US3733718A - Mathematical demonstration device - Google Patents

Abstract

A demonstration device incorporating an open frame mounting an XY plane, an XZ plane and two YZ planes. The planes are normally recessed so as to define a central demonstration area. Alternatively, the XY plane, XZ plane and one YZ plane can be oriented coplanar to each other. Point locating strings and rods, as well as a trigonometric function demonstration attachment in the nature of a compass pivotally mounting radially extending arms are also provided.

Description

United States Patent 1 Hill et al.

MATHEMATICAL DEMONSTRATION DEVICE Inventors: Fred D. Hill; Fred J. Hill; Stanley L.

Hill, all of Hattiesburg, Miss.

Assignee: R. A. Gray, Jr. and Frank D. Montague, Jr., both of l-lattiesburg, Miss., a part interest to each Filed: July 23, 1971 Appl. No.: 165,614

US. Cl. "35/34, 33/1 M Int. Cl. ..G09b 23/04 Field of Search ..35/34, 30, 26, 16;

References Cited UNITED STATES PATENTS 11/1934 l-lamley ..35/34 X 12/1943 Howard.... ..35/34 X 6/1933 McCully ..35/34 FOREIGN PATENTS OR APPLICATIONS 129,875 0/1960 U.S.S.R ..35/30 Primary Examiner-Wm. H. Grieb Attorney-Clarence A. OBrien et a1.

[57] ABSTRACT A demonstration device incorporating an open frame mounting an XY plane, an XZ plane and two YZ planes. The planes are normally recessed so as to define a central demonstration area. Alternatively, the XY plane, XZ plane and one YZ plane can be oriented coplanar to each other. Point locating strings and rods, as well as a trigonometric function demonstration attachment in the nature of a compass pivotally mounting radially extending arms are also provided.

16 Claims, 10 Drawing Figures PATENTEDMYZZ I975 SHEET 2 BF 4 NW QW Fred 0. Hill Fred J Hill Fig.3

Mm 0. m Fred J. Hill .SMn/ey L.

1x1 'ENTOK S PATENTEDMAYZZ'IBYS SHEEI 0F 4 Fred D. Hill Fred J. Hill Stanley L Hill MATHEMATICAL DEMONSTRATION DEVICE The present invention generally relates to a mathematical demonstration device, and is more particularly concerned with a uniquely structured device particularly adopted for visually illustrating spatial phenomena and space-time relationships utilizing X, Y and Z planes.

It is an intention of the invention to provide a demonstration device which, while primarily for use in classroom teaching of mathematics and related subjects, is capable of use in industrial design, architectural display, and related areas. The uniquely constructed device could also find utility in the home when constructed on a scale usable on a table.

Objects of the invention include the provision of a demonstration device which, while structurallysimple, is of a highly unique construction e iiab l' utilization of multiple planes in conjunction witli poiiif locat'ing means which cooperate with the planes for the demonstration of spatial relationships in a clear and straightforward manner.

Basically, the structure of the device includes an upstanding frame mounting an XY plane, two YZ planes and one XZ plane. The planes are normally recessed. However, should it become desirable for any particular purpose, the XY plane, XZ plane and one YZ plane can be oriented coplanar. Point locating rods are utilized in conjunction with the recessed planes, either alone or with locating strings. In addition, a compass attachment, mounted on the XY plane, incorporates radially extending arms which, through slidably adjustable vertical rods, provides a trigonometric demonstration addition to the basic device.

These together with other objects and advantages which will become subsequently apparent reside in the details of construction and operation as more fully hereinafter described and claimed, reference being had to the accompanying drawings forming a part hereof, wherein like numerals refer to like parts throughout, and in which:

FIG. 1 is a perspective view of the demonstration device comprising the instant invention;

FIG. 2 is an enlarged cross-sectional view taken substantially on the plane passing along the line 2-2 in FIG. 1;

FIG. 3 is a top plan view of the device with several of the planes within a coplanar orientation;

FIG. 4 is an enlarged cross-sectional detail through the XY plane in its top mounted position;

FIG. 5 is an enlarged partial elevational view of one of the rods provided to enable an expression of the Z values;

FIG. 6 is an enlarged cross-sectional view taken on the plane passing along line 6-6 in FIG. 5 and illustrating one of the open passages in the rod;

FIG. 7 is a plan view of the device illustrating the trigonometric function attachment mounted on the XY plane;

FIG. 8 is an enlarged cross-sectional view taken substantially on the plane passing along line 8-8 in FIG.

FIG. 9 is a perspective view of the attachment; and

FIG. 10 is an enlarged cross-sectional view taken on a plane generally passing along the line 10-10 in FIG. 9.

being provided along the opposed sides of the base and rising therefrom to an equal heighth with the rear frame 26. The two side frames 28 are interconnected at the rear edges thereof to the rear frame 26 and braced at the forward ends thereof by an appropriate rigid cross brace 30 extending horizontally therebetween and secured to the front vertical bars of the side frames 28.

The XY plane, designated by reference numeral 32, is in the nature of a rectangular panel which is selectively supported in a recessed position on the base 24 or in an elevated position between the upper edges of the side frames 28 on a pair of opposed panel receiving tracks or support angles 34. The panel which forms plane 32, as will be appreciated from FIG. 4 which illustrates the panel in its upper position, is formed of upper and lower space layers 36 with a peripheral edge spacer 38 therebetween.

One of the side frames 28 mounts a fixed YZ plane 40 which is defined by a single layer 42 secured to the four bars which comprises the frame 28, note FIG. 2 and the detail of FIG. 4.

The second YZ plane 44 fits the second side frame 28 and is pivotally mounted, by a pair of hinges 46, to the top bar of the frame 28 for pivotal movement between a vertical position and a horizontal position, note FIG. 2 in particular. The pivotally mounted YZ plane 44 consists of a single panel 48 peripherally reinforced by a frame-like border 50. When horizontally oriented, as illustrated in phantom lines in FIG. 2 and in full lines in FIG. 3, the pivotal YZ plane 44 is braced by a pair of pivotally interconnected and aligned locking arms 52 engaged between the rigidifying border and the mounting frame 28 along each side of the YZ plane 44. Other means for releasably locking the YZ plane 44 in its upwardly swung horizontal position can, of course, be used. As will be best appreciated from FIG. 2, when the YZ plane 44 is horizontally oriented, it is coplanar with the XY plane 32 when this plane 32 is supported in its upper position on the support rails 34.

The XZ plane 54 is constructed and pivotally mounted to the rear frame 26 in the same manner as the pivoted (Z frame 42 and is similarly movable from a vertical position to a horizontal position through supporting hinges 56.

Each of the four planes, preferably formed of a rigid transparent material, is laid out in a grid pattern with each plane, at each line intersection, having an aperture there-through. The apertures in the XY plane 32 extend through both layers 36 and are preferably slightly larger than those in the vertical plane for the snug releasable reception of vertical rods 58. The rods 58 are also provided with spaced markings calibrated to correspond with the grid patterns of the planes. At each calibration or mark, the rod 58 is provided with an aperture 60 therethrough.

In the basic arrangement of FIG. 1, the planes are recessed away from the mid-zero lines designated by the calibrated rod-like members 62 which centrally horizontally span the device from front to rear and from side to side to cross at a point corresponding to the center of the XY plane 32 at which point a vertical zero line indicator 64 is secured. Set up in this manner, both plus and minus values in the X, Y and Z planes can be illustrated. If so desired, the plus and minus signs can be separately color coded. Each of the vertical planes 40, 44 and 54 includes a centrally located vertical brace or thickened portion 66 which defines the zero line thereon and at the same time provides a base to which the corresponding end of one of the horizontal zero indicating members 62 can be affixed. As will be appreciated from the drawings, the front end of the front to rear member 62 is engaged with and supported by the cross brace 30. It is also contemplated that a thicker horizontal zero line be provided at mid-heighth along each of the vertical planes. Likewise, the horizontal XY plane 32 can have the centrally crossing zero lines thereon of a heavier or more visible nature.

Point location, for demonstration purposes, can be effected either by utilization of rods 58, which can be engaged within the holes of the XY plane 32 at the desired location, or by string supported markers, the strings, of a non-elastic nature, being secured at the ends thereof to the two opposed YZ planes 40 and 44. Such strings will preferably also be calibrated to facilitate a proper orientation of the point markers. The apertures or holes in the vertical planes are utilized for securing the point locating strings. As will be appreciated from FIGS. 1 and 2, the holes 60 of the rod 58 can also be used to accommodate string for the locating of an intermediate point between two such rods or a particular line in space between two predetermined points. The rods 58 are, of course, maintained perfectly vertical through an engagement within a pair of vertically aligned holes in the two layers 36 of the XY plane 32.

Noting FIGS. 3 and 4, when the XY plane 32 is in its upper position and the two pivotally mounted planes 44 and 54 swung to their horizontal position, the demonstration device lends itself to two teaching functions in particular. As one example, the apparatus can be tipped so as to stand on its forward open end and thereby present the three coplanar planes to the audience for the demonstration of various functions. It is contemplated that the hinges and pivot lines be readily visible so as to enable an easy distinguishing of the three planes, notwithstanding the coplanar orientation thereof. Further, with the planes in the coplanar orientation, the device is particularly adapted for the demonstration of space-time relationships through sequence photography utilizing motion pictures. In other words, the effect of variable time units can shown whether constant, straight line or exponential change. Mathematical points will be demonstrated by suitable discs shaded to photograph as spheres. Current points in time will have the greatest photographic contrast and past points in time, from present to most past, will have progressively less contract to give the illustion of after glow. This, ofcourse, will be done by solving each point in time, plotting the point with a disc marker and exposing a few film frames, with this being repeated for each point solution until the sequence is completed.

Incidentally, it should also be appreciated that the XY plane, being removable, can be used for one, two or three dimensional demonstrations.

FIGS. 7 through 10 illustrate an adjunct or attachment for the basic demonstration device 12. This attachment, designated by reference numeral 67, is particularly adopted for the demonstration of trigonometric functions. The attachment 67 includes a circular compass-like base 68 calibrated peripherally thereabout and pivotally mounting a pair of elongated radials or arms 70, also calibrated along the length thereof. Each of the arms/70 mounts one or more vertically extending calibrated rods 72, corresponding to the previously described rods 58, and similarly incorporating string or wire mounting apertures therethrough at predetermined point s therealong. The actual engagement of each rod 72 yvith the arm 70 is through a sliding bracket 74 which is movable along the arm 70 and selectively alignable with the calibrations thereon. This sliding mount rigidly receives and vertically retains the corresponding rod 72. As indicated, any appropriate number of rods and mounts can be provided on each of the arms 70. In order to insure a proper location of the attachment 67, such being used on the XY plane 32 in the recessed or minus orientation thereof as illustrated in FIG. 1, the base 68 is provided with a pair of depending locating lugs or pins 76 which engage within the apertures of at least the top layer 36 of the plane 32. The spaced lugs 76, in addition to properly orientating the base 68, provide for a stabilization thereof as the arms 70 are adjusted.

From the foregoing, it will be appreciated that a demonstration device of significant uniqueness has been devised, the device incorporating a versatility and practicality heretofore unknown in mathematical demonstration equipment. It will be readily appreciated that the adaptability of the device to demonstration procedures is practically without limit.

The foregoing is considered as illustrative only of the principles of the invention. Further, since numerous modifications and changes will readily occur to those skilled in the art, it is not desired to limit the invention to the exact construction and operation shown and described, and accordingly, all suitable modifications and equivalents may be resorted to, falling within the scope of the invention.

What is claimed as new is as follows:

1. A mathematical demonstration device comprising a plurality of point intersecting zero line indicators, each indicating a zero line between plus and minus values to the opposite side thereof, means for associating a physical plane with each zero line spaced to one side thereof, means for selectively positioning the plane associated with one of said zero line indicators to the opposite side thereof, the zero line indicators corresponding to X, Y and Z coordinate axes, said planes comprising an XY plane, an XZ plane, and a YZ plane, the selectively positionable plane constituting the XY plane, and means normally positioning said XZ plane and said YZ plane perpendicular to said XY plane.

2. The device of claim 1 wherein said last mentioned means enables a selective orientation of said XZ plane and said YZ plane coplanar with said XY plane.

3. The device of claim 2 including a supporting framework for said indicators and planes, said framework including opposed upstanding sides and an upstanding back, said XY plane being mounted between said sides and forward of said back, said means positioning said XZ plane pivotally suspending said XZ plane from said upstanding back, said means positioning said YZ plane pivotally suspending said YZ plane from one of said upstanding sides.

4. The device of claim 3 including a second YZ plane fixedly mounted on the second side.

5. The device of claim 4 wherein each plane is provided with a grid pattern, thereon.

6. The device of claim 5 wherein said XY plane includes an aperture therethr ough at each point of intersection on the grid pattern; and point locating rods selectively receivable in one or more of said apertures for vertical projection above the XY plane to define a Z point. f

7. The device of claim 6 herein said YZ planes also include apertures therethrough at the intersection points on the grid pattern, aid apertures being utilized in the mounting of point orientating strings between said YZ planes.

8. The device of claim 7 including a trigonometric function demonstrating at'tachment, said attachment including a circular base, ,means for positioning said base on said XY plane, a pair of radially extending arms pivotally mounted on said base for angular adjustment thereabout, and at least one vertical rod slidably mounted on each arm for longitudinal adjustment therealong.

9. A mathematical demonstration device comprising a supporting framework, said supporting framework including a pair of laterally spaced vertically orientated side frames, said frames having a forward end and a rear end, a vertically orientated back frame extending between and interconnecting the rear ends of said side frames, said side frames including lower edges and upper edges, an XY plane forming panel positioned between and supported at the lower edges of said side frames, an XZ plane defining panel mounted on said back frame, and a YZ plane defining panelmounted on one of said side frames, both of said latter panels rising perpendicularly from the corresponding edges of the first mentioned panel.

10. The device of claim 9 including a YZ plane defining panel mounted on said second side frame in parallel opposed relation to the first YZ plane defining panel.

11. The device of claim 10 wherein said side frames include means along the upper edges thereof for selectively receiving and supporting said XY plane defining panel.

12. The device of claim 11 wherein said XZ plane defining panel and the first YZ plane defining panel are respectively mounted on the associated back and side frames for pivotal movement between a vertical position and an upwardly swung horizontal position so as to be orientated substantiallycoplanar with the XY plane defining panel in the upper supported position thereof.

13. The device of claim 10 including a zero line indicatorextending perpendicularly from each plane at the center thereof for a central intersection thereof within the framework.

14. The device of claim 13 wherein each zero line indicator is in the nature of an elongated rod calibrated along the length thereof and provided with apertures therethrough at the calibrations.

15. The device of claim 10 wherein each plane panel has a grid defined thereon, the grid of at least the XY plane defining panel having a series of vertical apertures therethrough at each grid line intersection, said apertures selectively receiving point locating upstanding rods.

16. The device of claim 10 including a trigonometric function demonstrating attachment, said attachment including a circular base, means for positioning said base on said XY plane, a pair of radially extending arms pivotally mounted on said base for angular adjustment thereabout, and at least one vertical rod slidably mounted on each arm for longitudinal adjustment therealong.

Claims (15)

1. A mathematical demonstration device comprising a plurality of point intersecting zero line indicators, each indicating a zero line between plus and minus values to the opposite side thereof, means for associating a physical plane with each zero line spaced to one side thereof, means for selectively positioning the plane associated with one of said zero line indicators to the opposite side thereof, the zero line indicators corresponding to X, Y and Z coordinate axes, said planes comprising an XY plane, an XZ plane, and a YZ plane, the selectively positionable plane constituting the XY plane, and means normally positioning said XZ plane and said YZ plane perpendicular to said XY plane.

2. The device of claim 1 wherein said last mentioned means enables a selective orientation of said XZ plane and said YZ plane coplanar with said XY plane.

3. The device of claim 2 including a supporting framework for said indicators and planes, said framework including opposed upstanding sides and an upstanding back, said XY plane being mounted between said sides and forward of said back, said means positioning said XZ plane pivotally suspending said XZ plane from said upstanding back, said means positioning said YZ plane pivotally suspending said YZ plane from one of said upstanding sides.

4. The device of claim 3 including a second YZ plane fixedly mounted on the second side.

5. The device of claim 4 wherein each plane is provided with a grid pattern thereon.

6. The device of claim 5 wherein said XY plane includes an aperture therethrough at each point of intersection on the grid pattern, and point locating rods selectively receivable in one or more of said apertures for vertical projection above the XY plane to define a Z point.

7. The device of claim 6 wherein said YZ planes also include apertures therethrough at the intersection points on the grid pattern, said apertures being utilized in the mounting of point orientating strings between said YZ planes.

8. The device of claim 7 including a trigonometric function demonstrating attachment, said attachment including a circular base, means for positioning said base on said XY plane, a pair of radially extending arms pivotally mounted on said base for angular adjustment thereabout, and at least one vertical rod slidably mounted on each arm for longitudinal adjustment therealong. 9. A mathematical demonstration device comprising a supporting framework, said supporting framework including a pair of laterally spaced vertically orientated side frames, said frames having a forward end and a rear end, a vertically orientated back frame extending between and interconnecting the rear ends of said side frames, said side frames including lower edges and upper edges, an XY plane forming panel positioned between and supported at the lower edges of said side frames, an XZ plane defining panel mounted on said back frame, and a YZ plane defining panel mounted on one of said side frames, both of said latter panels rising perpendicularly from the corresponding edges of the first mentioned panel.

10. The device of claim 9 including a YZ plane defining panel mounted on said second side frame in parallel opposed relation to the first YZ plane defining panel.

11. The device of claim 10 wherein said side frames include means along the upper edges thereof for selectively receiving and supporting said XY plane defining panel.

12. The device of claim 11 wherein said XZ plane defining panel and the first YZ plane defining panel are respectively mounted on the associated back and side frames for pivotal movement between a vertical position and an upwardly swung horizontal position so as to be orientated substantially coplanar with the XY plane defining panel in the upper supported position thereof.

13. The device of claim 10 including a zero line indicator extending perpendicularly from each plane at the center thereof for a central intersection thereof within the framework.

14. The device of claim 13 wherein each zero line indicator is in the nature of an elongated rod calibrated along the length thereof and provided with apertures therethrough at the calibrations.

15. The device of claim 10 wherein each plane panel has a grid defined thereon, the grid of at least the XY plane defining panel having a series of vertical apertures therethrough at each grid line intersection, said apertures selectively receiving point locating upstanding rods.

16. The device of claim 10 including a trigonometric function demonstrating attachment, said attachment including a circular base, means for positioning said base on said XY plane, a pair of radially extending arms pivotally mounted on said base for angular adjustment thereabout, and at least one vertical rod slidably mounted on each arm for longitudinal adjustment therealong.

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