It is possible to determine piece length practically, having put to it a ruler or a roulette, having measured it by means of a scale. If the ends of a piece have coordinates, it is possible to find its length, having calculated by means of special formulas.
It is required to you
- - ruler;
- - roulette;
- - concept about the Cartesian coordinates.
Instruction
1. Apply a ruler with millimetric divisions to the piece constructed on the plane. Combine the initial point with in zeroscalesruler . After that note arrangement of a final point of a piece on a scale. It will also be its length. If the piece has rather big length, measure it by means of a roulette in the same way, as well as a ruler. This procedure can be made by means of a laser range finder, having established it in one of points and having sent to another. At the same time the beam has to be parallel to a piece. The result quickly will appear on the display of the device. Accuracy of such measurement is very high.
2. If coordinates of the ends of a piece are known (x1; y1; z1) and (x2; y2; z2), calculate its length. From the coordinate of the first point, subtract the corresponding coordinates of the second point. Receive three couples of numbers of x=x1-x2; y=y1-y2; z=z1-z2. Square each of the received numbers. Find the sum of these squares x²+y²+z². Take a root from the received number square. It will also be distance a boundary points with the specified coordinates. And as they are the ends of a piece, it also will be its length.
3. For example, find piece length from the ends which coordinates are equal (-5;8;4) and (2;6;-1). Find the difference of the corresponding coordinates of these two points of x=-5-2=-7; y=8-6=2; the z=4th (-1) =5. Three numbers which are coordinates of the vector including the measured piece (-7;2;5) will be result.
4. Square each of these numbers and find the sum of results (-7)²+2²+5²=78. The result always has to be positive. Take a root from the turned-out number square. √78≈8.83 linear units. One linear unit is equal to length of a single piece of a system of coordinates.
5. In case piece coordinates on the plane are set, then the coordinate of z is always equal to zero and it can just be not considered. For the rest, the method of calculation of length of a piece remains the same.