Eight piece dissection puzzle
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An eight-piece geometric puzzle includes five modified rectangular tiles each having a 45° interior angle, and three triangular tiles. The tiles are of rigid flat construction so as to be arrangeable on a flat surface edge to edge to form a variety of recognizable two-dimensional figures including, but not limited to, a rectangle, ship, cat head, cross, house, milk can, duck, temple, space capsule, elongated rectangle, polygon, and rocket.

Albers, John H. (Irvine, CA, US)
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1. A geometric puzzle apparatus comprising: three planar isosceles triangular tiles, each having three linear edges, two of the triangular tiles being identical; and five planar truncated rectangular tiles, each having four linear edges, two 90° interior angles and one 45° interior angle; two of the truncated rectangular tiles being identical; whereby said three triangular tiles and five truncated rectangular tiles are abuttingly arrangeable on a flat surface to form a plurality of recognizable figures.

2. The apparatus of claim 1 wherein the tiles are between 1/16th and 1/8th of an inch in thickness.

3. The apparatus of claim 1 wherein the tiles are of a rigid material, said material being at least one of plastic, wood and metal.

4. The apparatus of claim 1 wherein the tiles have a planar frontal surface spaced apart from a planar rear surface.

5. The apparatus of claim 1 wherein the linear edges are one of flat, beveled, and curved.

6. The apparatus of claim 1 wherein the solid figures, recognizable in outline, include at least: a rectangle, a ship, a cat's head, a cross, a house, a milk can, a duck, a temple, a space capsule, and a rocket ship.

7. (canceled)

8. The apparatus of claim 1 wherein the truncated rectangular tiles have two adjacent edges to forming a 45° angle.



1. Field of the Present Disclosure

This disclosure relates generally to dissection puzzles, and more particularly, to such a puzzle having eight pieces of only two types, a triangle and a modified rectangle.

2. Description of Related Art Including Information Disclosed Under 37 CFR 1.97 and 1.98

Silvey, U.S. D413361 discloses an ornamental design for a three-dimensional geometric puzzle.

Mehner, U.S. Pat. No. 2,605,94 discloses a puzzle comprising a certain number of block of such shapes that they may be united at their edges to produce a great variety of symmetrical figures, which figures are changed by changing the relative arrangement of said blocks to each other. In addition, a chart is provided representing a variety of figures which may be formed by uniting the blocks in the various relative positions to each other.

Jervis, U.S. Pat. No. 1,430,557 discloses a set of blocks for the amusement and instruction of children, comprising one block of trapezoidal outline, one block of triangular outline having two sides each of which is approximately the same length as the side of the first mentioned block, two smaller triangular blocks each of which has a base approximately equal in length to the length of a side of the first mentioned triangular block, and two rectangular blocks at least one of which has a length approximately equal to the length of the side of the first mentioned triangular block, and a width of approximately half the same.

Joseph, U.S. Pat. No. 1,656,117 discloses a nine figure puzzle comprising four isosceles triangles, three scalene triangles and two trapezoids, which when placed edgewise, form a plurality of figures including a rectangle and a star, the isosceles triangles including a pair of similar dimensions and another pair of dimensions, but of dissimilar dimensions from the first named pair.

Way, U.S. Pat. No. 2,901,256 discloses a block puzzle comprising a set of thirteen blocks constituting a regular pentagon when assembled in juxtaposition, seven of said blocks comprising at least three different types of polygons, each having at least two equal sides and angles of 45° and multiples thereof, the length of at least one side on a plurality of said seven blocks being equal to an even multiple of the length of at least one side on a plurality of the remainder of said seven blocks, said seven blocks forming an interior square having one side coincident with one side of the pentagon, and six of said blocks having angles of 18° and multiples thereof, two of said group of six blocks constituting side blocks each having one side equal in length to one side of said pentagon and each of said side blocks filling the space adjacent to one side of said square between said side and the adjacent side of said pentagon, and the remaining four of said group of six blocks each having one right angle and fitting together with one side of each in longitudinal alignment coincident with the fourth side of said square forming a line equal in length thereto and filing the space between said side of the square and the two sides of said pentagon remote from the side thereof which is coincident with the first named side of said square, two of said four blocks forming an interior pentagon within said first named pentagon and having two sides coincident with an apex of said first named pentagon, said two sides being of equal length and of the same length as two adjacent sides thereof and also of the same length as contiguous sides of the other two blocks of said group, and said first two of said four blocks each having one side of the same length as a non-adjacent side of each of said two other blocks of said group, each of said non-adjacent sides extending in the same line as one of the sides of said square contiguously to the inner side of one of said side blocks, whereby a large number of arrangements may be made wherein groups of adjoining blocks have contiguous sides of the same length.

Kanbar, U.S. Pat. No. 4,298,200 discloses a Geometric game assembly constituted by two sets of Geometric pieces capable of creating a variety of geometric or representational figures. Also included is a deck of cards, each having printed thereon a Geometric puzzle figure and the solution thereto at a position at which it is obscured in play. In play, a card is withdrawn from the deck and its front face presented to the players who with their respective sets of pieces then race to recreate the figure. The player who is first to succeed is awarded the card. Cards in the deck are played, the player who gains the greatest number being the winner. Any number of cards may be played depending on how long the players would like the game to last.

Calvert, U.S. Pat. No. 4,343,471 discloses a puzzle comprising a set of triangular, quadrilateral, and pentagonal tiles. Apical angles are in multiples of 36 degrees, and sides are proportional to integral powers of the golden section. Regular pentagons and other patterns are assembled from the tiles.

Di Gregorio, U.S. Pat. No. 4,522,404 discloses an invention concerned with the technical field of structures adapted to provide entertainment of a didactic character, and in particular with a block subdivided into suitable portions to compose three-dimensional figures. The technical problem to be solved was that of providing a simple structure whereby a very high number of three-dimensional configurations could be obtained, the elements which make up the game being in such mutual relationship as to favor the attainment of such three-dimensional configurations. The problem is solved by a didactic game defined by a cubic block subdivided into portions which comprise two first prismatic bodies defined by right prisms having isosceles right triangle bases and a combined volume equal to one half that of said block, a parallelepipedon-like inner body with square bases, and second prismatic bodies defined by eight prisms with isosceles right triangle bases and being separated into complementary bodies, defining together with said inner body the form of said first prismatic body, and auxiliary bodies which are identical to one another and together define the form of a further first prismatic body.

Uppstrom, U.S. Pat. No. 4,537,001 discloses building elements with matching side surfaces for fitting together to form constructions of varying shape, said building elements having the same length and each having two opposite, equiform, flat, parallel end surfaces and at least three flat, rectangular side surfaces extending between said end surfaces to effect said matching of the side surfaces, the cross-sectional surfaces of the building elements each having a size which is a multiple of a triangular area of the size, and the sides of the end surfaces having proportional lengths selected from the group. The building elements are non-congruent and are nine in number divided into a first group of building elements with non-congruent cross-sectional surfaces.

Lalvani, U.S. Pat. No. 4,723,382 discloses building structures based on polygonal members with coplanar straight edges and icosahedral symmetry. The building structures comprise a set of ten elementary polygonal members, including four triangular members and six parallelogram-shaped members, that are combined to form tetrahedral, octahedral and half-octahedral or truncated tetrahedral, cuboctahedral and truncated octahedral or rhombohedral and parallelpiped building members that in turn fill a three-dimensional space periodically or non-periodically. The orientation of the building members is such that all edges are parallel to the fifteen two-fold axes of rotation of icosahedral symmetry.

Li, U.S. Pat. No. 4,913,436 discloses planar puzzles and a game utilizing these puzzles exploiting simple geometric shapes for the design of a plurality of initial configurations that make up each of the puzzles. Each of the initial configurations may be further subdivided into elementary piece-parts. For each puzzle, it is possible to rearrange certain of the initial configurations to form a new puzzle configuration having the identical shape of the initial configurations by reassembling the piece-parts of each of the configurations. By proceeding in a series of merger steps, it is possible to rearrange all of the initial configurations into a single merged configuration that also has the same shape as the original configurations. The game aspect furnishes each player with the opportunity to generate mergers from configurations under control of the other players. The strategy is to generate as many mergers as possible in the time allowed while blocking other players from merger opportunities.

Kuo, U.S. Pat. No. 5,108,291 discloses a supplementary teaching instrument based on mathematical basic theories and principles as well as child psychology. The invention employs a number of rectangular blocks of a prescribed shape which occupy a predetermined area when assembled together, and a corresponding area of triangular shaped blocks of various sizes and shapes. In addition to creating artistic designs by different arrangements of the blocks which may be of different colors, the rectangular blocks can be used in the fashion of a domino game, and the dimensional relationship between the triangular blocks and the rectangular blocks teach the basic concepts of mathematics including addition, subtraction, multiplication, fractions, areas, and the like.

Stokes, U.S. Pat. No. 5,660,387 discloses a set of polyhedrons having shapes capable of fitting together, in one or more ways, into a solid geometric shape such as a rectangular solid or more specifically, a cube. The polyhedrons include five-sided polyhedrons made up of a regular tetrahedron and an irregular tetrahedron abutted together as one solid; alternately, the two separate tetrahedra can be included in lieu of one or more of the five-sided polyhedrons, for assembly in the puzzle. The set of polyhedrons includes separate irregular tetrahedra and may include a regular octahedron. Preferably each shape of polyhedron is in a different color. In a preferred embodiment, the polyhedrons are all solid throughout and are of the same density, and that density is preferably the same density as water to enable the teaching of certain relationships. The set of polyhedrons function not only as a puzzle, for fitting into a transparent housing such as a cube, but also for educational purposes in teaching geometry.

Chester, U.S. Pat. No. 5,746,430 discloses a Geometric puzzle game assembly in which the game is played with a set of geometric pieces formed of plastic material having magnetized particles dispersed therein. Also provided is a ferromagnetic play board on which the pieces are placed by a player and fitted to create a Geometric figure whose shape depends on how the pieces are fitted, the pieces being magnetically attracted to the board to maintain their respective positions. The pieces are stored in a tray having a side wall provided with an elongated slot to socket the lower end of the play board to support the board at a tilted upright position, thereby facilitating placement of the pieces on the board as the player observes a Geometric puzzle to be solved printed on the face of a playing card.

Aghevli, U.S. Pat. No. 5,873,729 discloses a mathematical triangle kit designed to teach children and adults mathematical and symmetry skills utilizing various sized patterned blocks. By manipulating the patterned blocks the participant learns mathematical skills, such as fractions, multiplication, trigonometry, and geometry. Additionally, by manipulating the patterned blocks the participant also learns geometric relations, such as mirror images and other symmetry relationships amongst the patterned blocks. In the preferred embodiment, the mathematical triangle kit comprises three sets of various sized and colored right triangles with 30° and 60° bases.

Silvey, U.S. Pat. No. 6,145,837 discloses a three-dimensional geometric puzzle having a cube element, five triangular prism elements and a parallelepiped element. Each one or all of the elements of the puzzle are capable of being oriented such that they have a thickness equal to the length of an edge of the face of the cube element. The elements can also be juxtaposed in a predetermined fashion to form various geometric solids, such as a parallelepiped having a square face and a height equal to the length of a side of an edge of the cube element.

The related art described above discloses the combining of a plurality of differing geometric tiles, including blocks, triangles, trapezoids, parallelograms, and rectangles, to form a variety of both two-dimensional and three-dimensional shapes and objects. However, the prior art fails to disclose a set of dissection tiles consisting only of isosceles triangles and modified rectangles. In addition, the prior art fails to disclose such a geometric puzzle, capable of forming silhouettes of a wide range of recognizable shapes and objects, with relatively few pieces, thus accommodating users of varying skill levels, ranging from small children to adults. The present disclosure distinguishes over the prior art providing heretofore unknown advantages as described in the following summary.


This disclosure teaches certain benefits in construction and use which give rise to the objectives described below.

Dissection puzzles are an early form of geometric puzzle. The earliest known descriptions of dissection puzzles are from the time of Plato and involve the challenge of turning two equal squares into one larger square using four pieces. Other ancient dissection puzzles were used as graphic depictions of the Pythagorean theorem. In the 10th century, Arabic mathematicians used geometric dissections in their commentaries on Euclid's Elements. In the 18th century, Chinese scholar Tai Chen described an elegant dissection for approximating the value of π. This type of puzzle saw a major increase in general popularity in the late 19th century when newspapers and magazines began running dissection puzzles. Puzzle creators Sam Loyd in the United States and Henry Dudeney in the United Kingdom were among the most published. Since then, dissection puzzles have been used for entertainment and math education, and creation of complex dissection puzzles is considered an entertaining use of geometric principles by mathematicians and math students.

Some types of dissection puzzle are intended to create a large number of different geometric shapes. Tangram is a popular dissection puzzle of this type. The seven pieces can be configured into one of a few home shapes, such as the large square and rectangle that the pieces are often stored in, to any number of smaller squares, triangles, parallelograms, or esoteric shapes and figures. Some geometric forms are easy to create, while others present an extreme challenge. This variability has ensured the puzzle's popularity. Other dissections are intended to move between a pair of geometric shapes, such as a triangle to a square, or a square to a five-pointed star. A dissection puzzle of this description is the Haberdasher's Problem, proposed by Henry Dudeney in 1907. This particular puzzle is a dissection of a triangle to a square, with only three cuts. It is one of the simplest regular polygon-to-square dissections known, and is now a classic example.

Much of the prior art teaches such geometric puzzles which use a great variety of tile shapes, including rectangles, triangles, trapezoids, parallelograms, and polygons. The present geometric puzzle is much simpler, using only triangular tiles and modified rectangular tiles. In addition, the tiles are of dimensions such that each angle is either 45°, 90°, or 135°. Many of the edges of the tiles are of equal length as well. Thus, each tile of the present geometric puzzle is of relatively similar dimensions.

While there are prior art references which teach geometric puzzles with relatively simple shapes, those particular references also use anywhere from nine to thirteen tiles. The present puzzle improves on this by using only eight tiles. It should be noted that while there are prior art puzzles which use less than eight tiles, those puzzles also use more complex shapes.

Therefore, the present invention discloses a geometric game capable of just as many arrangements, if not more than prior art puzzles, while using a relatively small number of simple triangular and modified rectangular tiles. Thus, the present dissection puzzle has simple tiles to accommodate the skill level of small children; but at the same time, it is capable of forming complex arrangements to challenge a puzzle master. The present invention is the result of the discovery that the combination of isosceles triangle shapes paired with rectangles modified by cutting one corner at a 45° angle are uniquely qualified to be arranged to produce a wide range of recognizable figures.

A primary objective inherent in the above described apparatus and method of use is to provide advantages not taught by the prior art.

Another objective is to provide a dissection puzzle that is capable of forming a relatively large number of solid silhouettes of recognizable shapes and objects with relatively few tiles.

A further objective is to provide a dissection puzzle comprising only isosceles triangular and modified rectangular tiles, but capable of challenging and amusing both children and adults by being arrangeable to form a large number of recognizable shapes.

A still further objective is to provide a dissection puzzle comprising only three isosceles triangular and five modified rectangular tiles, but capable of challenging and amusing both children and adults by being arrangeable to form a large number of recognizable shapes.

Other features and advantages of the present invention will become apparent from the following more detailed description, taken in conjunction with the accompanying drawings, which illustrate, by way of example, the principles of the presently described apparatus and method of its use.


Illustrated in the accompanying drawing(s) is at least one of the best mode embodiments of the present invention In such drawing(s):

FIG. 1 is a plan view of tiles comprising the presently described apparatus, configured in a rectangular-like arrangement; and

FIGS. 2-13 are further plan views of the tiles of FIG. 1 arranged to resemble: a cat head, cross, house, milk can, duck, temple, space capsule, elongated rectangle, a first polygon, rocket ship, and a symmetrical polygon, respectively.


The above described drawing figures illustrate the described apparatus and its method of use in at least one of its preferred, best mode embodiment, which is further defined in detail in the following description. Those having ordinary skill in the art may be able to make alterations and modifications to what is described herein without departing from its spirit and scope. Therefore, it must be understood that what is illustrated is set forth only for the purposes of example and that it should not be taken as a limitation in the scope of the present apparatus and method of use.

Described now in detail is a geometric puzzle apparatus 2 comprising eight planar solid geometric tiles. Each of the tiles is a rigid puzzle piece that may be handled easily and moved about and rotated on a flat surface. Each of the tiles has only linear edges. As shown in FIG. 1, the apparatus 2 includes three triangles 10A, 10B, and 10C and, five modified rectangles 20A, 20B, 20C, 20D, and 20E.

In the preferred embodiment, the tiles are preferably made of a rigid material such as plastic, wood, or metal, but other rigid or even flexible materials may be used instead.

Preferably, each of the tiles is between 1/16″ and ⅛″ in thickness, thus creating a planar frontal surface which is spaced apart from a planar rear surface. The linear edges may be flat, beveled, curved or of any other cross sectional shape, enabling the tiles to abut in an edge-to-edge fashion.

In the preferred embodiment, illustrated in the figures, and now referring to FIG. 1 in particular, each one of the triangles 10A, 10B, 10C is isosceles, each having interior angles of 45°, 45° and 90°. Triangles 10A and 10B are identical in size with edges of 1½″,1½″, and 2″ in length, while triangle 10C has edges 1⅝″, 1⅝″, and 2¼″ in length.

Each one of the modified rectangles 20A, 20B, 20C, 20D, and 20E has four interior angles of 45°, 135°, 90° and 90°. Modified rectangles 20A and 20B are identical with edges 2 1/16″, 1⅛″, 1½″, and 1″ in length, while modified rectangle 20C has edges 1½″, 1″, ¾″ and ¾″ in length, and modified rectangle 20D has edges 1 7/16″, ¾″, 1⅛″, and ⅝″ in length, and modified rectangle 20E has edges 3¼″, 1″, 1 7/16″, and 2 3/16″ in length.

It should be noted that the tile dimensions given herein are arbitrary and may be scaled up or scaled down

Each of the tiles is abuttingly arrangeable on a flat surface to form a plurality of solid figures recognizable in outline. FIGS. 2-13 demonstrate some of the many possible solid figure arrangements in which the tiles may be positioned. These arrangements include, but are not limited to, a ship, a cat's head, a cross, a house, a milk can, a duck, a temple, a space capsule, an elongated rectangle, a rocket ship, and various polygons. In order to form these figures, the tiles are positioned in any desired fashion by rotating and/or flipping them over. In addition, not every figure requires the use of all eight tiles; some figure arrangements require less than eight, as shown in FIGS. 1 and 9. It should also be recognized that not all figures that are products of the present set of tiles will be exactly the form that one might expect, but some may be approximately a form that is recognizable but not precisely what one might expect.

The enablements described in detail above are considered novel over the prior art of record and are considered critical to the operation of at least one aspect of the apparatus and its method of use and to the achievement of the above described objectives. The words used in this specification to describe the instant embodiments are to be understood not only in the sense of their commonly defined meanings, but to include by special definition in this specification: structure, material or acts beyond the scope of the commonly defined meanings. Thus if an element can be understood in the context of this specification as including more than one meaning, then its use must be understood as being generic to all possible meanings supported by the specification and by the word or words describing the element.

The definitions of the words or drawing elements described herein are meant to include not only the combination of elements which are literally set forth, but all equivalent structure, material or acts for performing substantially the same function in substantially the same way to obtain substantially the same result. In this sense it is therefore contemplated that an equivalent substitution of two or more elements may be made for any one of the elements described and its various embodiments or that a single element may be substituted for two or more elements in a claim.

Changes from the claimed subject matter as viewed by a person with ordinary skill in the art, now known or later devised, are expressly contemplated as being equivalents within the scope intended and its various embodiments. Therefore, obvious substitutions now or later known to one with ordinary skill in the art are defined to be within the scope of the defined elements. This disclosure is thus meant to be understood to include what is specifically illustrated and described above, what is conceptually equivalent, what can be obviously substituted, and also what incorporates the essential ideas.

The scope of this description is to be interpreted only in conjunction with the appended claims and it is made clear, here, that each named inventor believes that the claimed subject matter is what is intended to be patented.