About cookies

The NCETM site uses cookies. Read more about our privacy policy

Please agree to accept our cookies. If you continue to use the site, we'll assume you're happy to accept them.

 

Personal Learning Login






Sign Up | Forgotten password?
 
Register with the NCETM

Secondary Magazine - Issue 43: Focus on


This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 14 September 2009 by ncetm_administrator
Updated on 29 September 2009 by ncetm_administrator

Secondary Magazine Issue 43compass and map
 

Focus on...coordinates

orange circles
The commonly-used Cartesian coordinate system was first used by René Descartes in 1637 (it was also independently developed by Fermat, although Fermat’s version, which he didn’t publish, used three dimensions) in the appendix of his Discourse on the Method. Descartes introduces the new idea of specifying the position of a point or object on a surface, using two intersecting axes as measuring guides. He further expanded this idea in La Géométrie.
 

green circles
Descartes’ contributions to philosophy, mathematics and science are well known but it is perhaps less well known that he was the first to use superscripts as notation for powers (such as the 7 in x7).
 

purple circles
The Discourse on the Method (the full name of which is Discourse on the Method of Rightly Conducting One’s Reason and of Seeking Truth in the Sciences) in which Descartes explores Cartesian coordinates, is also the source of perhaps his most famous quote, I think therefore I am.


blue circles
The invention of Cartesian Coordinates is one of the foundations which allowed Newton and Leibniz to develop calculus.
 

red circles
In Cartesian coordinates in two dimensions, the coordinate axis split the plane into four quadrants. The quadrant in which both x and y are positive is the first quadrant and the second, third and fourth quadrants are labelled anticlockwise from here. In three dimensions, the first octant is the one where x, y and z are all positive but there is no convention for naming the other seven octants. 


 
orange circles
The polar coordinate system uses a distance from a fixed point and an angle from a fixed direction as the two variables. They first appeared in their recognisable form in the mid-17th century, with the Belgian mathematician Grégoire de Saint-Vincent and the Italian mathematician Bonaventura Francesco Cavalieri independently using them. The name polar coordinates has been attributed to the Italian mathematician Gregorio Fontana (1735 – 1803). You can see the relationship between polar and rectangular coordinates in this demonstration from Wolfram Mathworld.


 
green circles
Cylindrical coordinates are a three dimensional extension of polar coordinates in which the distance from a fixed point and an angle from a fixed direction, are combined with a height above a fixed plane to allow three variables to be represented. Although there is no single convention for writing the three coordinates, (ρ, φ, z) are commonly used.

 
 
 
 View this issue in PDF format
 
 Visit the Secondary Magazine Archive
 
 About Magazine feeds
 
 
 Previous page
Next page 
 
 
Back to top

 
 
 

Quicklinks

 
Secondary Magazine Issue 43 - download as a PDF
 
 
Magazine Feed - keep informed of forthcoming issues
 
Departmental Workshops - Structured professional development activities
 
Explore the Secondary Forum
 
Contact us - share your ideas and comments 

Comment on this item  
 
Add to your NCETM favourites
Remove from your NCETM favourites
Add a note on this item
Recommend to a friend
Comment on this item
Send to printer
Request a reminder of this item
Cancel a reminder of this item

Comments

 


There are no comments for this item yet...
Only registered users may comment. Log in to comment