Spherical geometry is the branch of mathematics that deals with figures placed on the surface of a sphere. It can also be defined as a three-dimensional view of more traditional planar geometry; although, there are numerous differences between the planar and spherical subsets of geometrical study. Some of the basic tenets of planar geometry don't carry over to spherical geometry because it deals with different mathematical concepts.
Know MoreSpherical geometry is useful because it creates easy metrics that can be used to study complex three-dimensional shapes, such as spheres. However, there are some caveats to this branch of mathematics because some of the laws and rules of planar geometry don't apply to spherical geometry. For this reason, spherical geometry is sometimes confusing to math students, notes the University of Georgia Mathematical Education Program. As an example, there are no parallel or straight lines in spherical geometry. Circles are the basic shape utilized in this mathematical branch, which stands in stark contrast to traditional planar geometry where students are introduced to lines as one of the simplest and most basic geometric constructs. Consider this: on a globe of the Earth, lines of longitude are parallel at the equator but cross at the poles.
Learn more about GeometryThe spherical coordinate system is the method of giving the specific direction of a point in a three dimensional space. The coordinates are represented by rho, theta and phi. The coordinates are first changed into rectangular coordinates. This is done in order to simplify the initial equation. The equation is then partially differentiated to determine the gradient.
Full Answer >The infinite series sum usually deals with geometric series. The sum of an infinite geometric series, denoted as "S", is t1 / (1 - r), where "t1" is the first term of the series and "r" is the common ratio between the numbers in the series.
Full Answer >To find the surface area of a sphere, use the formula 4(pi)r^{2}. In this formula, r is equivalent to the radius. Pi represents the infinite number 3.141592..., which is usually rounded to 3.14.
Full Answer >In geometry, converse, inverse and contrapositive are conditional statements consisting of a hypothesis and a conclusion. These statements are also known as “if-then statements.” The hypothesis part of a conditional statement is the “if," and the “then” part is the conclusion. The conclusion is the result of a hypothesis.
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