The Mathematics Of Curvature: Understanding Shapes Through Curves


How do you define shapes, especially geometrical shape? Mathematicians will answer you with one word: curvature. The techniques used in defining different shapes range from the simple to the complex but the fact remains that curves are important and that they have a reason for existence.

Curvature is defined in geometry as the degree where the "curve deviates from a straight line." Mathematicians calculate these curves to define the shape of an object.

For simple shapes, such as the sphere and the cone, defining the shape is pretty simple because the curvature of the sphere is distributed evenly in its body. On the other hand, the curvature of a cone is distributed evenly on its spaced vertices.

For such shapes, calculating the curvature is easy but how about for complex shapes. Mathematicians have a rather straightforward technique in doing that. First, they imagine it as just a flat surface then they draw a circle around a certain point of that flat surface.

Like all things in this world, curvature can be both positive and negative. A curvature is positive if it curves away from that point and goes to the same direction. Your head, the tip of your fingers, and the inside of your armpit are examples of positive curvature because the curves extend away from the main point.

Negative curvature, on the other hand, curves away from the point in separate directions. An example of that is the horse's saddle and the inside of your neck. For example, one curve in the horse's saddle goes from the head to the horse's tail while the other curves perpendicularly to the first curve.

Aside from shapes, the curvature is also important when measuring distances. When scientists measure the distance from one place to another, they have to consider the curvature; thus, if there are a lot of mountains, the distance would be greater because there are a lot of curvatures involved in that.

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