MODA: Geometry bashing

A tried and tested technique for attacking geometry problems is ‘bashing’ them with an algebraic approach. We’ve already seen how projective geometry can be based around a coordinate system (giving rise to areal and projective Cartesian coordinates as special cases). Two-dimensional Cartesian coordinates are more naturally manipulated as complex numbers, which is usually the best general approach if you’re stuck on a problem and don’t know how to progress.

The three- and four-dimensional counterparts of the complex number bash are Hamiltonian quaternion bashes, which are more difficult due to the lack of commutative multiplication. I used quaternions, for instance, to construct the discrete Hopf fibration. This is not covered in MODA, as problems in olympiad geometry are almost invariably two-dimensional.

This entry was posted in MODA. Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s