US3475030A - Geometric puzzle game - Google Patents

Description

Oct. 2 8, 1969 I T..C. PRESCOTT 3,475,030

GEOMETRIC PUZZLE GAME Filed March 21, 1968 3 Sheets-Sheet 1 I L B INYENT' OR 7720/1705 C. Prescofi Oct. 28, 1969 T. c. PRESCOTT v 3,475,030

GEOMETRIC PUZZLE GAME Filed March 21, 1968 s sheets-sheet :5

IN VENTOR.

7/70/7142}; C lqescoff United States Patent 3,475,030 GEOMETRIC PUZZLE GAME Thomas C. Prescott, 88 E. 3rd St., New York, N.Y. 10003 Filed Mar. 21, 1968, Ser. No. 714,827 Int. Cl. A63f 9/08 US. Cl. 273-156 6 Claims ABSTRACT OF THE DISCLOSURE A geometric puzzle game is described which has a plurality of fiat playing pieces. Each piece has four or more edges which are other than straight. Concave and convex edges alternate with each other. A concave or convex edge of each piece interfits with a convex or concave edge of another piece. The edges of the pieces are constructed from a template having slots radiating from an off-center point of an equilateral polygon. Edges of the pieces have different lengths and different curvature. Arrays of pieces have unusual shapes with perimeters having alternative concave and convex portions.

This invention relates to the art of amusement devices and more particularly concerns a new geometric puzzle. Geometric puzzles heretofore known have been of two general types. One type is the jig-saw puzzle in which the playing pieces have irregular and random shapes which can fit together in only one predetermined way. The interfitted pieces when properly assembled, define a picture whose periphery is rectangular. US. Patent No. 1,787,- 473, describes a puzzle of this general type. In a second type the game pieces have one or more straight sides. The pieces can be fitted together at their straight sides to define architectural, sculptural, or pictorial subjects. US. Patent No. 1,457,112 describes a puzzle of this general type.

The present invention concerns still another type of puzzle. The several puzzle pieces all have four or more edges alternately concave and convex, or other than straight; that is, one pair of opposite edges may be concave and the other pair of opposite edges may be convex. The pieces are constructed from a template laid out according to a certain geometric plan. When properly interfitted, the assembly of pieces defines no predetermined design, picture or construction. In the simplest way of assembly, the player seeks by trial and error to interfit all the pieces to form any continuous flat array. In a more difficult form of play, the player seeks to form a symmetrical or partially symmetrical array. The actual number of possible arrays the player can assemble will be almost unlimited, depending on the number of pieces provided in the puzzle. In any case, the completed puzzle is never square, rectangular or circular, or any other regular polygonal or geometrical shape, and almost never does it define a recognizable architectural, sculptural, pictorial or other common subject. The arrays which do result are all unusual, original and abstract in character so that the player retains his interest to play over and over again. This contrasts with conventional puzzles, such as jig-saw puzzles, where the player loses interest once he has solved the puzzle.

It is therefore one object of the invention to provide a geometric puzzle having a plurality of fiat playing pieces which interfit at their edges with each other, each piece having four curved edges, with adjacent edges alternately concave and convex, so that the convex edges of some pieces interfit with the concave edges of other pieces.

A further object, is to provide a geometric puzzle as described, wherein the puzzle pieces are constructed from a template, laid out according to a predetermined plan Patented Oct. 28, 1969 based on an equilateral polygon, such as an equilateral triangle, square, rhombus or hexagon.

For further comprehension of the invention, and of the objects and advantages thereof, reference will be had to the following description and accompanying drawings and to the appended claims in which the various novel features of the invention are more particularly set forth.

In the accompanying drawings, forming a material part of this disclosure:

FIG. 1 is an oblique plan view of a geometric puzzle embodying the invention, assembled in one possible array.

FIG. 2 is an oblique plan view of a template employed to laying out construction pieces of the puzzle of FIG. 1.

FIG. 3A through FIG. 3F are oblique plan views of the individual pieces of the puzzle of FIG. 1.

FIG. 4 is a geometric diagram employed in explaining how a template is laid out.

FIGS. 5 and 6 are plan views of other templates which can be used in constructing other puzzles according to the invention.

FIG. 7 is an oblique plan view of a playing board which can be used with geometric puzzle pieces according to the invention.

For purposes of explanation and for the sake of simplicity, the invention will be described in connection with a puzzle having six pieces, however, it should be under stood that this is only exemplary, since a different number of pieces can be provided according to the invention, as will be explained.

Referring first to FIG. 1, there is shown a geometric puzzle 10 which has six pieces 1 through 6 respectively. The four edges of piece 1 are designated 1-1 through 1-4 respectively. Similarly the edges of pieces 2-6 are designated 2-1 through 2-4, 3-1 through 3-4, 6-1 through 6-6. In the array as shown in FIG. -1, edge 3-1 of piece 3 interfits with concave edge 4-4, at least one concave or convex edge of each piece interfits with one convex or concave edge respectively of another piece. Thus the entire assembly forms a continuous array without any discontinuities or spaces between the several pieces. The periphery of the entire array consists of a series of connected arcs alternately convex or concave. In the particular array 10 as shown, piece 1 has two concave edges 1-2 and 1-4 juxtaposed to convex edges 2-1 and 4-3 of pieces 2 and 4 respectively. Convex edge 1-3 of piece 1 is adjacent concave edge 3-2 of piece 3. Piece 2 has concave edge 2-4 adjacent convex edge 5-1 of piece 5. Convex edge 2-3 is adjacent concave edge 6-2 of piece 6. Piece 3 has convex edge 3-1 interfitting with concave edge 4-4 of piece 4. Piece 5 has concave edge 5-2 receiving convex edge 6-1 of piece 6. Thus the entire array defines a novel, nonregular geometrical layout, which can be characterized as an abstract non-rectilinear design, since it is not a representation of any common pictorial subject, object or article. The arrangement of pieces is arbitrarily selected only to a limited extent. In the first place, any one piece is properly interfitted with another piece only when a concave or convex edge of the one piece interfits with a convex or concave edge of the same length and curvature of the other piece. Secondly, each piece must be interfitted with at least one other piece, and preferably with two or more other pieces.

The pieces should be differently colored; for example, pieces 1 through 6 are colored respectively red, orange, yellow, green, blue and purple. This facilitates identification of the pieces, increases the interest in the puzzle, and imparts an attractive multicolored appearance to the completed puzzle array,

FIG. 2 shows a template 12 which is used as a basis for laying out the several pieces. The template is a sheet of narrow, metal, wood or plastic, in which there are three narrow curved slots S1, S2 and S3, of progressively greater length and radius of curvature. They radiate outwardly of a common point 0. End points, A, B, and C are equidistant from each other and define equilateral triangle A, B, C. The slots are all curved in the same direction, going clockwise around the template. Point O is oif the center of the triangle. The pieces 1 through 6 of puzzle 10 are constructed by tracing along slots S1, S2 and S3 will be best understood by referring to FIGS. 3A-3F. Any piece can have opposite edges of the same length and curvature or of different lengths and curvature. In any case, opposite edges are all either concave or convex.

In FIG. 3A piece 1 has convex edges 1-1 and 1-3 of the same length and curvature as shortest slot S1 of the template 12. Concave edges 1-2 and 1-4 are both equal in length and curvature to intermediate slot S2 of the template. Piece 2 of FIG. 3B has convex edge 2-1 and concave edge 2-4 equal in length and curvature to intermediate slot S2 of the template. Convex edge 2-3 is shorter and is equal to slot S1 of the template. Concave edge 2-2 is equal in length and curvature to longest slot S3. Piece 3 of FIG. 3C has convex edges 3-1, 3-3 both equal to longest slot S3; and concave edges 3-2, 3-4 are both equal to shortest slot S1. Piece 4 in FIG, 3D has convex edges 4-1, 4-3 equal to slot S2 of the template. Concave edges 4-2 and 4-4 are equal to longest slot S3 of the template. Piece 5 in FIG. 3E has convex edges 5-1, 5-3 equal to slots S2 and S3 respectively; and concave edges 5-2, 5-4 are equal to slots S3 and S1 respectively. Piece 6 of FIG. 3F has convex edges 6-1, 6-3 equal to slots S3 and S1 respectively. Concave edges 6-2, 6-4 are equal to slots S1 and S2 respectively of the template.

In using the template to construct pieces, the template is set down so that any two of its end points A, B, C, coincide with two equally spaced points marked on a fiat sheet from which the pieces are to be cut. Since the points A, B and C define an equilateral triangle the three slots S1, S2 and S3 will extend outwardly to the corners of the triangle. Then by tracing the slots on the flat sheet, two edges of each of the three game pieces will be drawn. The template can then be shifted so that any two other ends of the slots coincide with the two ends of the traced edges of each piece. The outline of the piece can be then completed by tracing through the two slots which then extend between the two ends of the two edges already traced.

It will be apparent that it will always be possible to construct different shaped pieces by this method since the outer ends of all the slots are equidistant from each other, and yet the pieces wil be differently shaped as shown in FIGS. 3A through 3F, inclusive.

In any construction of game pieces each piece will have at least one edge which interfits with one edge of another piece, and preferably each piece should have at least two edges which interfit with two edges respectively of two other different pieces. Thus the minimum number of pieces possible for the simplest form of puzzle will be three, since three pieces will have a minimum of three pairs of abutting edges, where each form of edge is used at least one time. This is illustrated by two groups of adjacent pieces of puzzle 10, such as pieces 1, 3 and 4 and pieces, 2, 5 and 6. To sustain interest and to make the puule more challenging to a player of average ability, a set of at least six pieces should be provided. If duplicates are to be provided, the number of pieces which the puzzle can have is unlimited.

A multiplicity of puzzle pieces can be arranged to produce a very large variety of original attractive, multicolored abstract arrays. Each array will be characterized by edges which are alternatively concave and convex all around the perimeter of the array as clearly illustrated in FIG. 1. If pieces are properly selected it may be possible to produce an array which is symmetrical along some axis of the array, or partially symmetrical along some axis. The possible solutions of the puzzle can 'be graded in difiiculty by the amount of symmetry which is specified before the working of the puzzle begins.

FIG. 4 shows diagram 20 laid out on a template 12 prior to cutting the three slots S1, S2 and S3. To lay out the plot for the slots, three points, A, B and C located equally distant from each other are designated to define an equilateral triangle ABC. Three altitudes H1, H2 and H3 dropped from points A, B and C to the opposite sides of the triangle. These altitudes meet at a point D which is the center of the triangle. A point 0 is then selected which is oil center, that is, spaced from midpoint D and the three altitudes. Three intersecting curves C1, C2 and C3 are now drawn from point 0 to points A, B and C. The lengths of arcs on curves C1, C2 and C3 are all unequal and are of progressively longer length and greater radius of curvature. Slots S1, S2 and S3 can now be out along curves C1, C2 and C3. These slots determine the configuration of the puzzle pieces as explained above.

The puzzle can be based on a template having slots whose ends define a polygon other than an equilateral triangle, such as a square, rhombus or hexagon. Templates can only be derived from an equilateral geometric figure which itself can form a continuous flat array. The same principles as explained above will be followed in other templates and in constructing and in laying out pieces based on them. As one example, FIG. 5 shows a template 12A having four slots S1S4' of different lengths radiating from a common point 0. The ends A, B, C and D of the slots define a square pattern 20. The diagonals E, E of the square intersect at center point E. Point O is spaced from point E. Each pair of adjacent slots such as slots S1, S2 have their two outer ends A, B, spaced apart a distance equal to the spacing of outer ends B, C; C, D and D, A of each other pair of slots S2, S3; S3, S4; and S4, S1 respectively.

It should be understood that the slots can have any shape other than straight just so that they interfit; they need no be regularly curved at all. Thus referring to FIG. 6 there is shown template 12b based on an equilateral hexagon 20. Adjacent corners AF are equally spaced apart. These corners define the ends of slots S1"-S6 radiating from common point 0" which is located olf the center point 0". Point O is spaced from the point of intersection of the three diagonals G of the hexagon. Slots S2, S4 and S6 are arcuate and of unequal length. Slot S1 is arcuate only in the sense that it is not straight from point A" to point 0'. However, this slot has two straight sections SS1 and SS2 so that edges of pieces traced by using this slot will interfit with each other. Slots S3 and S5 have curved portions SS3 and SS4" interposed like keys. Edges of game pieces traced by using these irregularly shaped slots will interfit with each other.

It will be apparent that the numbers or and shapes of puzzle pieces which can be produced by using templates as described in the manner explained above, are unlimited. Nevertheless, all pieces of all puzzles are constructed according to the well defined geometric principles already explained. If desired, the edges of the pieces can be other than circularly curved. They can be elliptical or parabolic, or of some other regular or irregular shape as explained above. The puzzle pieces can be made out of metal, plastic wood or composition sheet material. They can be cut or stamped out by conventional material working machinery at low cost using mass production methods. The puzzles can be graded in difficulty for players of different ages and different skills.

In FIG. 7 is shown a playing board 50 having a pattern of dots 52 therein and a pattern or array of small studs or tits 54. The dots 52 are equally spaced from each other to define a plurality of equilateral triangles 55 one of which is indicated by dot and dash lines in FIG. 7. The distance between each pair of dots is equal to the common long length of each playing piece which is equal to the length of the triangle, from which the playing pieces are derived. Thus a playing piece such as piece 1 corresponding to pieces 1 shown in FIG. 3A may be placed on board 50 and aligned with any pair of dots 52 and a second piece interfitting with the first piece can also be aligned with another pair of dots.

To facilitate use of board 50 two small projecting studs 54 are located between each pair of dots 52. These studs are located between each pair of dots and are positioned within that area common to all the playing pieces. Two corresponding apertures or recesses 56 are provided in each piece. When a playing piece is properly positioned on a pair of studs the studs will be engaged in the apertures or recesses and the end points of the common-length of the playing piece will be located on the adjacent pair of dots, as shown in FIG. 7.

By using the board, any two playing pieces such as pieces 1' and 4 can be placed in non-adjacent positions on the board and the player or players will try to interconnect these spaced pieces by other pieces properly selected from the available game pieces to form a continuous array. In this way a game can be played in which players seek to form a complete puzzle array such as shown in FIG. 1.

While I have illustrated and described the preferred embodiments of my invention, it is to be understoodthat I do not limit myself to the precise construction. herein described and that various changes and modifications may be made within the scope of the invention as defined in the appended claims.

What is claimed is:

1. A puzzle game comprising a plurality of flat playing pieces each piece having edges shaped to correspond with slots in a template, said slots radiating from a common point with outer ends of said slots, equidistant from each other and defining corners of an equilateral polygon, said common point being located off the center of the polygon, the first pair of edges of each piece being defined by tracing through a pair of said slots from the common point to the respective corners while holding the template stationary, shifting the template and bringing any selected corners of the polygon into coincidence with the outermost ends of the first pair of edges, and tracing a second pair of edges from said common point to said selected corners along the slots which terminate at said selected corners, so that the two outer ends of each pair of adjacent edges of each piece are equidistant.

2. A puzzle game as recited in claim 1, wherein the edges of each piece are alternately convex and concave all around the piece, with at least one edge of each piece interfitting with one edge of another piece so that edges of all pieces interfit with each other to define an array of continuous pieces, the periphery of said array being irregular in geometric configuration and having alternate concave and convex portions all around the array.

3. A puzzle game as recited in claim 1, wherein each piece has four edges.

4. A puzzle game as recited in claim 3, wherein said edge of each playing piece in the array has any one of three possible lengths, and wherein said polygon is an equilateral triangle.

5. A puzzle game as defined by claim 4, wherein each playing piece has four edges with two opposite concave edges and with two opposite convex edges and wherein said polygon has more than three sides.

6. A puzzle game as recited in claim 1, further comprising a playing board on which the playing pieces can be mounted, said board having spaced dots arranged in equilateral triangular arrays upon which end points of playing pieces can be aligned, and means on the board to facilitate holding the playing pieces in place on the board.

References Cited UNITED STATES PATENTS 1,269,233 6/1918 Warga 273-157 1,532,875 4/1925 Brown 273156 X 2,885,207 5/1959 Wormser 273157 FOREIGN PATENTS 127,197 5/ 1919 Great Britain.

ANTON O. OECHSLE, Primary Examiner US. Cl. X.R. 3 3-174

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