner.
4) Use that new line as a radius (half the
width of your circle) and your dot as
the circle centre.
5) Draw an arc from the end of your
new line down to meet an extended
horizontal line from the base of your
original square.
6) Extend the top horizontal line
parallel with the extended bottom
line.
7) Complete your golden rectangle by
joining up the extended horizontal
lines with a straight line from the
outer edge of the arc line.
How do you know you’ve drawn the
Golden Ratio in a rectangle? Well, to
check, just divide the longest side by
the shortest. The answer should be
around 1.62.