The spherical geometry that was discussed in the previous posts actually has a surprising number of real-world applications. For example, pilots and sailors use it all the time in their jobs to find the shortest path to their destination. Remember, that Earth has a spherical form and therefore the Euclidean rules of the plane applied to the surface of the planet won’t work like that.
This means that the shortest path between Los Angeles and London on Earth’s map is not a straight line (red), but rather a curve (purple) that follows a line on the sphere that is Earth.
So, the pilots, who deal with spherical geometry on a daily bases, have to go through mathematical calculations discussed here, along with other more complex derivations, every time they want to analyze the direction or the path of their journey. A perfect career choice for people who want to do math all day long.
Have you ever wondered how far the distance from New York City to London is? How about from New York City to Venice? Rome? The distance from one place on Earth to any other place on Earth is the great circle distance. The great circle distance is the distance from any two points on a sphere. The formula for distance is d = r ∆θ, where r is length of the sphere’s radius and ∆θ is the central angle between two given points.
Here is an interesting site that calculates distances from any two points on Earth.
In spherical geometry, all great circles (lines) intersect. All great circles intersect because they are created by intersection of a plane going through the center of the sphere, which creates great circle from the intersection like the circumference of the circle created. There are two intersection points created by two great circles. An angle can be found at one of the point of intersection, which can be defined as an intersection by two planes of the great circles.
After reading this cool post on applications of spherical geometry, I decided to look for all sphere-related objects in my life. This week I saw many spherical objects:
-The fake wooden or plastic or some kind of egg that Mr. Honner showed us on 3/9/11, which also reminds me of lunes.
– Google Earth, at which I usually look at my home only.
-I saw millions and millions of black frog eggs, so many…. enough to fill my stomach 🙂
-The copper ornament that Mr. Honner was juggling during Major selection [he doesn’t seem to juggle well]. Three of the copper ornaments might be infected all because Mr.Honner unleashed water on shapes and used them as test subjects… Poor Shapes..
-On 3/8/11, I saw mini circle shaped pizza during lunch. So cheap… Obviously, I went for some other food.
-Your head is related to spherical geometry. 🙂
-I saw many pictures, more pictures and more pictures of spheres…. All looked beautiful.
Spherical geometry is the geometry of shapes on the sphere’s surface. It is a type of non-Euclidean geometry that is unlike your everyday geometry of lines and flat planes. The paramount idea overlaying spherical geometry is that no lines are ever parallel. Thus, shapes like triangles are a bit obscure in appearance in spherical geometry as their internal angles add up to beyond 180 degrees. Spherical trigonometry, however, is quite similar to Euclidean trigonometry.