# Approximate measurements

When the hot summer days come, it's hard to stay at home. It's time to collect things and get ready for rest. The best rest is a hike, or excursions, during which one often has to measure distances. But the dimensional ruler or tape is not always at hand, and it is useful to be able to manage somehow without them, producing at least **approximate measurements**.

It is easiest to measure long distances in steps. With normal walking, we make steps of approximately the same length, and if we know their average length and be able to count, then we can make approximate measurements of distance without a big mistake.

To do this, on an even place with a tape measure the distance of 20 m. Along the tape draw a line on the ground. Now go along the line in the usual step and count the number of steps taken. It is possible that the step can not be met an entire number of times at a measured length. Then, if the remainder is shorter than half the length of the step, it can simply be thrown away; If it is longer than a half-step, the rest is taken as a whole step. Dividing the total length of 20 m by the number of steps, we will learn the average length of one step. This number must be remembered, so that when necessary, make approximate measurements of the distance.

By the way, we can note the following old rule: the length of the average step of an adult is equal to half the distance from his eyes to his feet. There is a second rule: a man passes at an hour as many kilometers as he does in 3 seconds. But we can prove that this rule is true only for a certain step length. In fact: let the length of the step *x* m, and the number of steps in 3 seconds. is equal to *n*. Then in 3 seconds. pedestrian makes *nx* m, and per hour (3600 seconds) - 1200*nx* m, or 1,2*nx* km. To make this path equal to the number of steps taken in 3 seconds, there must be an equality: *1,2nx = n*, from which:

*õ = 0,83 m*.

If the length of the step depends on the growth of a person, then the second rule is justified only for people of medium height - about 175 cm.

Approximate measurements of medium-sized items can be done as follows. If you pull a rope or stick from the end of an arm stretched out to the opposite shoulder of an adult man - this will be the approximate length of a meter. Another method of approximate measurements of the length of a meter is to lay the distances between the ends of the large and index fingers, arranged as far as possible, along a straight line 6 (Fig. 1a).

Approximate measurements with bare hands can be turned into art: for this you only need to first measure the brush of your hand and firmly memorize the results of measurements.

In the hand, first of all, you need to measure the width of the palm, (Fig. 1b). In an adult, it is approximately 10 cm. Then you need to measure how large the distance between the ends of the middle and index fingers is widened as far as possible (Figure 1c). Further, it is useful to know the length of your index finger, counting from the base of the thumb (Fig. 1d). And, finally, measure the distance between the ends of the thumb and the little finger when they are widely spaced (Figure 1e).

Using this "live scale", you can make approximate measurements of small objects.