US181637A - Improvement in puzzle-blocks - Google Patents

Description

R. R. CALKINS.

PUzzLE-BLocKs. No.181,637. Patented Aug.z9,187e.

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NPETERS. PHOTOJJTHDGRAPHEH, WASHINGTON. D C4 UNITED STATES PATENT OEEIoEL BIFLEY R. CALKINS, OF ST.V JOSEPH, MISSOURI.

IMPROVEMENT IN PUZZLE-BLOCKS.

Specification forming part of Letters Patent No. 18 [5637, dated August 29, 1876; application tiled August 7, 1876. Y

To all rwhom it mag/.concern Be it known that I, RIPLEY R. GALKrNs, of St. Joseph, in the county ot' Buchanan and State ot' Missouri, have invented a new and Improved Geometrical-Pnzzle 5. and I do hereby declare that the following is a full, clear, and exact description ot' the same, reference being had to the accompanying drawing, forming part ot' this specilcation, in which- Figure l is al plan view of the blocks arranged 'or the two squares upon the base and altitude ot' a right-angle triangle, with the square upon the hypotenuse constructed therefrom in dotted lines. Figs. 2 and 3 are diagrams illustrating vthe method of cutting two square blocks ot' any relative size, so as to torm the tive blocks.

The object of my invention is to provide a mechanical or material verification of the geometrical problem that the square described upon thc hypotenuse ot' a right-angle triangle is equal to the sum of the squares upon the other two sides.77 To this end my invention consists in the combination ot'tive blocks, three ot' which are in the shape ot' similar right-angle triangles, one in the shape ot' a trapezium, and the other in the shape otl a trapezoid, which blocks are adapted to be put together to form a single square upon the hypoten'use of a right-angle triangle, or to be transferred and arranged in two squares upon the other two sides, the same to be used in schools for purposes of illustration, or to be used as a puzzle for general amusement.

In the accompanying drawing, 1 2 3 L 5 represent the five blocks, which may be made of wood, metal, ivory, rubber, or other suitable material. Ot' these blocks, l, 3, and 4 are similar right-angle triangles-that is to say, rightangle triangles having allot' these angles equal and their sides parallel-,while 2 is a trapezoid, or a quadrilateral ligure having but two ot' its sides parallel, and 5 a trapezium, or a quadrilateral ligure having none of its sides parallel. These blocks will vary in size and shape for the different sizes and shapes ot" right-angle triangles upon which they are to be arranged, but will always Ymaintain their character as trapezium,trapezoid, and three similar right-angle triangles, and will be capable ot' illustrating the proposition. Thus in Fig.

1 the two squares A and B represent the squares constructed upon the base and altitude of a right-angle triangle, while the larger square O (shown in dotted lilies) represents the square constructed upon the hypotenuse, which is equal to the sum ot' the squares A and B, as proven by the following: The blocks l and 5, being in common to both the dotted square O and the two smaller squares B A, respectively, remain xed. Triangle 4 is then transferred to and coincides with the dotted space 4, tra-pezoid 2 is transferred and coincides with dotted space 2, and triangle 3 is vtransferred and coincides with the dotted space 3, thus completing or fulfilling the square upon the hypotenuse from the irregular disiutegrated fragments of the squares constructed upon the base and altitude of the same rightangle triangle, and thereby illustrating in a concrete form, and \\'eriiying mechanically, the truth ofthe proposition above referred to.

In cutting my blocks the same can readily be accomplished in an accurate and rapid manner without the use of patterns, and in a manner also to produce variable sizes or shapes ot' the three geometric forms. To do this, two squares ot' any absolute or relative size are taken and placed adjacent to each other, and with one ot their sides in alignment, so as to form one hundred and eighty degrees, as shown in Fig. 2. Upon their aligned sides x w', as a base, a point, y, is established, which may be determined in two ways: first, by measuring from m the distance of one side of the small square, which will be a' y, or by measuring from x the distance of the side of the large square, which will be y, either and both of which always determine the point y. Now, it' lines be drawn to the extreme upper most and outermost angles z z', these lines will, when the squares are placed as above,

` always indicate the line ot' cut which will divide the two squares into the ive blocks capable ot` effect-ing the illustration before given.

The point y varies in its position on the line .z according to the relative size of the squares. Thus the greater the difference in size between the same the more nearly will the point y approach m, as illustrated in Fig. 3, and vice versa. The angle z y z will be a right angle, and the sides z y and z y will be two of the sides of the square constructed upon the hypotenuse.

By means of the blocks as constructed and variably arranged, it will be seen that a teacher may, in a concrete form, give an abstract demonstration of the-proposition referredto, whilev he, at the saine time, secures the ready attention and interest of the scholar, thereby reaching his understanding.

' I am aware ofthe fact that it is not new to divide a square into aliquot parts,so that they may be capable ot arrangement' to form two perfect squares, incidental to which is the idea of illustrating the same proposition; but in this case the parts are equal squares or triangles, and present nothing more than a calculation by commcnsuration, or a mere aggregation of equal or similar parts, and goes no further than the arithmetical truth that the square of 10 is equal to the sums of the squares of 64 and 8, respectively. My invention,it will be seen, demonstrates the proposition with the smallest possible number of parts, which is nota mere aggregation of similar and equal parts, but an arrangement of' irregular parts founded upon a fixed principle, which partakes ot the nature ot' a puzzle, and is correspondingly interesting.

Incidental to my invention, as hereinbcfore described, it may be added that a great variety of other geometric i'orms may be produced besides those for which it was more particularly invented.

RIPLEY R.v CALKINS.

Witnesses: V A. P. GoFF,

W. W. MGFARLAND.

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