world around us, despite the variety of objects and phenomena happening to them, full of harmony Thanks to a clear effect of the laws of nature.Behind the apparent freedom with which nature draws the outlines of shapes and creates things lurk clear rules and laws inadvertently suggests the idea of the presence in the process of building some kind of higher power.On the verge of a pragmatic science, giving a description of the phenomena from the standpoint of mathematical formulas and theosophical worldview, there is a world, giving us a whole bunch of emotions and impressions from filling his things and events happening to them.
Bowl as a geometric figure is the most common naturally occurring form for physical bodies.Most of the bodies of the macrocosm and microcosm have a spherical shape, or seek to get closer to that.Essentially, the ball is an example of an ideal shape.The generally accepted definition for the ball is considered to be the following: a geometrical body, a set of (set) of all points of which are at a distance from the center, not exceeding a given.In geometry, the distance was called the radius, and with reference to the figure, it is called the radius of the sphere.In other words, the volume of a sphere contains all the points located at a distance from the center, no more than the length of the radius.
Bowl still regarded as a result of rotation of the semi-circle around its diameter, which thus remains fixed.Thus such elements and characteristics as the radius and volume of the ball, the ball axis is added (fixed diameter), and the ends of the ball are called poles.The surface of a sphere called the sphere.If you are dealing with a closed ball, he includes this area when open, it eliminates it.
considering further related to the determination of the ball, it should be said about the cutting plane.Passing through the center of the ball cutting plane is called a great circle.For other plane sections of a sphere made to apply the name of "small circles".When calculating the area of these sections using a formula πR².
Calculating the volume of a sphere, mathematicians faced with a rather exciting regularities and features.It turned out that this value is either repeats or very close by to the method for determining the volume of a pyramid or a cylinder circumscribing a sphere.It turns out that the volume of a sphere is equal to the volume of the pyramid, if it has the same base area, the surface of the ball, and the height is equal to the radius of the sphere.If we consider a cylinder circumscribing a sphere, you can calculate the pattern according to which the volume of a sphere is less than the volume of the cylinder in half.
looks attractive and original way of derivation of the volume of a sphere using Cavalieri's principle.It is to find the volume of any figure by adding the area received its section of an infinite number of parallel planes.To output take hemisphere of radius R and a barrel having a height-R with a base circle radius R (the base of the hemisphere and a cylinder located in the same plane).As we enter the cylinder cone with vertex in the center of the bottom of its base.Proving that the volume of the hemisphere and the cylinder left out of the cone are easy to calculate the volume of a sphere.Formula it takes the form of a cube four third product range on π (V = 4 / 3R ^ 3 × π).It is easy to prove, having a total section plane through the hemisphere and the cylinder.Square small circle and the annulus bounded by the parties outside the cylinder and cone are equal.And, using the principle of Cavalieri, it is easy to come to the proof of the basic formula by which we assess the extent of the world.
It is not only a problem related to the study of natural bodies find ways to determine their different characteristics and properties.This figure is solid geometry as the ball is widely used in the practice of human rights.The mass of technical devices has in its design details not only the spherical shape, but made up of elements of the world.It is up to the ideal of natural solutions of human activity provides the highest quality results.
