US2394864A - Jig-saw puzzle - Google Patents

Description

Patented Feb. 12, 1946 UNITED STATES PATENT OFFICE :II'G-SAW rozznn Thomas :Ol'cveland Luton, Evansville, Ind; Application November 22,1942, Serial No. 511,328

2 Claims.

- This invention relates topuzzles and more particularly to thattypek-nown-as jigsaw puzzles;

A primary object of this invention is the provision .of .a puzzle of such nature .as to provide increased entertainment value. 7

An additional' object is the provision of a puzzle comprising two puzzles of distinct shape in =one.

the Jigsaw type having a number of pieces which may be inserted with either face up, only one of such .faces being pertinent to the puzzle being solved.

A still further object is the provision of .ajigsaw puzzle which will provide an apparent mathematical paradox, in that the identical pieces when put together to form one shape, as for-example, a square will present either a greater .or lesser surface .area than will the identical pieces when put together to form another shape, as for example .a rectangle.

Other objects will in part be obvious and in part pointed .out hereinafter.

Having reference now to the accompanying drawing wherein there isillustratedpne form of .theinventive concept,

Fig.1 is a plan view of one modification of this invention showing the first basic cuts'nec- I essary to permitreassemblyin a different form.

Fig. 23s a plan view of the partsofiFig. 1 re- .assemblediin .a different form.

Fig. 3 is an enlarged views'imilar to Fig. .2 but disclosing exaggerated form the slight misfit of certain pieces.

Fig. 4 is an enlarged plan view of certain elements shown in Figs. 1 and .2.

Fig. '5 is a plan View of a modified form of the parts shown in Fig, 4, and

Fig. 6 is a view similar to Fig. 1 but showing portions of the additional cuts necessary to provide a complete jigsaw puzzle.

Similar reference characters refer to similar parts throughout the several views of the drawing.

As conducive to a clearer understanding of this invention it may here be pointed out that applicant is aware that heretofore jigsaw puzzles have been manufactured having pictures on both sides. Such puzzles, however, have had the uniform disadvantage that when the picture on one side was completed, if the puzzle were to be turned over without disturbing the component parts, the picture on the other side would be found also to have been completed. Thus the solver, after having finished one side would remember the relationship of certain parts by. shape and have materially less difficulty in completing the picture on the opposite side.

With the puzzle of the instant invention, however, the completion of one side in no way diminishes the difliculty of solving the other side,

.A further object is the provision of .a puzzle of i arranged as shown in Fig. 2.

These four parts, a'f-ter :being turned over, have aiiixed to their opposite surfaces a rectangular picture.

Then by the use of a jigsaw each of the four major parts of the puzzle may be cut into as many additional parts as desired, as shown in Fig. .6.

Referring-now to the location and nature of the basic cuts, it has previously been stated that any desired size square may be employed. However,

for the sake of ease of mathematical illustration only-one size will be hereinai ten'described, namely a square:8"" b 8 Fig. '1.

Having reference now to Fig. 1 there is .disclosed asquare, .ABCD, 8" by .8" .(64 square inches) ,Acut EF, is made 3 aboveand parallel to side AB and the resulting rectangle, ABEF, out along either diagonal, illustratively BF, to form two right triangles, ABF and EBF. Three inches are now measured along the line and I 5" along the line or vice versa, and a .cut

made between the resultant points G and H resulting in two identical uadrangles, DFGH and ECGH. 4

The two triangles may be designated l and 2 and thetwc quadrang-les's and I.

' Rearrangement er the parts as shown inFig. 2

-will, however, result in-a rectangle: 5"" by I 65 square'inches) since-the side-AB :of triangle I is 8" long and abuts one 5" side of quadrangle 4, the other 5" side of which forms a second side of the rectangle. There is then produced an apparent gain of one square inch in area utilizing the same component parts.

The reason for this discrepancy is best shown in Figs. 3 and 4. While the juxtaposition of parts i and l, and 2 and 3 apparently results in the formation of two right triangles, such, with the dimensions given, is not actually the case. Such right triangles may be formed, as will be pointed out hereinafter, but the absence of perfection in the triangles produces the entertaim'ng apparent paradox above mentioned.

If the parts dimensioned as indicated are rearranged as in Fig. 2 their outer edges form a rectangle but the inner edges will be out of contact, as shown in exaggerated form in Fig. 4. Assuming the outer rectangle to be perfect the empty space in the interior of Fig. 3 assumes the form of an elongated parallelogram.

The two edges of the parallelogram, Fig. 3, which meet parts 3 and 4 are each equal to V29 (since the right triangle forming the adjacent portion of the quadrangle measures by 3") or 5.385" while the other two sides of the parallelogram abutting the hypotenuse of right triangles I and 2 (th e legs of which equal 3" and 8") are equal to V73 or 8.544".

Since the area of this empty parallelogram,

which from trigonometry tables discloses 0=1 15' or 178 45' From which it follows that the parallelogram, in a small rectangle, is so long and narrow as to render detection difiicult in the completed puzzle.

These compilations apply to any similar puzzle so long as the ratio of the parts remains constant, and similar compliations may of course be made for other ratios.

It should here be pointed out that in certain instances, as for example in larger puzzles, the amusement value of the apparent mathematical paradox may be outweighed by the desirability of having a uniform picture without gaps or irregularity. In such case the puzzle may be so constructed that the parts I and 4, or 2 and 3 actually, Fig. 5, do form a right triangle, as indicated.

This can be achieved by cutting the square of Fig. 1 along the lines indicated in such manner that Where 1 represents the length of each side of the square ABCD and d represents the number Now it is easily proven by geometry that if one of the triangles, say 1, is placed in juxtaposition with one of the rectangles, say 3, in the manner indicated in Fig. 5, the resultant figure will form a right triangle, as canbe seen by the following reasoning. Since the angles GCE and FAD are both right angles, their sum, the angle EAB, formed by superimposing C on A and G on F (which is possible because by construction CG=AF must be a straight angle. The angle HEC is obviously a right angle, by construction, so that all that remains to be proven is that the points B, F and H are co-linear. To prove this it is sufficient, according to the theory of similar triangles, to prove the equality Thus given any desired size of square by cutting the same in accordance with the above formula the parts may be rearranged to form a perfect rectangle.

It will now be seen that there is herein provided a novel puzzle presenting exceptional entertainment value and other advantages of great practical utility.

As many embodiments may be made of this inventive concept and as many modifications may be made in the embodiment herein shown and described it is to be understood that all matter hereinafter set forth or shown in the accompanying drawing is to be interpreted merely as illustrative and not in a limiting sense.

I claim:

1. In a jigsaw puzzle in combination a plurality of pieces including two right triangles and two quadrangles adapted to form a square, a picture on said square, a disorganized picture on the opposite side of said pieces when arranged as a square, said pieces being so cut that upon reversal they may be arranged to form a difierent geometrical shape and when so arranged present a different picture on the then reversible side.

2. A method of forming jigsaw puzzles which comprises cutting a square having a picture thereon into a plurality of pieces turning said pieces over, reassembling said pieces to form a differently shaped geometric figure, aiiixing a different picture to the opposite side of sai pieces corresponding in shape to said differently shaped geometric figure and subdividing the picture according to the shape of the parts to which the second picture is afiixed.

THOMAS CLEVELAND LUTON.

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