CN101853593B - 3X+1 conjecture scientific demonstrator - Google Patents
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- CN101853593B CN101853593B CN201010140999A CN201010140999A CN101853593B CN 101853593 B CN101853593 B CN 101853593B CN 201010140999 A CN201010140999 A CN 201010140999A CN 201010140999 A CN201010140999 A CN 201010140999A CN 101853593 B CN101853593 B CN 101853593B
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Abstract
The invention discloses a 3X conjecture scientific demonstrator which comprises an odd nested soleplate frame (4), an odd nested plate (1) and an even nested plate (2) and is characterized in that a two-dimensional numerical table is printed on the odd nested plate (1), and different positive odd numbers conforming to a 3X conjecture are printed in the cells of the two-dimensional numerical table; a two-dimensional numerical table is also printed on the even nested plate (2), different positive even numbers conforming to the 3X conjecture are printed in the cells of the two-dimensional numerical table and are nested by continuously multiplying the positive odd numbers on a 0th zone bit of the table by 2. A common bulb, a power supply and an electric-knife double-throw switch are installed in each cell, and the 3X conjecture scientific demonstrator has the advantages that the operation result and the operation process of changing any positive integer into 1 by computing according to a 3X conjecture algorithm can be searched, and the operation result and the operation process of simultaneously changing infinite positive integers in odd nesting and even nesting determined by the positive integer into 1 are displayed. Demonstration proves the research result of the science difficult problem 3X conjecture.
Description
Technical field
The present invention relates to mathematical education teaching and scientific research field, particularly a kind of mathematical education and scientific research demonstration device that is used for the 3X+1 guess.
Background technology
The 3X+1 guess is one of global science difficult problem; China Ministry of Education, the Ministry of Science and Technology, the Chinese Academy of Sciences, NSFC(National Natural Science Foundation of China) and Science Press's associating in 2007; Listed the 3X+1 guess in " 10000 science difficult problems " book; And come on the 4th of the key difficult problem of mathematics called after " 3X+1 guess ".More than 60 years, external a lot of teachers and students of university use state-of-the-art COMPUTER CALCULATION, do not explore the good thinking and the method for proof 3X+1 guess so far yet.
Summary of the invention
The present invention wants to solve a present global science difficult problem " 3X+1 guess " can't express and find the solution the technical matters that waits through simply deriving to calculate, and purpose is to provide a kind of derive calculating, the teaching of expressing and finding the solution and scientific research of using simple assembled panel can accomplish " 3X+1 guess " to use demonstration device.
The objective of the invention is to realize: a kind of 3X+1 guess scientific demonstrator through following technical proposals; Constitute with the integrated circuit coupling by strange nested bottom plate frame, strange nested plates and even nested plates; It is characterized in that: strange nested bottom plate frame, strange nested plates and even nested plates all are rectangle tabular; Respectively be provided with a strange nest card pig's tongue on two long limits of strange nested bottom plate frame; One long side of strange nest card pig's tongue is provided with 10～30 teeth groove, and strange nested plates flatly is stuck in the strange nested bottom plate frame, and even nested plates is stuck in two relative teeth groove of strange nest card pig's tongue vertically; Be printed on two-dimentional numerical table on the described strange nested plates, be printed on the different positive odd numbers that meet the 3X+1 guess in the cell of two-dimentional numerical table; Be printed on two-dimentional numerical table on the described even nested plates, be printed on the different positive even numbers that meet 3X+1 guess in the cell of two-dimentional numerical table, take advantage of 2 nested come out continuously by the positive odd number on this table the 0 position.
Two-dimentional numerical table on the described strange nested plates with corresponding integrated circuit coupling, and is installed a power supply, a bulb commonly used and a single-pole double-throw switch (SPDT) in each cell; Two-dimentional numerical table on the described even nested plates with corresponding integrated circuit coupling, and is installed a power supply, a bulb commonly used and a single-pole double-throw switch (SPDT) in each cell.
Bulb commonly used on the said even nested plates is pressed the jacket layer series connection, and the bulb commonly used on the said strange nested plates is by the parallel connection of number family, and the single-pole double-throw switch (SPDT) of using in each cell is realized the light Presentation Function.
The supply voltage of the present invention in each cell of even nested plates is identical, and each row can only use a single-pole double-throw switch (SPDT) at every turn, can respectively use a single-pole double-throw switch (SPDT) simultaneously between each row; Supply voltage in strange each cell of nested plates is identical, can use two or more single-pole double-throw switch (SPDT)s simultaneously.
In 3X+1 guess, take advantage of 3 to add 1 to positive odd number, divided by 2, respectively be that the computing in 1 step is called the computing of rudimentary horn paddy to positive even numbers, represent formula with symbol " → ", 3 * 3+1=10 for example, table is 3 → 10; 56 ÷ 2=28, table are 56 → 28.Wherein, The process that becomes another positive odd number to a positive odd number is called has carried out the computing of a standard angle paddy; With symbol
expression formula; For example; 11 → 34 → 17, be the standard angle paddy computing of carrying out 11, show to become to a positive integer at 1 o'clock for
; With regard to the computing of end angle paddy, be called this positive integer angle paddyization.With angle paddyization statement 3X+1 guess, the 3X+1 guess can define rigorously and be " but all positive integers all angle paddyization ".The 3X+1 guess is called angle paddy guess again.The number of times that paddyization positive odd number in angle carries out the computing of standard angle paddy is called the energy level of this positive odd number.Population of levels is that the positive odd number of n is designated as P
n, work as P
n=1 o'clock, energy level n=0; Work as P
n＞1 o'clock, energy level was a positive integer n, and the meaning is to carry out the paddy computing of n substandard angle, can be positive odd number P
nAngle paddyization.Angle paddyization positive odd number 7 for example; Get
so 7 energy level is 5; 11 energy level is that 4,17 energy level is that 3,13 energy level is 2; 5 energy level is that 1,1 energy level is 0.If positive integer Z=2
m* P
n, P
nBe positive odd number, m and n are natural numbers, and natural number is to n so in order, and m is called the angle paddy coordinate of positive integer Z, show that (n, m), the angle identical positive integer of paddy coordinate is called isotopic number into Z.Carry out the computing of standard angle paddy, positive odd number 3,5,7,9 ..., 2
k-1,2
k+ 1 jiao of paddyization is obtained the energy level of each positive odd number, earlier 1,3,5,7,9 ..., 2
k-1,2
k+ 1 is divided into 0,1,2 ..., N different energy levels on each energy level, counted the cover source of family to minimum positive odd number as I, takes advantage of 4 to add 1 continuously, different jacket layers, ascending from left to right arrangement is nested into I and counts family; Again the minimum positive odd number in the remaining positive odd number as the cover source, take advantage of 4 to add 1 continuously, different jacket layers, ascending from left to right arrangement is nested into II again and counts family; Circulation is carried out.The 0th energy level has only a unique positive odd number 1, counts family as the 0th energy level I, also counts the cover source of family as the 0th energy level I; The 1st energy level has only I to count family 5,21,85,341 ....From the 2nd energy level, infinite a plurality of several families are all arranged, each count family by the cover source from small to large layout become I, II, III, IV ... each counts family, processes very nested, as shown in Figure 4.Each infinite a plurality of positive odd number of counting in the family all takes advantage of 2 continuously in strange nested, extends to the space, and it is nested to generate infinite a plurality of idol.Such " very nested " constitutes simple type " 3X+1 guesses scientific demonstrator " with several such " idol are nested "; With the surface-mounted integrated circuit coupling of producing, process " 3X+1 guesses scientific demonstrator " again by bulb commonly used, power supply and single-pole double-throw switch (SPDT) design.
Patent 3X+1 guess scientific demonstrator of the present invention; Use simple assembled panel; Solved a present global science difficult problem " 3X+1 guess " and can't express and find the solution the technical matters that waits, derived calculating, express and find the solution with the mode that mathematical law is simple, clear through simply deriving to calculate; Promote the process of student's study and people's brain activity, can promote on a large scale, also can extensively popularize and use in kindergarten, countries in the world and all kinds of public area in national middle and primary schools and R&D institution; Can use cheap timber, plastics, iron plate, aluminium sheet, cardboard etc. during manufacturing, patent structure of the present invention is simple, and manufacturing process is easy; Cost of products is low, has no side effect, and can save the energy in the use; Can directly use solar cell, operation is convenient in environmental protection; Plurality of advantages such as the demonstration effect is obvious, and is accurate.Squeeze into the international market easily,, get into the palace of various countries' science with its teaching and scientific value and the leading position that is in international mathematics circle.
The beneficial effect of patent 3X+1 guess scientific demonstrator of the present invention: can find out any positive integer and become 1 operation result and calculating process according to the calculating of 3X+1 guess algorithm; And show by this positive integer confirm strange nested and by chance nested in infinite a plurality of positive integers become 1 operation result and calculating process simultaneously; Be infinite a plurality of positive even numbers in the two-dimentional numerical table on each even nested plates on the same high level; Guess rudimentary horn paddy computing through 3X+1 divided by 2; Become on the with it corresponding strange nested plates the infinite a plurality of positive odd numbers in the same number family in the two-dimentional numerical table; Through the computing of a standard angle paddy, the infinite a plurality of positive odd numbers in this number family all become the same positive odd number on time high level again, develop like this; Returning at last is positive odd number 1 unique on the 0th energy level, thus the achievement in research of demonstration proof science difficult problem 3X+1 guess.
Description of drawings
Fig. 1 is a structural representation of the present invention;
Fig. 2 is a strange nested bottom plate frame synoptic diagram of the present invention;
Fig. 3 is the impart knowledge to students strange nested plates synoptic diagram of time spent of the present invention;
Fig. 4 makes the strange nested plates synoptic diagram of scientific research time spent for the present invention;
Fig. 5 is an even nested plates synoptic diagram one of the present invention;
Fig. 6 is an even nested plates synoptic diagram two of the present invention;
Fig. 7 is a strange nested plates integrated circuit diagram of the present invention;
Fig. 8 is even nested plates universal integrated circuit figure of the present invention;
Label declaration among the figure:
The 1st, strange nested plates, the 2nd, even nested plates, 3 strange nest card pig's tongues, the 4th, strange nested bottom plate frame, the 5th, bulb commonly used, the 6th, power supply, the 7th, single-pole double-throw switch (SPDT), the 8th, high level is connected special line, the 9th, connection place that binding post d and binding post g are unique with time high level.
Embodiment
According to accompanying drawing and through embodiment the present invention is described further below:
Can know from Fig. 1, Fig. 2; The present invention is made up of strange nested bottom plate frame 4, strange nested plates 1 and even nested plates 2; Strange nested bottom plate frame 4 is a box; Respectively be provided with a strange nest card pig's tongue 3 on two long limits above it, a long side of strange nest card pig's tongue 3 is provided with 10～30 teeth groove, and strange nested plates 1 all is rectangle tabular with even nested plates 2; The length of strange nested plates 1 and width all are slightly less than the length and the width of strange nested bottom plate frame 4 inner edges, and the base length of even nested plates 2 is greater than the width of strange nested bottom plate frame 4 inner edges and be slightly less than two distances between strange nest card pig's tongue 3 relative gullet base.Can know from Fig. 3, Fig. 4 and Fig. 7; Be printed on two-dimentional numerical table on the strange nested plates 1, numerical table first is classified the energy level row as, is printed on the order integer of 0-N downwards by second row; The first behavior jacket layer is capable; Be printed on the order integer of 0-N to the right by secondary series, in the cell of the capable N row of cell to the N of the second row secondary series, be printed on the different positive odd numbers that meet the 3X+1 guess, in strange each cell of nested plates a power supply, a bulb commonly used and a single-pole double-throw switch (SPDT) are installed.Can know from Fig. 5, Fig. 6 and Fig. 8, be printed on two-dimentional numerical table on the even nested plates 2, numerical table first is classified the position row as; Be printed on the order integer of N-0 downwards by second row; The first behavior jacket layer is capable, is printed on the order integer of 0-N to the right by secondary series, in the cell of the capable N row of cell to the N of the second row secondary series, is printed on the different positive even numbers that meet the 3X+1 guess; Take advantage of 2 nested come out continuously by the positive odd number on this table the 0 position; This delegation's positive odd number on the 0th position in the idol nested plates is exactly corresponding to the number family on the strange nested plates, and a power supply, a bulb commonly used and a single-pole double-throw switch (SPDT) are installed in each cell of even nested plates.Electric light on the idol nested plates 2 is pressed the jacket layer series connection, and the electric light on the strange nested plates 1 is by the parallel connection of number family, and the single-pole double-throw switch (SPDT) of using in each cell is realized the light Presentation Function through integrated circuit.The electric light of idol nested plates 2 each row series connection is connected with the electric light in the strange nested plates 1 corresponding unit lattice through the binding post e behind the 1st position, and each all electric light of row is parallel to the binding post d of this row respectively; The single-pole double-throw switch (SPDT) of each row series connection of idol nested plates 2 through behind the 1st position with strange nested plates 1 on the movable contact b of switch connect fixed contact a; Each all switch of row is parallel to the binding post g of this row respectively; Promptly on strange nested plates 1; It is capable to walk to N from the 2nd, all is parallel to binding post d with the other end of each electric light in all cells of delegation, and the fixed contact a of each single-pole double-throw switch (SPDT) is parallel to binding post g; On strange nested plates 1; On the N energy level each binding post d that counts family must and only need with (N-1) energy level in the some cells of corresponding number family the binding post e of that electric light connect; On the 0th energy level (the 2nd row), binding post d must connect with binding post g, and is d and two unique connections place of binding post of g; Shown in (9) among Fig. 7, each binding post d and binding post g that counts family (the 3rd walk to N capable) of all the other each energy levels can not connect.
In Fig. 7 and Fig. 8, electric light is an electric light commonly used, and switch is a single-pole double-throw switch (SPDT), at electric light L
16In the cell of place, a and b break off heel c and connect, and then direction of current is a → c → power supply → d → L
16→ d → L
13→ d → L
10→ d → L
6→ d → L
2→ d → L
1→ d → g → a forms a closed series circuit, operate as normal, electric light L
16, L
13, L
10, L
6, L
2, L
1All luminous, show electric light L
16The angle paddyization process and the operation result thereof of the positive even numbers 1108 in the cell of place are
1108→554→277→13→5→1.
Showing the working rule after finishing, is that the fixed contact a and the movable contact c of single-pole double-throw switch (SPDT) breaks off, and connects with movable contact b again, promptly resets.
Attention: use " 3X+1 guesses scientific demonstrator ", use arbitrary single-pole double-throw switch (SPDT) to show the angle paddyization result of a positive integer, must reset after the end, promptly a and c break off heel b connection; On the different positions of same jacket layer, can only use a single-pole double-throw switch (SPDT) at every turn.
Below through instance the method for making of two-dimentional numerical table in strange nested plates 1 and the even nested plates 2 is further explained:
Method for making 1: " 3X+1 guesses scientific demonstrator " theoretical method for making.
Make the theoretical method of " 3X+1 guess scientific demonstrator ", need to make earlier two-dimentional numerical table, matching integrated circuit again, key is to make two-dimentional numerical table, be exactly make strange nested and even nested; Difficult design respectively can with strange nested and the integrated circuit of nested coupling by chance.
Very nested: carry out the computing of standard angle paddy, positive odd number 3,5,7,9 ..., 2
k-1,2
k+ 1 jiao of paddyization is obtained the energy level of each positive odd number, earlier 1,3,5,7,9 ..., 2
k-1,2
k+ 1 is divided into 0,1,2 ..., N different energy levels on each energy level, counted the cover source of family to minimum positive odd number as I, takes advantage of 4 to add 1 continuously, different jacket layers, ascending from left to right arrangement is nested into I and counts family; Again the minimum positive odd number in the remaining positive odd number as the cover source, take advantage of 4 to add 1 continuously, different jacket layers, ascending from left to right arrangement is nested into II and counts family; Circulation is carried out.The 0th energy level has only a unique positive odd number 1, counts family as the 0th energy level I, also as the cover source of the 0th energy level; The 1st energy level has only I to count family 5,21,85,341 ....From the 2nd energy level, infinite a plurality of several families are all arranged, each count family by the cover source from small to large layout become I, II, III, IV ... each counts family, processes very nested, as shown in Figure 4.
Idol is nested: strange nested in each each positive odd number of counting family all take advantage of 2 continuously, line up the the 0th, the 1, the 2nd, the 3 from the bottom to top ..., each position of N, the idol of processing different energy levels difference number family is nested, like Fig. 5 and shown in Figure 6.
Strange nested and strange nested surface-mounted integrated circuit coupling, as shown in Figure 7, process strange nested plates, level is inserted in the strange nested bottom plate frame; The nested nested universal integrated circuit plate coupling of idol with idol, as shown in Figure 8, process even nested plates, vertically insert in two relative teeth groove of bayonet socket bar of strange nested bottom plate frame, press energy level and arrange, process the present invention.Especially, the demonstration device without integrated circuit is simple type " 3X+1 guesses scientific demonstrator ".
Method for making 2: " 3X+1 guesses scientific calculator " general method for making.
Make " 3X+1 guesses scientific demonstrator " with conventional method; Mainly be to make unique be present in natural " very nested "; Use " very nested "; Make easily " idol is nested ", key is that each count the cover source of family on each energy level of definite " very nested " lining, and the surface-mounted integrated circuit that matees with " very nested " and " even nested " is produced respectively in design.
(1) judgement and the nested rule thereof in cover source
1, the judgement in cover source: if positive odd number x satisfies formula y=(x-1) ÷ 4, and nonnegative number y is not the positive odd number greater than 1, and then x is the cover source. for example, (37-1) ÷ 4=9, (9-1) ÷ 4=2, (5-1) ÷ 4=1, (1-1) ÷ 4=0,
So 4
k+ 1 type of positive odd number 37 is not the cover source, 4
k+ 1 type of positive odd number 9,5 and 1 all is the cover source; 8
k+ 3 and 8
k+ 7 types of two types of positive odd numbers all are the cover sources also, and k is a natural number in the base.
2, the classification in cover source: the cover source is divided into primary cover source and derives two types in cover source, with the primary cover of symbol " zero " expression source, representes to derive the cover source with symbol " △ " or " ".
3, the nested rule in cover source: can not the recursion nested cover source that goes out with energy level, primary cover source, for example, with symbol " zero " represent 4
k+ 1 type of positive odd number 1 and 5 all is primary cover source.Because 1 energy level is 0, can not participate in angle paddyization computing, through 1 substandard angle paddy computing, but the minimum positive odd number of angle paddyization is 5, is the primary cover source on the 0th energy level so can confirm positive odd number 1 naturally, positive odd number 5 is the primary cover sources on the 1st energy level.The cover source of deriving with symbol " △ " expression; Be to have recurrence relation; Obtained and the high cover source of an energy level with algorithm 2 positive odd number of 1 surplus mould 3 minimum on the low-lying level; Take advantage of 64 to add 49 afterwards continuously, just can be nested go out with infinite a plurality of covers source on the energy level, wherein minimum positive odd number is exactly the cover source of being obtained of deriving; The cover source of deriving with symbol " " expression; Be to have recurrence relation; Obtained and the high cover source of an energy level with algorithm 1 positive odd number of 2 surplus mould 3 minimum on the low-lying level, taken advantage of 64 to add 35 afterwards continuously, just can be nested have gone out with infinite a plurality of covers source on the energy level; Wherein minimum positive odd number is exactly the cover source of being obtained of deriving, after algorithm 1 is described in algorithm 2.
(2) ask the cover source on the low-lying level by the positive odd number on the high level, make " very nested "
Appoint and get a positive odd number x, confirm the energy level of x.X is carried out the paddy computing of n substandard angle, and x angle paddyization, the energy level of trying to achieve x is natural number n; And obtain each positive odd number from n energy level to the 0 energy level, and each positive odd number is subtracted 1 back continuously divided by 4 computing, judge the cover source of also confirming on each energy level; All take advantage of 4 to add 1 continuously to each cover source (except 1) again; Be nested into a number family of different jacket layers, obtain from n energy level to the 0 energy level, respectively having " very nested " of a number family, as shown in Figure 3.
(3) ask the cover source on the high level by the positive odd number on the low-lying level, make " very nested "
By following algorithm 1, algorithm 2 and algorithm 3, since the cover source 5 of the 1st energy level, according to all positive odd numbers on the low-lying level; Can obtain all the cover sources on the high energy level; Afterwards, all take advantage of 4 to add 1 continuously, be nested into several different several families the positive odd number in each cover source; Just processed " very nested " of " 3X+1 guesses scientific demonstrator ", as shown in Figure 4.
(4) usefulness is asked the step that the way in cover source is made " 3X+1 guesses scientific demonstrator "
The 1st step: at random selected positive odd number, and the energy level of definite this positive odd number.
For example; The positive odd number of choosing arbitrarily is 405; Carry out 7 substandard angle paddy computings to 405; Just can get 405 jiaos of paddyization of positive odd number
and confirm that thus the energy level of positive odd number 405 is 7.
The 2nd step: the positive odd number by on " very nested " high level is asked the cover source on the low-lying level.
For example, by the positive odd number on the 7th energy level 405, obtain the cover source on the 7th to the 0th energy level: at the operation result 405,19,29 of the 1st step angle paddyization 405; In 11,17,13,5,1; Each odd number is subtracted 1 back continuously divided by 4 computing, judges and whether definite positive odd number x is the cover source by formula y=(x-1) ÷ 4, the cover source of the 7th energy level to the 0 energy level is respectively 25,19,29; 11,17,3,5,1.Wherein, the cover source 25 on the 7th energy level is by (405-1) ÷ 4=101, (101-1) ÷ 4=25, and (25-1) three formulas of ÷ 4=6 are judged and are obtained; Cover source 3 on the 2nd energy level is by (13-1) ÷ 4=3, and (3-1) two formulas judgements of ÷ 2=0.5 obtain, and remaining number is respectively the cover source of place energy level.
The 3rd step: the positive odd number by on " very nested " low-lying level is asked the cover source on the high level.
For example; Ask the cover source 33 on the 8th energy level by the cover source 25 on the 7th energy level: because 25 are positive odd numbers of 1 surplus the mould 3; So by algorithm 2, take advantage of 4 earlier, get even number 100; Subtract 1 back again divided by 3, on the 8th energy level cover source 33 (here: the 33rd, have nested rule take advantage of continuously 64 add 49 the minimum cover source of deriving).
Ask the cover source 177 on the 9th energy level by the cover source 33 on the 8th energy level: because 33 are multiples of 3, so, take advantage of 4 to add 1 earlier by algorithm 3; Become surplus the mould 31 positive odd number 133; So by algorithm 2, take advantage of 4 again, become even number 532; Subtract 1 back again divided by 3, on the 9th energy level cover source 177 (here: the 177th, have nested rule take advantage of continuously 64 add 49 the minimum cover source of deriving).
In like manner: try to achieve the cover source 945 on the 10th energy level by the cover source 177 on the 9th energy level; ....Carry out thus, can forever ask down.
The 4th step: make " 3X+1 guesses education demonstrator ".
10 the cover sources 1,5,3,17 on the 0th energy level to the 9 energy levels of having obtained; 11,29,19,25; 33,177 ... vertical setting of types is on the 0th jacket layer, from the 1st energy level; All take advantage of 4 to add 1 computing continuously to each cover source, each jacket layer, ascendingly from left to right be arranged in " very nested " that each energy level has only a number family; Each positive odd number in " very nested " all takes advantage of 2 continuously; Extend to the space; Each position, on ascending from bottom to top 10 " idol is nested " distinguishing with energy level that are arranged in, Manufactured " very nested " and each energy level existing one " idol is nested "; Totally 1 " very nested " and 10 " idol is nested " constitute " 3X+1 guesses education demonstrator ".
" very nested " as shown in Figure 3 is another " very nested " of " 3X+1 guesses education demonstrator ", and 11 cover sources on its 0th energy level to the 10 energy levels are respectively 1; 5,3,35,23; 15,81,433,577; 769,1025, each cover source all takes advantage of 4 to add 1 continuously, has just obtained this " very nested ".In theory, " very nested " in " 3X+1 guesses education demonstrator " is not unique because use different with the data of research, so have infinite a plurality of as shown in Figure 3 different very nested.
For example, construction drawing 3 by algorithm 1, takes advantage of 2 minimum positive odd number 5 surplus the 1st energy level mould 32 to become 10 earlier, subtracts 1 back divided by 3, the cover source 3 on the 2nd energy level; By algorithm 1, take advantage of 2 minimum positive odd number 53 surplus the 2nd energy level mould 32 to become 106 earlier, subtract 1 back divided by 3, the cover source 35 on the 3rd energy level; By algorithm 1, take advantage of 2 minimum positive odd number 35 surplus the 3rd energy level mould 32 to become 70 earlier, subtract 1 back divided by 3, the cover source 23 on the 4th energy level; By algorithm 1, take advantage of 2 minimum positive odd number 23 surplus the 4th energy level mould 32 to become 46 earlier, subtract 1 back divided by 3, the cover source 15 on the 5th energy level; By algorithm 3, being 3 multiple on the 5th energy level and being that minimum positive odd number 15 takes advantage of 4 to add 1 earlier, become surplus the mould 31 minimum positive odd number 61, take advantage of 4 to become 244 again, subtract 1 back divided by 3, the cover source 81 on the 6th energy level; By algorithm 3, being 3 multiple on the 6th energy level and being that minimum positive odd number 81 takes advantage of 4 to add 1 earlier, become surplus the mould 31 minimum positive odd number 325, take advantage of 4 to become 1300 again, subtract 1 back divided by 3, the cover source 433 on the 7th energy level; By algorithm 2, take advantage of 1 minimum positive odd number 433 surplus the 7th energy level patrix 34 to become 1732 earlier, subtract 1 back divided by 3, the cover source 577 on the 8th energy level; By algorithm 2, take advantage of 1 minimum just strange 577 surplus the 8th energy level patrix 34 to become 2308 earlier, subtract 1 back divided by 3, the cover source 769 on the 9th energy level; By algorithm 2, take advantage of 1 minimum positive odd number 769 surplus the 9th energy level patrix 34 to become 3076 earlier, subtract 1 back divided by 3, the cover source 1025 on the 10th energy level.Play the 10th energy level from the 1st energy level then, all take advantage of 4 to add 1 continuously, get each jacket layer, be nested into the number family on each energy level, process the critical piece " very nested " that can constitute " 3X+1 guesses education demonstrator " each cover source, as shown in Figure 3.Application drawing 3 is produced Fig. 4, Fig. 5 and Fig. 6 easily.
The 5th step: make simple type " 3X+1 guesses scientific demonstrator ".
In " very nested " of " 3X+1 guesses education demonstrator ", from the 1st energy level, multiple that can 3, only surplus low-lying level patrix 31 with mould 3 surplus two types of positive odd numbers of 2; Just can obtain the infinite a plurality of covers source on the high level respectively, so infinite, and each cover source all takes advantage of 4 to add 1 continuously, is nested into different several families; All count the size that the cover source is pressed by family on each energy level, the ascending I that is arranged in, II, III; IV ... each counts family, " very nested " processed like this; Be " very nested " of " 3X+1 guesses scientific demonstrator ", as shown in Figure 4, be unique existence.Again all positive odd numbers of the different number of each energy level family in this " very nested " are all taken advantage of 2 continuously, extend, process several " idol is nested " to the space.In theory, can be present in natural this " very nested " and forms simple type " 3X+1 guesses scientific demonstrator " by unique with direction demonstration and symbol display function with several " idols nested ".
The 6th step: process " 3X+1 guesses scientific demonstrator ".
With " very nested " shown in Figure 4 and surface-mounted integrated circuit coupling, process " strange nested plates ", with " idol is nested " and surface-mounted integrated circuit coupling, process " even nested plates ".Wherein, A bulb commonly used, a power supply and a single-pole double-throw switch (SPDT) are installed in each cell, with the strange nested plates that " very nested " matching integrated circuit is processed, as shown in Figure 7; With the even nested plates that each " idol is nested " matching integrated circuit is processed, as shown in Figure 8.One " strange nested plates " and several " even nested plates " are formed " 3X+1 guesses scientific demonstrator " with light demonstration, symbol display and direction Presentation Function.
Below be further described through the method for application of instance to patent of invention " 3X+1 guesses scientific demonstrator ":
" 3X+1 guesses scientific demonstrator " demonstration device principle and method has light demonstration, symbol display and direction to show 3 kinds.
1, light shows
(1) light displaying principle
Use the arbitrary single-pole double-throw switch (SPDT) in " even nested plates "; The movable contact b of the single-pole double-throw switch (SPDT) of arbitrary cell in the even nested plates is broken off the back connects with movable contact c, electric current by the fixed contact a of this single-pole double-throw switch (SPDT) to movable contact c, through an interior power supply of this cell; At least connect with the electric light that this cell belongs on each position of jacket layer; Through connecting with the binding post e of the 0th position behind the 1st position, arrive in the strange nested plates, through this electric light; Again with strange nested plates on binding post d connect; On strange nested, the binding post d of the every row of N energy level can and can only and must and only need to connect with the binding post e of the corresponding a certain small cup electric light of (N-1) energy level, and energy level ground of an energy level is from the high level to the low-lying level; Through arriving binding post d behind the electric light in the unique positive odd number 1 place cell of the 0th energy level, connect with g more at last.Afterwards, at least with even nested plates on a switch connect, make electric current pass through the fixed contact a that g arrives the switch of this use later on, form closed series circuit.
Use any single-pole double-throw switch (SPDT) in " strange nested plates "; The movable contact b of the single-pole double-throw switch (SPDT) in the arbitrary cell in the strange nested plates is broken off back and movable contact c connection; To movable contact c, through flowing to binding post d behind power supply in this cell and the electric light, energy level ground of an energy level is from high level to the 0 energy level afterwards by fixed contact a for electric current; Each energy level has and has only an electric light to connect with this single-pole double-throw switch (SPDT); Arrive the binding post e on the 0th energy level at last, count the electric light in the positive odd number 1 place cell of family's the 0th jacket layer through I again after, on strange nested plates binding post d and binding post g connection; Make current reflux arrive the fixed contact a of employed single-pole double-throw switch (SPDT), form closed series circuit.
(2) lamplight display method
For example, the movable contact b of the single-pole double-throw switch (SPDT) of each positive integer place cell breaks off back and movable contact c connection in the demonstration device, just can show the simplest angle paddyization process of this positive integer.For example, in Fig. 5, break off the back to the movable contact b of switch in the positive even numbers 866 place cells and connect, just can show that the process of angle paddyization 866 and result are with movable contact c:
Like Fig. 8 and shown in Figure 7, electric light L
14Movable contact b break off the back and connect with movable contact c, show that the process and the result of angle paddyization 68 does
If electric light L
14The movable contact b of switch and movable contact c reset after breaking off in the cell, and electric light L
11Switch movable contact b breaks off back and movable contact c connection in the cell, just shows that the angle paddyization process and the result of positive even numbers 34 does
2, symbol display
(1) symbol display principle
Infinite a plurality of positive even numbers in the two-dimentional numerical table on each even nested plates on the same high level; Through divided by 2 rudimentary horn paddy computing, can become on the corresponding with it strange nested plates the infinite a plurality of positive odd numbers in the same number family of certain delegation in the two-dimentional numerical table, the infinite a plurality of positive odd numbers on the strange nested plates in any number family; Through 1 substandard angle paddy computing; Can become the same positive odd number on time high level, develop like this, become at last that I counts the positive odd number 1 in the family on the 0th energy level.
(2) computer program product
As intend the inquiry positive odd number 433 how to revert to 1 (paddy changes into 1 at the angle) through " 3X+1 guess " mode; Then directly use strange nested plates as shown in Figure 4; After finding numeral 433, the mode of upwards successively decreasing along energy level just can inquire its return path and be: 433,325,61,23,35,53,5,1.Wherein 433 is that the 7th energy level IV counts in the cover source (jacket layer 0) of family, indicates " III 1. " printed words, and expression 433 results through the computing of a standard angle paddy are that the 6th energy level III counts 325 of family's the 1st jacket layer; Indicate " II 1. " printed words in 325 81 hurdles, cover source of being expert at, expression is through the computing of a standard angle paddy, and existing 81 become the result that the 5th energy level II counts family's the 1st jacket layer positive odd number 61, also have 325 to become the positive odd number 61 that the 5th energy level II counts family's the 1st jacket layer; Indicate
printed words in 61 cover sources 15 of being expert at; Expression is through the result of standard angle paddy computing; Existing 15 become the 4th energy level II counts 23 of family's the 0th jacket layer, also has 61 to become this result 23; Indicate
printed words in 23 hurdles, expression is that the 3rd energy level II counts 35 of family's the 0th jacket layer through the result of standard angle paddy computing; Indicate " I 2. " printed words in 35 hurdles, expression 35 results through the computing of a standard angle paddy are that the 2nd energy level I counts 53 of family's the 2nd jacket layer; Indicate
printed words in 53 3 hurdles, cover source of being expert at; Expression is through the computing of a standard angle paddy; Existing 3 become the 1st energy level I counts 5 of family's the 0th jacket layer, also has 53 to become this result 5; Indicate
printed words in 5 hurdles; Expression is the positive odd number 1 on the 0th energy level through a standard angle paddy operation result; Make 5 to become 1, thereby make 433 to become 1.
As intend the inquiry even number 866 how to revert to 1 (paddy turns to 1 at the angle) through " 3X+1 guess " mode; Then use even nested plates as shown in Figure 5 earlier; After finding numeral 866; The mode of successively decreasing downwards along the position just can inquire it: 866,433, re-use strange nested plates as shown in Figure 4 afterwards, find the numeral 433 after; The mode of upwards successively decreasing along energy level just can inquire its return path and be: 433,325,61,23,35,53,5,1, and therefore 866 modes through the demonstration device symbol display of can trying to achieve revert to 1 path and are: 866,433,325,61,23,35,53,5,1.
3, direction shows
(1) direction displaying principle
The angle paddy coordinate of isotopic number is identical.All isotopic number angle paddy calculating processes are similar, and all isotopic number angle paddy operation results are almost consistent.If the angle paddy coordinate of positive integer Z is that (n m), then through the computing of m step rudimentary horn paddy, passes through the paddy computing of n substandard angle again, just necessarily can become 1 to positive integer Z.
(2) direction display packing
For example; As shown in Figure 6, on this even nested plates, the angle paddy coordinate of the positive even numbers 9236 of the 8th energy level isotopic number V family the 1st jacket layer the 2nd position and the positive even numbers 36948 of the 2nd jacket layer the 2nd position all is (8; 2); So through the rudimentary horn paddy computing of 2 steps, again through 8 substandard angle paddy computings, just can be 9236 and 36948 angle paddyization all.Wherein,, just can become positive odd number 2309 to positive even numbers 9236, become positive odd number 9237 to positive even numbers 36948 through the rudimentary horn paddy computing of two steps; Through 1 substandard angle paddy computing, just can all become 433 to these two positive odd numbers 2309 and 9237, again through 7 substandard angle paddy computings, just can be 433 jiaos of paddyization.
As intend the inquiry positive odd number 433 how to revert to 1 (paddy changes into 1 at the angle) through " 3X+1 guess " mode; Then directly use strange nested plates as shown in Figure 4; After finding numeral 433, the mode of upwards successively decreasing along energy level just can inquire its return path and be: 433,325,61,23,35,53,5,1.Also can be by the direction of letter head " ↑ " indication operation result that makes progress in the energy level hurdle among Fig. 3, find out that directly 433 become 1 by the calculating process of angle paddyization and operation result: 433,325,61,23,35,53,5,1, shown in the data that scribble dark line among Fig. 3.
From the above; Patent 3X+1 guess scientific demonstrator of the present invention; Use simple assembled panel; Solved a present global science difficult problem " 3X+1 guess " and can't express and find the solution the technical matters that waits through simply deriving to calculate, patent of the present invention " 3X+1 guess scientific demonstrator " through simple model and demonstration device with " 3X+1 guess " with mathematical law simply, clear mode derives calculating, expresses and finds the solution; Promote the process of student's study and people's brain activity, can promote on a large scale, also can extensively popularize and use at the kindergarten and all kinds of public area of countries in the world in national middle and primary schools and R&D institution; Manufacturing can be used cheap timber, plastics, aluminium sheet, iron plate, cardboard etc., and simple in structure, manufacturing process is easy, and cost of products is low; Have no side effect, can save the energy in the use, can directly use solar cell, environmental protection; Be convenient to operation, the demonstration effect is obvious, plurality of advantages such as accurate.Squeeze into the international market, with its teaching and scientific value and be in the leading position of international mathematics circle, get into the palace of various countries' science.
Utilize the principle of the invention simultaneously; The design AES; Through carry out the jacket layer of confirming by energy level, position, cover source, several families four direction that the cover source generates carries out nested control; Can produce the four-dimensional coded lock of civil and military, it is quite big to decode difficulty, is financial security, economic construction, nation-building, national defense construction and national security service.
Claims (2)
1. a 3X+1 guesses scientific demonstrator; Constitute by strange nested bottom plate frame (4), strange nested plates (1) and even nested plates (2); It is characterized in that: strange nested bottom plate frame (4), strange nested plates (1) and even nested plates (2) all are rectangle tabular; Respectively be provided with a strange nest card pig's tongue (3) on two long limits of strange nested bottom plate frame (4); One long side of strange nest card pig's tongue (3) is provided with 10～30 teeth groove, and strange nested plates (1) flatly is stuck in the strange nested bottom plate frame (4), and even nested plates (2) is stuck in the relative teeth groove of two strange nest card pig's tongues (3) vertically; In the 3X+1 guess, take advantage of 3 to add 1 to positive odd number, divided by 2, respectively be that the computing in 1 step is called the computing of rudimentary horn paddy to positive even numbers; The process that becomes another positive odd number to a positive odd number is called has carried out the computing of a standard angle paddy; Become to a positive integer at 1 o'clock,, be called this positive integer angle paddyization with regard to the computing of end angle paddy; The number of times that paddyization positive odd number in angle carries out the computing of standard angle paddy is called the energy level of this positive odd number; Be printed on two-dimentional numerical table on the described strange nested plates (1), numerical table first is classified the energy level row as, and this energy level is listed as the order integer that is printed on 0-N by second row downwards, and the first behavior jacket layer of this numerical table is capable, the capable order integer that is printed on 0-N by secondary series to the right of this jacket layer; In the cell of the capable N of cell to the N row of the second row secondary series of this numerical table, be printed on the different positive odd numbers that meet the 3X+1 guess, it is 5,21 that the 0th energy level has only 1 positive odd number, 1, the 1 energy level that 1 row positive odd number is arranged; 85,341 ..., by cover source 5 " take advantage of 4 add 1 " ascending from left to right arrangement continuously; Be nested into unique I and count family, according to algorithm 1, algorithm 2, algorithm 3; By 5,21,85,341; Each counts the cover source of family can to obtain the 2nd energy level, and go out each and count family " take advantage of 4 add 1 " is nested respectively continuously each cover source, and the like, process strange nested plates (1); Be printed on two-dimentional numerical table on the said even nested plates (2); Be printed on positive odd number in each each cell of two-dimentional numerical table the 0th position; It is exactly 1 number family on the strange nested plates (1); This even nested plates (2) goes up in all the other each cells and is printed on positive even numbers, is nested into even nested plates (2) by 1 on the 0th position row positive odd number each continuous " taking advantage of 2 "; Demonstration divided by 2 computing, becomes positive odd number to the positive even numbers on the even nested plates (2) through continuously, and again through the computing of standard angle paddy, the positive odd number angle paddyization on the strange nested plates (1) obtains result 1, demonstrates 3X+1 and guesses establishment;
Aforementioned algorithm 1 means if the positive odd number on strange nested plates (1) low-lying level is 2 a positive odd number surplus the mould 3, then takes advantage of 2, becomes even number, subtracts 1 back again divided by 3, and the positive odd number that obtains is the cover source on the high energy level, and positive odd number minimum in these cover sources is the cover source of deriving;
Aforementioned algorithm 2 means if the positive odd number on strange nested plates (1) low-lying level is 1 a positive odd number surplus the mould 3, then takes advantage of 4, becomes even number, subtracts 1 back again divided by 3, and the positive odd number that obtains is the cover source on the high energy level, and positive odd number minimum in these cover sources is the cover source of deriving;
Aforementioned algorithm 3 means if the positive odd number on strange nested plates (1) low-lying level is 3 multiple, then takes advantage of 4 to add 1, becomes surplus the mould 31 positive odd number, takes advantage of 4 again, becomes even number, subtracts 1 back again divided by 3, and the positive odd number that obtains is the cover source on the high energy level.
2. 3X+1 guess scientific demonstrator as claimed in claim 1; It is characterized in that: the two-dimentional numerical table on the described strange nested plates (1); With corresponding integrated circuit coupling, and a power supply, a bulb commonly used and a single-pole double-throw switch (SPDT) are installed in each cell in the two-dimentional numerical table on the said strange nested plates (1); Two-dimentional numerical table on the described even nested plates (2); With corresponding integrated circuit coupling; And a power supply, a bulb commonly used and a single-pole double-throw switch (SPDT) are installed in each cell in the two-dimentional numerical table on the said even nested plates (2); Bulb commonly used on the said even nested plates (2) is pressed the jacket layer series connection, and the bulb commonly used on the said strange nested plates (1) is by the parallel connection of number family, and the single-pole double-throw switch (SPDT) of using in each cell is realized the light Presentation Function.
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| CN201142156Y (en) * | 2007-11-23 | 2008-10-29 | 马庆华 | Christian Goldbach conjecture demonstration ruler |
| CN101441824A (en) * | 2007-11-23 | 2009-05-27 | 上海市嘉定区第二中学 | Demonstrator for nautical conjecture observation of circular earth |
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| CN201142156Y (en) * | 2007-11-23 | 2008-10-29 | 马庆华 | Christian Goldbach conjecture demonstration ruler |
| CN101441824A (en) * | 2007-11-23 | 2009-05-27 | 上海市嘉定区第二中学 | Demonstrator for nautical conjecture observation of circular earth |
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