Equality of Cylinder and Sphere Volumes

FIRST CONSLUSIONS ABOUT WHAT IS A PLANE

 

(TAKEN FROM THE FIRST BOOK “The inequality of the Curve and the Straight Lines”)

 

 

Equality of Cylinder and Sphere Volumes 

PLANES

If we align an infinite number of spheres (see Page 51), but this time with their respective circumscribed cubes; the joints themselves of these originate planes located on infinity itself…, with zero width…, which we don’t see, but we know they exist. If we separate the cubes, we may see what we call surface or solid limit.

In geometry, surface is defined as “An extension where only two dimensions are included”. Now, we may understand this definition more clearly, because we know that the lacking dimension is zero, and is located in infinity itself and exists-

It is impossible for human beings to see and touch a two-dimensional surface, so what we see and touch are volume surfaces.

I believe I may clarify how mistaken we were when imagining an Euclidian geometry proposed for plane figures in a two-dimensional space, separated from a three-dimensional spherical geometry when these are a whole, because what we call a plane geometry I determined by the intersection of a sphere and a plane.

The sphere is a good tool to be able to understand best the concept of finite and infinite.

For example, when we say that the plane is an infinite continuum, we place squares in such a way so that each of their sides is adjacent to other side of another square; this construction will never end. When we said that our space is infinite, if we place equal little cubes, one beside the other, on top and under, we know these construction has no end. Thus, we will say we have an infinite space. The reality is that if these examples happen within a spherical universe, these examples are finite with regards compared to its universe that is the sphere.

There are explanations in texts, where it is mentioned that “The Spherical Surface Area is a Limitless Continuum,” and on the other hand they give explanations to show that the spherical surface area is a finite continuum.

 

 

Conclusion:

I again insist on what I stated on the 3^rd stage of the “Study of Surfaces of Circles and Squares,” where I insist that the same way it is carried out in the Japanese system, the focus should be placed in that the student develops his/her own system to solve mathematical problems.

So, there are many problems you may solve by using the systems exposed in these studies on this blog, such as calculating curved volumes with smaller diameter spheres; in other cases, volumes of cylinders with cylinders or spheres, etc. And being able to compare these results with the systems that are currently used.

Published by Mr. Walter Meyer