Adi's Mathematics

Subtitle

Adi's Mathematics

Adrian Cox
A collection of mathematics related files written by Adrian Cox.

Educated at the Open University and received a B.Sc, (Open) degree in Mathematics.

Adrian Cox also plays guitar and has music under the name of EMO Adi
0:00/6:20
Music by EMO Adi - Do What You Want


Applications And Non Euclidean Geometry
by Adi Cox 29th April 2013

________________________________________________________

A curious thing is that the area of a circle with radius
one has an area of pi. Is this true if a circle is
measured by a unit larger than a galaxy, or some tiny
quantum unit smaller than an atom, I wonder if space is
really that consistantly euclidean.

Non Euclidean geometry is something I was taught at the
Open University and this is a subject I very often find
myself thinking about. I have often thought about
exploring this subject and so here I am writing this
small piece.

Geometry is generally considered to be a pure
mathematical subject but I argue here that really
Eucldean geometry could be seen as a more applied
mathematics because it replicates the space we live in
around us. Whereas Non Euclidean geometry is a litte
more exotic.

Although Non Euclidean geometry is easy to find
applications for finding the areas of curved surfaces
like second order quadrics in a real three dimentional
space with equations like the following:

    Ax^2 + By^2 + Cz^2 + Dxy + Exz + Fyz
    + Gx + Hy + Iz + J = 0

This world we live in is very much three dimensional. Is
there anything that is not three dimensional in the real
world? Even shadows are projections onto uneven surfaces
with three dimensional irregularity. The truth is that a
two dimensional Non Euclidean area needs three
coordinates.


So my final point here is that to take Non Euclidean
geometry up another dimension we will be out of this
physical space because we shall require third order
quadrics in a four dimensional space with equations like
the following:

    Aw^3 + Bx^3 + Cy^3 + Dz^3
    + Ewxy + Fwxz + Gwyz + Hxyz
    + Iw^2 + Jx^2 + Ky^2 + Lz^2
    + Mwx + Nwy + Owz + Pxy + Qxz + Ryz
    + Sw + Tx + Uy + Vz + W = 0
    
Three dimensional Geometry in a four dimensinal space is
more abstract and trully a pure mathematics because it
takes us into a mathematical place that is not
immediately representative of the physical world around
us.

0:00/2:12
EMO Adi - The Working Poor Is Who We Are.