By using Euclidean and non-Euclidean geometry, you are able to visualize problems that you may not have been able to before, that is as long as they are in 2 dimensional or 3 dimensional spaces. 4 dimensional spaces are a bit harder to visualize, like the Klein bottle for example. But knowing how Euclidean and Non-Euclidean geometry work helps when solving geometric problems.

Non-Euclidean geometry is especially important within the world of architecture. A great example of where this is used is the Cathedral of Saint Mary, pictured below, in San Francisco, California. This great work was built in 1971 and designed by a man by the name of P.L. Nervi. Within this cathedral, hyperbolic geometry was used to skew individual planes (or panels) in the upward direction, this ended up creating a cross at the point where all the planes intersect. Due to the design of the inside of the cathedral and the unique outside, the roof is only supported by four pillars! Without knowledge of hyperbolic geometry, the unique construction of this cathedral may not have been possible.

It is important to note that the quality of buildings and other types of architecture we have today also depend on the effectiveness of the geometry we use. When using geometry effectively, we are able to find ways to reduce material usage and increase dependability. Luckily for us, we live in an age where technology is getting bigger and better every single day. This means more technologies are being developed to help architectures create more complex structures that could not have been done before.

Another important idea included in geometry is the mobius strip. Another important object included in geometry is the mobius strip. An important application of this object is a part of the type of engineering which deals with heavy machinery. This non-orientable, one-sided object is often used to create belts on machinery that last longer than normal types of belts. A normal belt is one which is two-sided instead of one-sided like the Mobius strip. When using Mobius strips as belts on machinery, the one side wears down evenly throughout the entire belt and helps to make it last longer, and therefore saves companies money because it does not have to be replaced as often. When using a normal belt, one side wears out faster than the other, so a normal belt does not last as long.

If you have also seen a movie or video which uses a tape to play, you have probably experienced the use of a Mobius strip without even knowing it. Mobius strips are great when needing a long video to play without any interruptions as it does not stop in the middle of the video. This also makes it possible for movies and videos to be twice as long since there is more room for footage.