In relativity theory, velocities can be represented by points in a certain "rapidity space" in which the distance between two neighboring points is ds = [2/(1 r2)]./dr2 r 2 d02, where r and 0 are polar coordinates, and we consider just a two-dimensional space. (An expression like this for the distance in a non-Euclidean space is often called the metric of the space). Use the EulerLagrange equation to show that the shortest distance from the origin to any other point is a straight line.

like poles repel so keep pushing north to north and repels funny to see this

the aurora is formed when charged particles emitted from the sun during a solar flare penetrate the earth's magnetic shield and collide with atoms and molecules in our atmosphere. these collisions result in countless little bursts of light, called photons, which make up the aurora.

auroras are generated by charged solar particles hitting molecules in earth's atmosphere. this usually happens in high latitudes, because our planet’s magnetic field tends to funnel these particles toward the poles. that’s why it can be experienced in northern ohio.

0 = 0.40 / 0 = 0

= 0.20 = 9.80 ⁄2 =?

=0 , = = 0.20 =0.50 0 0.40 ⁄

=0−122 =0−12(9.80 ⁄2)(0.50)2 =1.2