CN2692760Y - Magic square device series - Google Patents

Abstract

The utility model provides a magic square device series which relates to a cultural recreation business appliance and can also be a learning aid or a teaching aid. The utility model is composed of a box body, a column jetton seat, column jettons and an equidifferent number exchanging board. The column jetton seat is provided with n multiplied n column jetton holes (n is an order number); the inner part of each column jetton hole is provided with a column-shaped jetton which can be inserted in and pulled out of the column jetton hole; the upper and the lower end faces of each column jetton are respectively provided with a serial number code. The equidifferent number exchanging board is provided with (n+1) multiplied (n+1) through holes and hole cells. The front side and the back side of the equidifferent number exchanging board are labeled by specified numbers in correlated hole cells. The equidifferent number exchanging board can change a number (a column jetton) to any position in the magic square and keep the magic constant of the magic square unchanged. The magic square device is a tool for compiling magic square number landscape and a function compiling device for number 'astrology' landscape. Magic square number landscape which can be compiled by an odd order perfect number magic square has Pn<2><n> kinds to be explored by human. Four and five order magic square devices is suitable for children to train adding, subtracting, adding and subtracting in succession; magic square devices of more than seven order can compile number landscape. The magic square device series is an interesting toy which appeals to both cultured and popular tastes.

Description

Series magic square instrument

One, affiliated technical field:

The utility model relates to a kind of culture and entertainment supplies, is a kind of multistage serial magic square instrument specifically.

Two, background technology:

According to the record of " entertaining knowledge pandect " and " recreational mathematics " book series, the most ancient in the world magic square sees the Chinese "The Book of Changes" in B.C. 12nd century.B.C. 2000, in the age that Da Yu harnesses the river, people dragged for a tortoise that swims in the flood of river, Lip river, find to have decorative pattern dot chart mark on this tortoise plastron, analysed and made three rank dot matrix magic squares.India's quadravalence magic square on the temple stone tablet of reviving very much is engraved on Pius XI and records.Christian era, China in 1275 mathematician Yang Hui proposed the quadravalence magic square by natural square formation structure.Numeral on certain review hall floor tile of existing Europe is exactly five rank magic squares, and these book series are also on the books to six rank magic squares, but does not have the above magic square record in seven rank.

From study existing several magic square, find: every row of six rank magic squares, every row, up and down, during the shift of the left and right sides, six number sums on the diagonal line have the phenomenon of infidelity, this class magic square is general magic square; Every row of quadravalence, five rank magic squares, every row, up and down, during the shift of the left and right sides, fidelity absolutely, this class magic square is total magic square.According to the reality of magic square, three problems have been proposed in " recreational mathematics " book series: the one, the existence of which several rank magic square is arranged; The 2nd, how to go to construct it; The 3rd, the magic square of structure has how many kinds of.This is academic one of problem greatly of mathematics that current common people pay close attention to, and also numerous and jumbled incomparable because of other, entertaining profoundness is used for inspiration intelligence by increasing people, carries out a kind of high culture amusement article of amusement.

Three, summary of the invention:

Few for overcoming existing magic square exponent number, structure is difficult, and the number that of changing irregularly is few, makes the entertainer feel defectives such as " unfulfilling ", and the utility model provides a kind of exponent number variable magic square instrument family amusement article.Enriching the magic square kind, inspire juvenile intelligence, strengthen that it is recreational and interesting.

For solving its technical matters, the technical scheme that the utility model adopted is: because in the magic square family, exponent number N can be total magic square by 4 magic squares of dividing exactly; Exponent number can only be divided exactly by 2, and N is general magic square greater than 2 even-order magic square; Adjacent two odd numbers with can be two total odd-order magic squares by 12 magic squares of dividing exactly, other odd number is general magic square greater than 1 odd-order magic square.According to the probability statistics of these 100 routine magic square tabulations of rank, 3 rank to 102, general magic square accounts for 42%, and total magic square accounts for 58%.The change constant of magic square be on every row of N rank magic square, every row, the every diagonal line N number and, the change constant of general magic square is 2 (N+1) group only, the change constant of total magic square has the 4N group.It is ever-changing to have total magic square only, could unusual fluctuation and not disorderly.Even number magic square in the total magic square serves as that foundation is made up with natural structured approach, and the odd number magic square in the total magic square is to make up out with structure of the present utility model, the technical problems to be solved in the utility model that Here it is.

Its design proposal is: design a casing that includes case body and case lid, in casing, be provided with a post sign indicating number seat, design has n * n post code holes on the post sign indicating number seat, be furnished with a polygon that can inject or take out or columniform cylindricality numeral in each post code holes, on the cylindricality numeral, be equipped with identical arabic numeral on the lower surface, and be red word on the end face, another end face is the black word, being provided with one on post sign indicating number seat can be arbitrarily along putting or putting upside down, just put, instead put and overlap the equal difference Plunder that is used in the post numeral and count plate, this Plunder counts plate and is provided with (N+1) * (N+1) or (N+1) * (N+2) individual through hole, the position of each through hole and diameter are identical with post code holes on the post sign indicating number seat, at the other grid that indicates of each through hole of pouring several plate pro and con, mark has two identical numerals in the relevant through hole grid, and these two identical numerical references are on the diagonal line of hole lattice.

The beneficial effects of the utility model are: 1. because the utility model can develop into multiple magic square instrument, therefore can be made into multistage magic square series of products, fill up the blank that does not also have the above magic square in six rank now, have certain theoretical significance.Can increase to 102 from 3 according to the measuring and calculating exponent, the magic square of 100 kinds of exponents can be arranged, and have only the magic square data plot on 3 to 6 rank at present.2. use this magic square instrument, can make up, view and admire and find the digital view of each total magic square in rank, the entertaining of appreciating various magic square numeric structures develops.According to research, the change constant calculations formula of total several rank magic square of arbitrary arithmetic progression is N _n=n/2 (2a+bn ²-b), and in the formula: number headed by a, b is the tolerance of equal difference ordinal number, n is an exponent number, N _nChange constant for certain total magic square in rank.The computing formula of the conversion kind number of the n rank magic square of arbitrary arithmetic progression is P _N2 ⁿUtilize the constant principle of change constant, can change irregularly P _N2 ⁿPlant digital view.Conversion kind number as 7 rank magic squares is $P_{49}^7=4.3293894336\&times;{10}^{11}$ Kind, be fit to club and magic square fan and give birth to flower, amusement self-admiration with brocade.

3. of many uses, because of counting two-sided can the overlapping arbitrarily of plate, equal difference Plunder is used in the total magic square post sign indicating number of n rank, it is right that each order equal difference Plunder by same tag counts n, any several Plunder in the magic square are changed to any position in the magic square, although arbitrarily or painstakingly the Plunder number stirs endlessly, can keep the eternal rule of magic square change constant forever.As: quadravalence, five rank magic square instrument are fit to children and learn adding, subtracting of number, or even add, even subtract training; Allow children in the unusual change of number is drilled, use one's hands and brains, carry out intelligence and inspire, also can make up out simple five rank magic square numeral views.Seven rank magic square instrument are fit to compile digital view, and are complicated and simple moderate; Ten single orders, 13 rank magic square instrument, be fit to make up magic square numeral view, be fit to do digital implementation, in addition, the digital basic cloth sign indicating number figure of each rank magic square can be used for mathematics and scientific research service, as the density of selecting alloying element forms the different structures that contain gold, and making this center that contains golden structure count sum on place row, column, the diagonal line of reporting to the leadship after accomplishing a task each is constant, is the standard focus point.

Four, description of drawings:

The utility model is described in further detail below in conjunction with drawings and Examples.

Fig. 1 is the structural representation of seven rank magic square instrument.

Fig. 2 is a cylindricality numeral structural representation of seven rank magic square instrument.

Fig. 3 is the structural representation that the equal difference Plunder of seven rank magic square instrument counts plate.

Fig. 4 is that the digital view Plunder of seven rank magic square instrument (the change constant is 175) counts program record reference diagram.

Fig. 5 is the structural representation of ten single order magic square instrument.

Fig. 6 is the cylindricality numeral structural representation of ten single order magic square instrument.

Fig. 7 is that the equal difference Plunder of ten single order magic square instrument counts the plate structure synoptic diagram.

Fig. 8 is the basic cloth sign indicating number figure of ten single order magic square instrument (the change constant is 671) post sign indicating number seat upper prop font code.

Fig. 9 is that 13 rank magic square instrument change constants are the basic cloth sign indicating number figure of 1105 post sign indicating number seat upper prop font code.

Five, embodiment:

Fig. 1～Fig. 4 is an important embodiment of the present utility model, and by post sign indicating number case (1), case lid (5) connects as one by hinge (4), is provided with a transparent panel (6) in case lid (5), tastes effect in order to strengthen seeing; In post sign indicating number case (1), be provided with square post sign indicating number seat (2), post sign indicating number seat (2) is provided with 7 * 7 totally 49 jacks and grids (3), other designs 49 polygonal numerals (7), all mark identical numeral on the upper and lower end face of each polygon numeral, wherein, numeral on end face is a black, numeral on the another end face is red, numeral on each numeral end face is only represented in 1～49, do not weigh and do not leak, the diameter of polygon numeral is slightly less than the diameter of set each jack on the post sign indicating number seat, and the height of polygon numeral is all greater than the degree of depth of set each jack on the post sign indicating number seat; In post sign indicating number casing (1), also be provided with an energy along putting, put upside down, just put, instead putting and overlap the seven rank magic square equal difference Plunder that are used on the numeral (7) and count plate (8), this plate is provided with 8 * 8 totally 64 through holes and grids, the position of through hole and aperture are all identical with jack on the post sign indicating number seat (2), the associated through-holes of counting the plate pro and con at equal difference Plunder is marked with two identical numerals with the grid inner prop, be used for Plunder and change the polygon numeral, to make up digital view, do various recreation.The magic square kind number of seven rank magic square instrument by formula $P_{49}^7=4.3293894336\&times;{10}^{11}$ Kind, just wherein several shown in Figure 4.

Fig. 5～Fig. 8 is another embodiment, is respectively the structural representation of ten single order magic square instrument, and equal difference Plunder counts plate figure and relevant digital landscape map.Ten single order magic square instrument also are by casing (1), connect as one by hinge (4) and case lid (5), be provided with transparent panel (6) in the case lid (5), in post sign indicating number case (1), be provided with 11 * 11 totally 121 jacks and grids (3) on the set square column sign indicating number seat (2), is furnished with a cylindrical numeral (7) that numeral is different in each jack, totally 121 this numerals, the upper and lower end face of each numeral (7) is used red respectively, black color mark has identical numeral, count plate (8) with the equal difference Plunder of ten single order magic square instrument of square column sign indicating number seat (2) adapted and be provided with 12 * 13 totally 156 through holes and grids, and just counting plate at this Plunder, mark has two identical numerals in the corresponding grid of reverse side, Fig. 8 is the cloth sign indicating number figure on the square column sign indicating number seat (2) of ten single order magic square instrument, every row of this cloth sign indicating number, 11 number sums on every row or the diagonal line are that the change constant of ten single order magic squares is 671.Fig. 9 is another embodiment, i.e. basic cloth sign indicating number figure on the post sign indicating number seat of 13 rank magic square instrument, and the change constant of 13 rank magic squares is 1105.Then 11 or 13 rank equal difference Plunder are counted plate along put or put upside down, just put, the anti-cover of putting is used in and carries out various Plunder by game rule on this cloth sign indicating number figure and change recreation, observe digital view, or do scientific research.

Claims (3)

1, a kind of serial magic square instrument, comprise casing (1), the hinge (4) of case lid (5) and connect box and case lid, transparent panel (6) in the case lid, it is characterized in that: in casing (1), be provided with a post sign indicating number seat (2), post sign indicating number seat is provided with exponent number * exponent number post code holes and grid (3), be furnished with a polygon that can inject or take out or columniform post numeral (7) in each post code holes, the upper and lower end face of each post numeral is equipped with identical arabic numeral, and an end face is red word, another end face is the black word, being provided with one on post sign indicating number seat (2) can be arbitrarily along putting, put upside down, just put, instead put and overlap the equal difference Plunder that is used in the post numeral (7) and count plate (8), equal difference Plunder counts plate and is provided with the individual through hole in (exponent number+1) * (exponent number+1) or (exponent number+1) * (exponent number+2), the position of each through hole and diameter are identical with post code holes on the post sign indicating number seat (2), the other all marks of each through hole of counting the pro and con of plate (8) at equal difference Plunder have grid, and mark has two identical numerals in relevant through hole grid.

2, serial magic square instrument according to claim 1, it is characterized in that: exponent number is that the post sign indicating number seat (2) of 77 rank magic square instrument is provided with 7 * 7 totally 49 post code holes and grids (3), be provided with 49 polygon numerals (7) simultaneously, be inserted in accordance with regulations in 49 post code holes of post sign indicating number seat, the pro and con of each numeral (7) all marks identical numeral, and an end face is red word, another end face is the black word, the diameter of polygon numeral is slightly less than the diameter of each post code holes, and the height of polygon numeral is all greater than the degree of depth of each post code holes; On post sign indicating number seat (2), be furnished with an energy along put or put upside down, just put, the counter seven rank equal difference Plunder of putting and applying mechanically in each numeral (7) count plate (8), this Plunder counts plate and is provided with 8 * 8 totally 64 through holes and grids, the position of through hole and diameter are identical with post code holes on the post sign indicating number seat (2), in equal difference Plunder counted the associated through-holes and grid of plate pro and con, mark had two identical numerals.

3, serial magic square instrument according to claim 1 and 2, it is characterized in that: exponent number is that the post sign indicating number seat (2) of 11 ten single order magic square instrument is provided with 11 * 11 totally 121 post code holes and grids (3), is furnished with a cylindrical numeral (7) that numeral is different in each post code holes, totally 121 numerals, each numeral upper and lower end face has identical numeral with red color with black color mark respectively, count plate (8) with ten single order magic square instrument equal difference Plunder of square column sign indicating number seat (2) adapted and be provided with 12 * 13 totally 156 through holes and grids, in this Plunder counted the corresponding grid of pro and con of plate, mark had numeral identical on two.