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WONDER WHEEL OR "PERPETUUM MOBILE"?
- The geometry -

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The circle in the geometry is a simple figure with well-known formulas for finding the area and circumference of a circle. The wording sounds like figure, whose distance from the center to any point on the circumference are equal. This distance is indicated by a radius "R" and is the starting point for building a circle. After determining the number of "Pi", this figure became clearer and clearer. The correct mathematical perfection of the circle attracts, but also limits its use.

Offer each figure will call around and try to prove that it is a circle. To establish a family relationship, first change the very perception of the circle by removing its component radius. And most importantly the wording of this figure Radius diametrically. Circle called the figure, in which all the lines intersect at the center of its equal. To change and find a formula area Radius diametrically. equal to the area of ​​a circle (circumference times the diameter) and divide by four. The word perimeter is no coincidence, because this formula gives the area and the other
figure-square. The perimeter of the circumference and the sum of all sides of the square. For the diameter of the take and the length of the square. The area of ​​the circle and the square can be linked and interest. area of ​​a circle is 78.5% of the area of ​​a square that fits in the circle. But the basic for further constructions, this formulation avoids ever radius.

To create a new circle will need a simple tool geometry shown in Fig.

geometric tools

It is a transparent bar made of organic glass, in the form of a high line. In the middle of a through longitudinal hole with two sliding pencils, which are easy to lock the required points. Between them, and sliding freely, allowing the pin to the device to press the instrument to the drawing sheet. In addition to using a tool like a ruler, it may be used as a compass. Using the pin and a pencil (or two but equidistant from it) get a compass. But its main application to use as a "mirror", is as follows.

Take one of simple shapes - square and find the intersection of the diagonals set the center pin on it and we fix pencils in diagonal corners. Then, holding the pin, hold a pencil around the perimeter of the square and get it display another pencil.

See the photo of building example

Likewise, using this tool, that is, taking the maximum straight line intersecting at the center of the figure we get interesting results.

Similar figures, unlike their mathematical "relatives", enjoyed nature, creating different kinds of flora and fauna.

Based on the return, taking some types of organisms, or plants can be replenished arsenal of geometric shapes. But where are the mechanics and the circle? The circle is the only figure not giving display, or more precisely they are fully reported - a circle with his reflection. represented by the figure of the same is aligned with its display, since it is also spinning. To eliminate confusion in the future, we will be called the normal circle - radius (or dead) around. Mathematically, for single differ from this range, presents the figure should be called without radius circle.

To simplify the demonstration of its creation, we take as a basis Radius circle.

Draw a horizontal line "AB" crossing the center "O" Fig.1. From this point, we drop the perpendicular and choose any point "C" on it. By installing this (call it point display) compasses point, join the points A and B, Figure 2. Now, using our tools - a mirror, get a map of the curve "AB" through the center of the "O" shutting it (Figure 3.). So we got the desired figuru- circle with a diameter equal to the circle from which began the work.

A similar figure can obtain a three-dimensional display of radius-circle on
two-dimensional plane, welcome all well-known artists.

The point "C" can be selected, and at the intersection of the perpendicular with the circumference, and it is possible for a circle. The maximum distance from the center point "C" is the diameter of the distance.

From the center of the circle radius-drop the perpendicular of the circle, take a compass distance "AB" and out of cars A or B and the note on the perpendicular point "C". Radius obtain the best possible terms (Figure 1). With increasing distance the circle moves in another figure (Figure 2).

At maximum range dot display "C" appears on the circumference of the circle of radius-free as we took the circular diameter of the circle for the distance to build without radius-circle (Figure 1). Connecting points A and B of the compass point "C" appears in the point "E" with the distance from a point "C" equal to the distance AB and BC. But the radius can not be equal to the diameter. Moreover, a line AB (Figure 1) and divides the circle Radius without middle, but not on the area and the number of points constituting a circle.

Paradoxically, since the second half of the circumference of the VA has a much greater length than AB. Being a closed figure, have to argue that point at half BA greater in length than the opposite half of them on the AB.

To argue about the equality of the area of a square, with a side equal to the diameter of a circle with an area of no radius-circle, and the like on a par with the perimeter of the unknown circumference. A simple computer program for geometric constructions finding areas and perimeters of the circumference was not found.

We assume the existence of proven without radius-circle. Let us examine this in mathematical walks and disputes, and practically prove that it is still a circle, or rather the ability to rotate the wheel.

print version
Author: Elman Jamilov
PS material is protected.
Publication date 02.25.2004gg

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