Wedges are a special formulation, with a triangulation (direct or tilted) cut off by a cross-section ( straight or tilted) that intersects with it and the resulting geometry is called wedge. It is a proposed column with a ladder or parallel quadrilateral at the bottom and a line segment parallel to the parallel at the bottom. Figure 1 depicts wedges ab-cdef. In china's ancient book "the nine chapters" the size formula known as envious when the ae is vertically on the ce side is:
Figure 1
Wedges and pillars
The proposed column is called the proposed column, with all the vertes on two parallel plane levels. It is called the bottom of the proposed column on the inside of these two planes, and the other sides are called the side of the proposed column, and the distance between the two sides is called the height of the proposed column, which is called the middle cross of the proposed column through the high mid-point parallel to the bottom (figure 2)。
Figure 2
Wedges the proposed column is rectangled at both ends and parallel to the corresponding side, called the rectangular table (figure 3 left). If the bottom of the proposed column is a ladder or parallel quadrilateral, the upper bottom becomes a line parallel to the bottom of the proposed column, which is called wedge (figure 3 right)。
Figure 3
In addition to the two special circumstances of the proposed column, the following are known by definition:
1. A proposed column is the prism if it has a full polygon on both sides and has parallel sides。
2. If one of the bottoms of the proposed column becomes a point, the proposed column becomes a prism。
3. If the two bottoms of the proposed column are similar polygons and parallel to the opposite side, the proposed column is the prism。
It is clear that the prism is also a special case of the rectangular, and that the prism can also be considered a special case of wedges。
Volume formula for proposed columns and wedges
Now we're working on a simplistic formula:
Theoretically, the volume of any proposed column is equal to one sixth of its high h and upper-floor s1, lower-floor s2, and upper-floor s04. Namely:
V column =
[example 1] it is known that parallels are a, b, parallel to their elliptical kls and c, vertically to these elastic straight-sided areas are s', wedge size。
Figure 4
The direct line of the wedge is e. F. G. With the middle line'g' (figure 4) because wedges are the special case of the proposed column。
So it's volume v weeds:
Because..
So, wedge v
