# Geometric metrics

axiomatic system

D. Hilbert in the establishment of Euclidean geometry axioms (see

This series 0. thus limit the number of columns before the two have the same limit. Thus, this limit is defined as the area of ​​a rectangle. provable so that rectangular area is equal to the product of the length of two adjacent sides.

About circumferential length and area of ​​a circle, the elementary geometry is defined by: Since a circle inscribed n-gon and circumscribed n-gon, when the number of edges infinite multiplication, a series of circumferential regular polygon inscribed incrementing infinite length constituting a series, a series of circumscribed regular polygon constituting a circumferential length infinite decreasing the number of columns, two columns have the same limit. Thus, this limit is defined as the circumferential length.

< p> Similarly, the polygon area two series also constitute a infinitesimal increment the number of columns and a infinite decreasing the number of columns. These two series have the same limit. Thus, this limit is defined as the area of ​​a circle.

according to the above definition, it may prove circumferential length C = 2πr; circular area S = πr, where r is the radius of the circle; [pi] is pi

discussion of the simple polyhedron volume are imitation simple polygon area. discussed.

discussion of surface area and volume of the sphere, are discussed imitation circumferential length and area.

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