# Monday Maths: Coordinates

The man ignorant of mathematics will be increasingly limited in his grasp of the main forces of civilization.
~ John Kemeny

Geometry is the study of shapes.  There is so much that you can do with shapes that it’s hard to know where to start.  The four colour theorem is part of geometry.

Geometry has a long and interesting history, but it really came into its own when Descartes (pronounced “day cart”) introduced coordinates.  That meant that complex shapes could be described by numbers and equations, allowing mathematicians to do some very interesting things with them.

We’re going to do some less complicated, but much more fun, things with them.

For a basic introduction to coordinates, why not play Battleships?  You can do this with a pen and paper – just have the girls draw a grid and deploy their ships.  They can call out coordinates to each other to try to sink their opponent’s fleet.

More fun can be had with maps.  Get an ordinance survey map of your area and note the coordinates of some interesting features.  Give the girls a list of coordinates and challenge them to figure out what they are.

Do the same thing with a very large-scale map of the area around your meeting place – and actually go there.  You could dress like pirates and pretend you are searching for buried treasure!

If it’s raining, or you have a group of girls who prefer drawing pretty things rather than walking, you could give them a list of coordinates for a “join the dots” picture and see what variations you get.  Even better, get them to draw something of their own, and then write out the instructions.  Give it to another girl to re-create!

Here’s a couple of examples to get you started:

A House

Outline:
(-10,0) (-10,10) (0,16) (10,10) (10,0) (-10,0)

Door:
(-5,0) (-5,4) (-2,4) (-2,0)

Windows:
(2,4) (6,4) (6,2) (2,2) (2,4)
(2,8) (6,8) (6,6) (2,6) (2,8)
(-2,8) (-6,8) (-6,6) (-2,6) (-2,8)

Cedric the Cat

(Courtesy of my mother, who never throws anything away!)

Axis x from -20 to +30 and y from 0 to +70.  Vertical axis runs through his nose.

body
(0,65) (5,64) (12,70) (10,60) (12,55) (10,50) (6,45) (9,40) (7,35) (9,33) (10,31) (10,25) (8,15) (9,10) (8,5) (10,4) (11,3) (11,1) (8,0) (5,0) (4,2) (5,6) (5,10) (4,15) (5,20) (4,25) (0,26)
and then the reverse (-4,25) (-5,20) (-4,15) etc.

bottom
(10,25) (15,15) (14,9) (12,6) (10,4)
(4,2) (0,2) (-4,2)
(-10,25) (-15,15) (-14,9) (-12,6) (-10,4)

tail
(14,9) (17,10) (23,8) (25,11) (27,13) (29,13) (28,11) (29,8) (28,7) (26,5) (23,5) (17,7) (14,6) (12,6)

eyebrows
(1,56) (2,58) (4,58) (5,56)
(-1,56) (-2,58) (-4,58) (-5,56)

eyes
(3,54) (4,55) (3,56) (2,55) (3,54) and reverse

whiskers
(4,50) (7,52) (9,52) (15,50) and reverse
(4,49) (7,50) (10,50) (12,49) and reverse
(3,48) (6,48) (9,47) (15,43) and reverse

mouth
(6,48) (4,45) (2,45) (0,47) (-2,45) (-4,45) (-6,48)
(-2,45) (0,44) (2,45)

A Challenge

I have a challenge for you.  I’m not happy with my trefoil:

Can anyone do better?  As always, the prize is a combination of virtual cookies and the pride of having achieved something.