OBSERVATION DEVICE

Abstract: A three-dimensional observation device for observation of mathematical, physical and other figures, dimensions or properties, comprising several nesting ball shells (a, b, c...), which can be opened separately. Each ball shell (a, b, c...) is formed of six spherical caps (1) tangent to one another and of eight triangular ball surface sections (2), between caps (1) all of them independent parts while the thickness of the shell section formed by them is R - R 2ROOT 2.

Description: OBSERVATION DEVICE The invention relates to an observations device in accordance with patent claim 1, by means of which it is possible to illustrate figures, ratios and angles of plane geometry and stereometry etc as well as physical properties, for instance the travel of light. Different observation objects are known which illustrate a ball, cube, pyramid, cones, plane figures etc. Further, objects similar to the above mentioned ones are known, which are split- ted into puzzle type pieces for doing layouts and compositions. In addition, a cleavable ball is known, inside of which a smaller cleavable ball is nesting a.s.o. However, with the known single observation objects one has not achieved a very versatile result and by means of them one can¬ not produce an adequate picture of the correlations and ratios of figures and forms. By means of an observation device according to this invention anunexpected improvement is reached with respect to former solutions. The invention is characterized in what is presented in the patent claims. By means of the invention it is possible to visualize, three- dimensionally^, numerous correlations between a ball, circle, cube, triangle etc. By means of nesting ball shells the serial nature of figures can be visualized as well as the reciprocal movements of the shells. In using transparent material in the parts, it is possible to observe, among other, a bigger variety of physical phenomenons, as for instance the travel of light. Thanks to the great number of independent shell parts the device can be observed even when taken partly into pieces, whereat the observation can be easily extended to several shell layers simultaneously. It is also possible to make the device a three-dimensional picture that can be observed on a computer screen and thereby delete or insert wanted parts. In the following the invention is disclosed with reference to the enclosed drawing, where Fig. 1 shows a side view of the observation device. Fig. 2 shows a side view of the observation device, partly taken into pieces. Fig. 3 shows a spherical cap part viewed from different angles. Fig. 4 shows a triangular part of a ball shell viewed from different angles. Figure 1 is an observation device according to the invention, the shape of which is a ball. The ball surface is formed of two different parts la and 2a. The configuration of part la is a spherical cap and thus its sphere is a circle and the con¬ figuration of part 2a is a triangle with uniform sides curved to the inside. The ball radius is Ra. The sphere line of part la is visible to the outside in form of a circle with a radius of Ra/ Y?. Figure 1 is a side view exactly from the spherical cap la direction, whereat one can observe that the complete ball surface is formed of six spherical caps la and eight triangular parts 2a. When such a ratio and parts are chosen, the outcome is a ball as per figure 1 viewed from the outside. Parts la and 2a can be taken into parts. Figure 2 shows a ball from which parts la and 2a have been taken off and the next ball shell has become visible. The radius of ball shell b is Rb, which is Ra/ ∑. Accordingly, the radius of the inner ball is equal to the radius of the cap circle of the former ball surface. With this choice the outcome is a ball shell thickness of Ra - Ra/ Again the ball shell is formed of part lb and 2b. The radius of the circle of spherical cap lb is equal to the radius Ra of ball a. Furthermore, this is equal to the radius of ball cell c. The radius of the nesting balls a,b,c,d... etc is reached in dividing it by 2 1 . Naturally, the difference of successive radius is always the thickness of the shell. Each ball shell can freely rotate inside the former ball and loose structural elements can be deleted. Dashed lines in the figure show a base 3 supporting the device. Figure 3 shows a cap section lb illustrated from 3 different angles. Its circle has a radius of Ra/2 = Re. Into its sphere circle a square with a side length of Rb is placed, which is also equal to the radius of curvature of spherical cap lb. A broken pyramid runs from the square to the centre of the radius of curvature. The pyramid is broken by a ball surface illu¬ strated by radius Re running from the center of the radius of curvature. In this way the ball shell is formed at the spherical cap. Figure 4 is a triangular section of ball surface 2b which is used with the same shell b together with the section shown in figure 3. Section 2b covers a triangel with uniform sides, the dimension of which is Rb and which takes its position in the device against side Rb of the square of cap section lb. Section 2b in figure 4A is illustrated with the concave side upwards. The radius of curvature of the concave section is Re. A broken triangel runs from the triangel points according to figure c, the cone of which is broken by the radius of curvature Re. Section 2b in figure 4B is illustrated with the convex side upwards. The diagonal lateral surfaces illustrated in the figure are counter faces of the segments of spherical cap lb. In figure 4C the section is viewed from one end, whereat the thickness of the section in the ball shell is determined by the radius of curvature Rb and Re. All parts 1 among themselves and parts 2 among themselves are uniform and in shifting over from one shell to another their ratio of size is ?- The geometrical properties of the parts can be mathematically derived when, at first, an unexpected choice is made to compose a ball shell of six cap shells tangent to each other, the radius of whose circle is the radius of the ball R/ Y?, and of eight trianglular shells between them when the thickness of shell has been determined as R - R/ V?. Advantageously, the device is made of transparent material. strongly translucent, if possible, so that refractions and reflections of light can be studied. The parts can also be magnetic on a shell in order to retain their spherical form better. As a three-dimensional device the unit is excellent means for observation of stereometry when the shells remain immobile or while rotating them into different positions with regard to each other. Generally, a small gap must be made bet¬ ween shells so that they can rotate among themselves and even the outermost shell parts can be accurately connected to each other. Up to a certain volume the core of the device can be an open ball, whereby a source of light has been placed in it to illuminate outwards refractingly and reflectingly through the transparent shell parts. With shells in different colors it is also possile to observe color combinations. It is also possible to reach unexpected structures by dividing the ball shell in some other ways, for instance in dividing the shell instead of the circular cap into pentagular, hexagonal or polygonal caps or combinations of the same and determining the thickness of each nesting shell by variables obtainable from the polygon. By means of a computer and a monitor connected to it, the observation device can be watched on the screen in using a three-dimensional program in order to represent the device from different angles and as a complete or partly assembled version and also so that the configurations of the innermost shells are visible. Numerous modifications of the invention are possible within the limits of the inventional concept determined in the enclosed patent claims.

Claims: PATENT CLAIMS 1. A three-dimensional observation device or a similar device representable as a three-dimensional picture for observation of mathematical, physical and other figures, dimensions or proper¬ ties, comprising several nesting ball shells (a,b,c...), which can be separately added or removed, characterized in that each ball shell (a,b,c...) is composed of six spherical caps (1) tangent to one another and of eight triangular ball surface sections (2) between caps (1), all of them being independent parts whilw the thickness of the shell section formed by them is R - R/ V?. 2. An observation device according to patent claim 1 charac¬ terized in that the ratio (Ra:Rb), (Rb:Rc),... of the outer diameters of the nesting shell balls is VF. 3. An observation device according to patent claims 1 and 2 characterized in that the interface of spherical cap (1) and triangular part (2) is the side of a square placed inside the cap circle of spherical cap (1). 4. An observation device according to any of the former patent claims 1 - 3 characterized in that the shell part (l),(2) is of transparent material. 5. An observation device according to any of the former patent claims 1 - 4 characterized in that the shell part (1),(2) is of magnetic material. 6. An observation device according to any of the former patent claims 1 - 5 characterized in that each shell part (a,b,c...) is freely rotating inside the former shell.

Inventors: LEIVISKAE SEPPO ILMARI, LEIVISKAE, SEPPO, ILMARI
Applicants: LEIVISKAE SEPPO ILMARI, LEIVISKAE, SEPPO, ILMARI
Application year: 1995
Main classification: G09B23
IPC codes: G09B23