Mathsy thing

1. “What is Non-Euclidean Geometry
and where can it be applied?”
Presented by Matthew Tully

2. Euclidean Geometry
Euclid originally set out 5 axioms of geometry.
1) There is a unique straight line segement
between 2 points.
2) Any straight line segment can be infinitely
extended to form a straight line.
3) Given a straight line segment, there is a
circle with one end at the centre with radius
equal to the length of the line segment.
4) All right angles are congruent.

3. The parallel postulate
5) Given any 2 lines, if a third is drawn which
intersects them such that the interior angles on
one side are less than the sum of 2 right
angles, the 2 original lines will intersect on that
side of the line.
Sound controversial?

4. Elliptic Geometry
This is the geometry of surfaces with constant
positive curvature, such as the surface of a
sphere.
On the surface of a sphere, the shortest line
between 2 points is called a “great circle”,
which are circles on a plane upon which the
centre of the sphere is also.
This has some interesting consequences.

5. Applications
Navigation- the surface of the Earth follows this
Non-Euclidean Geometry.
The shape of the universe.

6. References
● Weisstein, Eric W. "Euclid's Postulates." From
MathWorld--A Wolfram Web Resource.
http://mathworld.wolfram.com/EuclidsPostulates.htm
● Weisstein, Eric W. "Elliptic Geometry." From
MathWorld--A Wolfram Web Resource.
http://mathworld.wolfram.com/EllipticGeometry.
html

7. References
● Weisstein, Eric W. "Euclid's Postulates." From
MathWorld--A Wolfram Web Resource.
http://mathworld.wolfram.com/EuclidsPostulates.htm
● Weisstein, Eric W. "Elliptic Geometry." From
MathWorld--A Wolfram Web Resource.
http://mathworld.wolfram.com/EllipticGeometry.
html