WO1987000668A1

WO1987000668A1 - Educational visual aid particularly for demonstration in solid geometry

Info

Publication number: WO1987000668A1
Application number: PCT/HU1986/000042
Authority: WO
Inventors: István LÉNÁRT
Original assignee: Orszagos Tanszergyarto Es Ertekesito^" Vallalat
Current assignee: Orszagos Tanszergyarto Es Ertekesito^" Vallalat
Priority date: 1985-07-25
Filing date: 1986-07-15
Publication date: 1987-01-29
Anticipated expiration: 1988-01-25
Also published as: IL79441A; DD255022A5; HU192681B; IN163289B; EP0267911A1; DK149187A; ES2000761A6; DK149187D0; JPS63501175A; KR880700376A; IL79441A0; AU6139586A

Abstract

An educational visual aid, particularly for reproducing and studying various configurations and problems in solid geometry, consisting of a ball (1), with a surface suitable for being drawn or written on, and made of transparent or translucent or some other king of material; a support (2) to hold the ball in position; and a spherical ruler, adapted to the ball surface in any position. The spherical ruler is constructed from a hoop (3), a saddle (4) perpendicular to the hoop (3), and one or more handles (5). The support (2) is a torus under the ball (1), in order to hold the ball (1) firmly in any position on the torus (2). The tracer edges of the hoop (3) and the saddle (4) lie on arcs of great circles. Between the hoop (3) and the saddle (4) of the spherical ruler, a joint (6) is inserted, perpendicular to both of them, and also adapted to the surface of the ball (1). On the inner side of the joint (6) there are two tips of contact (10, 11), appropriately spaced; on the outer side of the joint (6) there is a long-shaped, rounded supporting nose (7). The saddle (4) has a thin and solid handle plate (5) on its side preferably adjacent to the joint (6), with two rounded tips (5a, 5b) on the top of the plate (5).

Description

EDUCATIONAL VISUAL AID PARTICULARLY FOR DEMONSTRATION IN SOLID GEOMETRY

Field of the invention

The invention relates to an educational visual aid, particularly for demonstration in solid geometry, consisting of a ball, a support under the ball, and a spherical ruler, adapted to the ball surface, the ball has a surface suitable for being drawn and written on, the spherical ruler being constructed from a hoop, a saddle perpendicular to the hoop, and at least one handle, suitable for being placed onto the ball sur¬ face in any position, the support being a torus under the ball to hold it in any position, and with the tracer edges of the hoop and the saddle lying on arcs of great circles of the ball.

Background of the invention

Many levels of science, technology and education need a satisfactory knowledge of solid geometry. Descrip- tive geometry, axonometric projection or technical drawings often deal with solids of three dimensions, projected onto the planar surface of the draft paper, with the help of drawing-boards, straight edges, French curves, compasses, stencils etc. These de- vices are appropriate for the representation of such one- o r two-dimensional forms as straight lines, cir¬ cles, conic sections or plane curves. The representa¬ tion of three-dimensional forms, however, requires a very advanced stage of space perception. This percep- tion can and should be developed and trained by due educational aids.

Such an aid is described in the HU-A 185 190, mainly for representing and studying various concepts, con¬ figurations and problems in spherical and solid ge¬ ometry, and facilitating the demonstration of compli¬ cated three-dimensional notions. This aid consists of three separate parts: a rigid ball, preferably made of plastic, with a smooth and closed surface for being drawn and written on; a spherical ruler, constructed from a hoop and a saddle, perpendicular to the hoop, in such a manner that the ruler is pre¬ cisely adapted to the surface of the ball in any po- sition and at last, a support under the ball to hold it firmly in any position on this support.

The above-mentioned device has been tested and exam¬ ined in various kindergartens, elementary and second- ary schools, colleges, universities, educational institutions and even video recordings, as a toy and a visual aid. It has proved useful, versatile and amusing in a wide variety of subjects, as mathematics, geometry, geography, drawing, astronomy, crystallog- raphy etc.

However, these tests have also revealed serious defi¬ ciencies of the set that delayed its general use by various ages and interests. Small children, in partic- ular, had problems with the safe and comfortable use of the seto The main deficiencies are as follows:

- The impact resistance of the spherical ruler is often insufficient. Both the saddle and the handle on it can be deformed or even broken in use or transport. - In some cases, the supporting torus is inadequate to hold the ball firmly in position. Schoolboys and girls, wrapped up in their work on the ball, may push it out of the torus, particularly on the skew surfaces of some school-desks. This may lead to frequent and inconveniently noisy droppings, even crackings of the balls in classroom use.

- With the ball on the torus, and the spherical ruler on the ball, we can easily draw arcs up to 180°, either by the tracer edge of the hoop or the saddle. Arcs equal to or longer than 180 , or even full great circles are, however, a nuisance to draw, since the marker has to be pressed to the surface of the ball with its tip upwards, and the ball and the ruler simultaneously and cautiously turned round while drawing. This is far from being an easy task for adults, let alone children. Since the arcs longer than 180 or full great circles are frequently encountered in various problems and tasks, this difficulty consid¬ erably interferes with the widespread use of the set.

- As with squared or lined paper, it can be very help¬ ful to trace the ball surface with various graphs or figures. For example, geographical graticule can be of good use in mathematics or geography,' or, a blank map of the Earth with the contours of continents in geography, biology, world history etc. Now, marking the ball surface so traced and removing the mark with the usual solvents or detergents, we may remove the trace graph, too. It is very clumsy, and, with home¬ made aids, often unaccomplishable, to trace the graph again and again. Summary of the Invention

The main object of the present invention lies in the disposal of the before-mentioned disadvantages. In order to attain this object following improvements of the prior art have been carried out;

- Between the hoop and the saddle of the spherical ruler, a joint is put perpendicular to both of them, and also adapted to the ball surface. The imaginary bisector of this joint lies on a great circle of the ball. Therefore, its real boundaries do not follow arcs of great circles.

Two small lenticular tips are formed on the inner side of this joint serving for points of contact with the ball surface.

- On the outer side of t he joint, nearer to the hoop than the saddle a long-shaped, rounded supporting nose is formed out.

- The handle is a thin and solid plate on the saddle, adjacent to the joint, with rounded tips and a V- shaped excision on its top.

With these characteristics of the set, the two tips on the inner side of the joint keep the surfaces of the ball and the joint from being in close contact, and, in this way, they prevent drawings or figures on the ball surface from being smeared.

Turning the spherical ruler with its hoop upwards, and putting it in this position on the planar surface of a table, a stable and safe three-point support can be obtained, one point being the nose on the joint, and the other ones the two rounded tips of the handle on both ends of the V-shaped excision. Now, putting the ball into the spherical ruler, the ruler gives a firm foundation and support of the ball, yet permits it to be freely and comfortably revolved or lifted up by any axes of the ball. In addition, we can easily and precisely strike arcs of arbitrary length or full great circles, or measure angles or great circle distances along the tracer edge of the hoop in this position. The two planes of the three- point support and the great circle of the tracer edge of the hoop have a solid angle of 25 , an ideal situ- ation for drawing and measuring on the ball surface. Even for small children, this position of the ruler gives a firm and safe support of the ball while drawing The ruler stably supports the ball on skew-boarded desks, with a bedding angle up to 15°.

The inserted joint remarkably increases the impact resistance and stability of the ruler. With the ruler supporting the ball, we can lean on the ball without causing any deformation or breaking of the ruler. In like manner, the joint increases the resistance of the ruler to overstrain due to rough handling or transport.

Similarly, the above-mentioned design of the handle is to the advantage of the set in several ways. The thin, solid and not too raised plate of the handle satisfac¬ torily tolerates overstrain. Its two rounded tips and the nose on the joint give a steady support of the ball. Also, this design of the handle and the ruler significantly reduces cost of production, since it needs only one casting mould to manufacture the ruler, in contrast with the two moulds of the old version.

In order to settle the problem of the graphs or fig¬ ures traced on the ball surface, we construct two hemispheres with flanges on their equators, and stick them together to obtain a closed ball. Now, before sticking them, we trace the inner sides of the hemi¬ spheres with due graphs or figures. If we made the hemispheres of transparent or translucent plastic, then, sticking them together, the graphs or figures on their inner sides are distinctly visible, yet out of touch for solvents and detergents used for the re¬ moval of markings on the outer surface of the ball. These traces can be of great help in the employment of the set in various subjects and topics.

Brief Description of the Drawings

Further features of the invention will now be partic- ularly described by way of example with reference to the accompanying drawings in which:

Figure 1 is a side elevation view of the edu¬ cational visual aid, consisting of the ball, the spherical ruler and the support, partly in section, and

Figure 2 is a fragmentary view of the set from another side.

Description of the Preferred Embodiment

Figures 1 and 2 show a ball 1 made of transparent plastic, consisting of an upper hemisphere la, and a lower hemisphere lb, and placed onto a support 2 in an arbitrary position.. This support 2 is a ring-shaped torus, preferably made of the same kind of plastic as the ball 1, and also an important and intriguing geometrical surface for drawing, playing and study¬ ing.

A spherical ruler, consisting of a hoop 3, a saddle 4 and a joint 6, is placed in an arbitrary position onto the surface of the ball 1. As it can be seen on Figure 1, the tracer edges of the hoop 3 and the sad- die 4 lie on arcs of great circles of the ball 1. Figure 2 shows the bisector of the joint 5 lying on the arc of a great circle. This same bisector halves a long-shaped, rounded supporting nose 7, on the outer side of the joint 5, near to the hoop 3, serving as a point of support of the spherical ruler. The hoop 3 has a chamfer 3a and a scale division 8 by its tracer edge, whereas the saddle 4 has a scale division 9 by its tracer edge.

In this embodiment the tips 10 and 11 are long-shaped, but round or other versions are also acceptable. Their heights are about 0,5 mm, in order to prevent the surfaces of the ball 1 and the ruler from close contact and, in this way, smearing of drawings on the surface of the ball 1.

The angle ^~ , shown on Figure 1, and preferably about of 5-6°, serves for preventing the tracer edge of the hoop 3 from close contact with the surface of the ball 1. In like manner, the angle , shown on Figure 1, also about 5 - 6 , has the same function as angle <= , in connection with the tracer edge of the saddle 4 and the surface of the ball 1.

As we can see on Figure 2, the thin and solid plate of the handle 5 has two rounded tips 5a and 5b at its top, in order to obtain two points of support for the spherical ruler. Figure 1 shows that the handle plate 5 lies on the side o the saddle 4 adjacent to the joint 6, as to constitute a firm and safe three-point support in the plane of the triangle determined by the tips 5a and 5b and the nose 7. This plane includes a solid angle preferably about 25 with the plane de¬ termined by the tracing edge of the hoop 3.

In the present invention, tha ball can be supported either by the torus or the spherical ruler, corre¬ sponding to the nature of the drawing or problem to be solved. The torus, for example, is very appropriate for supporting the ball while drawing short arcs, or figures not involving great circles at all. According to the tests, the ratio of the problems solved with the torus or the ruler supporting the ball is about 50 - 50 percent. However, checking a detail of the drawing or displaying the finished work, this ratio is about 90 - 10 percent to the torus. Both of them promoting accurate and comfortable drawing on the ball surface, these two ways of support are, in fact, complementary to each other in use.

Claims

1. An educational visual aid, particularly for repro¬ ducing and studying configurations and problems in solid geometry, consisting of a ball, a support under the ball, and a spherical ruler, adapted to the ball surface, the ball has a surface suitable for being drawn and written on, the spherical ruler being con¬ structed from a hoop, a saddle perpendicular to the hoop, and at least one handle, suitable for being placed onto the ball surface in any position, the support being a torus under the ball to hold it in any position, and with the tracer edges of the hoop and the saddle lying on arcs of great circles of the ball, c h a r a c t e r i z e d by an inserted joint (5) between the hoop (3) and the saddle (4) of the spherical ruler, perpendicular to both of them, and adapted to the surface of the ball (1), with two tips (10, 11) appropriately spaced on the inner side of the joint (5), and a long-shaped, rounded supporting nose (7) on the outer side of the joint (5), and a thin and solid handle plate (5) with rounded tips (5a, 5b), placed on the saddle (4).

2. Educational visual aid as claimed in Claim 1, c h a r a c t e r i z e d in that the transparent ball (1) is constructed from two hemispheres (la, lb) by sticking them together, and with graphs or figures on the inner sides of the hemispheres (la, lb), according to the purposes of the given version of the aid, these graphs or figures being traced on the inner sides by the help of some printing or photochemical or other processes, before sticking the hemispheres (la, lb) together, in order to obtain a closed ball (1)₀