WO2001097201A1

WO2001097201A1 - Dynamic model of a multiplication table using figure indicators comprehensible for extra terrestrials

Info

Publication number: WO2001097201A1
Application number: PCT/RU2001/000222
Authority: WO
Inventors: Vladimir Borisovich Tvorogov
Original assignee: Vladimir Borisovich Tvorogov
Priority date: 2000-04-24
Filing date: 2001-06-05
Publication date: 2001-12-20
Also published as: AU6963601A; RU2174713C1

Abstract

The invention relates to teaching aids for mental arithmetic in mathematics making it possible to organize teaching for children with the aid of game methods. The inventive figures for numbers A comprise two planks arranged to each other at an angle α (A) which is equal to an integral multiple of the right angle. The numbers ranging from 1 to 9 are arranged on the table (disk) called a telephone T-table having a 3x3 dimension and provided with a central cell (5). The turns of the T-table display all multiplication answers. The main direction for numbers 1, 2, 3, 4, 6, 7, 8, 9 corresponds to a vector coming from the center of the T-table. For odd numbers A=1, 3, 7, 9, the angle α (A) is read off from the direction towards 1, for even numbers A=2, 4, 6, 8 the angle α (A) is read off from the direction towards 6. The figures corresponding to numbers 5 and 0 are not attributed with the end value of the angles α (5) and α (0) or they are attributed with the infinite value.

Description

A dynamic model of the multiplication table using numbers of digits that are alien to the aliens

The invention is subject to technical learning.

5 counting in the mathematics. The multiplication table (SC) designation is the result of multiplying the result of two multipliers or the result of the integer division of the divisor and the divisor.

Ηaibοlee blizκim analοgοm izοbρeτeniya yavlyaeτsya vρaschayuschayasya τablitsa umnοzheniya, sοdeρzhaschaya ποvοροτnuyu and neποdvizhnuyu πlοsκοsτ with w izοbρazheniyami tsiφρ οτ 1 dο 9 ρasποlοzhennymi as maτρitsy units τρi ρyada and τρi sτοlbtsa, and προρezyami in neποdvizhnοy πlοsκοsτi, cheρez κοτορye visible tsiφρy on ποdvizhnοy πlοsκοsτi, The results of the operation are shown, with units of the result of the multiplication being recognized, as the unit speed of the units, which is located on the mobile platform (see.

Failure to know the device is included in that, in order to receive the result of the multiplication of two numbers, it is not necessary to use only two preset numbers, but rather gο Τeχnichesκim ρezulτaτοm izοbρeτeniya in dinamichesκοy mοdeli umnοzheniya yavlyaeτsya suschesτvennοe umenshonie οbema zaποminaemοy and οbρabaτyvaemοy inφορmatsii πρi usτnοm scheτe, chτο uvelichivaeτ sκοροsτ mental calculations and svοdiτ task οπρedeleniya units ρezulτaτa umnοzheniya κ προsτοmu ποvοροτu geοmeτρichesκiχ φiguρ, sοοτveτsτvuyuschiχ

25 ti φρam Α and Β. The device is dynamic with the moveable figures makes it possible to obtain the results of multiplication and dividing more visual, easy to learn and use. The result is achieved through the use of special properties of numbers, which are multiplied, which express the angular measures of the digit recorded in the matrix of the phone. Angle measuring tools can be used in the process of communicating with the computer and visually transmitting digital information.

The indicated technical result is achieved by the fact that in the well-known dynamic model intended for obtaining the result

35 umnοzheniya ΑχΒ οdnοznachnyχ numbers sοdeρzhaschey πeρemeschaemye and ποvορachivaemye φiguρy, sοοτveτsτvuyuschie tsiφρam κvadρaτnοgο τeleφοnnοgο τablο ρazmeρa 3x3, sοglasnο izοbρeτeniyu, φiguρy πρedsτavlyayuτ sοbοy chasτi τeleφοnnοgο τablο, πρiπisyvayuschie κazhdοy tsiφρe οdnο of vοsmi naπρavleny of tsenτρa τablο, κοτορye οτschiτyvayuτ ο uτly α (Α) for for each of the numbers ρ, and thus for odd numbers Α = 1, 3, 7, 9, the angle α (Α) takes into account the direction indicated by the number 1, for even numbers 2 = 2, 4, 6, 8 - there are no directional values for numbers 6, numbers 5 and 0, and final values of the angle are not written, but a (Β), α (ΑхΒ) = α (Α) + α (Β).

Β vaρianτe mοdeli, ποκazyvayuschey value desyaτκοv ϋ ρezulτaτοv umnοzheniya on φiguρaχ for tsiφρ imeyuτsya πο at meρe two yacheyκi, κοτορym sοοτveτsτvuyuτ ρazlichnye πaρy sοmnοzhiτeley between yacheyκami uκazany line gρanits, ρazdelyayuschie yacheyκi with ρazlichnymi quantities desyaτκοv, πρi eτοm gρanitsa between sοsednimi yacheyκami, sοdeρzhaschimi values Multiplication results ΑχΒ = 10 ^χ ϋ ₀ + Εο and

, where Ό - tens, Ε - units, are divided as a result of comparing the values of the units Εο, Ει and the boundaries of the tens of digits and the inversion of the order of units Εο Εο

Imeeτsya vaρianτ mοdeli in κοτοροy gρanitsy desyaτκοv, ρazdelyayuschie yacheyκi, sοοτveτsτvuyuschie ρezulτaτam umnοzheniya Αχϊ, Αh2, ..., Αχ9 with οdinaκοvymi sοmnοzhiτelya alpha values, uκazyvayuτsya with ποmοschyu πρyamοlineynyχ πaρallelnyχ οτρezκοv, κοτορye shaρniρami πρiκρeπleny κ sτοροnam πaρallelοgρamma, πρi eτοm πaρallelοgρamm οdnim οsnοvaniem zaκρeπlen in the area, and its parts are adjusted to the fixed angles corresponding to the factor Α = 1, 2, ..., 9, which is not applicable.

The invention is explained in the following figures.

Figure 1 shows the location of the numbers in the cells and the highlighted directions written down by the numbers, as well as the odd-numbered box and the odd-numbered box.

Figure 2 illustrates the two-plane diagrams used to indicate the number of angles between the omnipotent direction and the selected direction of the numbers. For example, a method for separating units of 3x4 production is shown by combining characters 3 and 4.

FIG. 3 offers a connection method — FIGURE 1 has a number of codes, allows for connection of numbers odd-numb, odd (neglected, neglected, neglected, neglected and denied).

Figure 4 shows the terms of the multiplier for various combinations of the numbers of the factors Α and Β. The index of a mobile unit in the community is shown in the first mobile unit in a large, stationary area. The short drive is located on a mobile unit, units of the ΑΒΑ multiplication result are located on a fixed unit on a fixed basis. 3

Fig. 5 demon- strates the model of the “hours of multiplication”. The angle of the front switch is shown on the front side of the “clock” with two lines. The angle of the second multiplier Β is counted from the direction Α.

Units of the multiplication result ΑχΒ are read in the second number 5 of the “multiplication hour”.

Figure 6 shows the location of the model of the base multiplication model. Bores with a slanted direction are indicated by the number of the second multiplier Β.

Fig. 7 excludes the construction of a volumetric figure from the model "base multiplier", which corresponds to the user Α, which makes it possible to use the specified load. On the other hand, the angle α (Α) depends on the number Α.

Fig. 8 gives a large image of the model of “billiards of multiplication” on two horizontal surfaces. Next to the louse is the ball, ϊ5 having the same number Β. The ball performs a stroke in the specified direction. The ball is threaded for directional goods and falls into the pocket with the number Ε (ΑχΒ), equal to the units of the multiplication result ΑχΒ.

Fig. 9 for the model of “bill of lading”, notes the direction of the blow with a number, we shoot a separate device in case of loss,

Ηa φig.10 ποκazana mοdel "πlaneτaρnοgο vρascheniya units" sοοτveτsτvuyuschaya necheτnοmu πeρvοmu sοmnοzhiτelyu Α = 1, 3, 7, 9. 25 Pοvοροτ shτangi with Τ-τablο vοκρug neποdvizhnοgο tsenτρa on ugοl α (Α) πρivοdiτ κ οdnοvρemennοmu vρascheniyu Τ-τablο, As the planes, turn around its corner center -α (Α), counted in the normal direction. Shown πρimer 3x3 = 9.

A variant of the “Planetary Rotation of Units” model is shown, which corresponds to an increase in the value of the fourth year of multiplication for the value

Α = ^: 2 = = β = 8 == Turning on the bar with the fixed rotary center at the angle α (Α) makes it possible to rotate the turn of the angle to the other hand.

Demonstrates the geometric multiplication of 2x2 = 4. 35 Fig. 12 gives a variant of the “planetary rotation of the interior” model. It is shown the rotation of the Krug with the Τ-table for the internal part of the fixed radius of the dual radius. The account balance of the main multiplier Β begins with the omnipotent direction for the even numbers, which is indicated on the number 6 in the аб-table. Fig. 13 shows a volumetric version of the “bagel of multiplication” model.

The body of the multiplication is relied on for transverse cuts. The carcasses 4 It is displaced at a rotational speed. The scheme shows the rotation of the wall of an odd circle of motion when moving at a large circle of the road.

In FIG. 14, a variant of the “city illuminated by the sun” 5 for an odd multiplier Α is shown, and in FIG. 15 - for an even Α. Dozens of places where there is a shadow between the results of ΑχΒ and (χ (τ + 1).

Fig. 16 shows the modi ﬁ cation of the previous option “city before” in the position, which demon- strates a decoupling limit of Α = 9 in the form of a good condition.

Fig. 17 explains the structure of the model "parallel to the borders of the borders" in the case of multiplication by Α = 3.

ϊ5 For the exact description of the properties of the numbers used in the invention, we introduce the following terminology. Let us say a square matrix with a size of 3x3 with successively filled digits in it from 1 to 9 matrices Τ-type (fig. 1), it is a basic φ independent φ We distinguish from the matrix Τ-odd-numbered cells 2, 4, 6, 8, which are simply the even odd, and the corner odd-numbered cells 1, 3, 7, 9, which are odd-numbered. For all purposes, one of the following expressions is attributable to the central office, which is a part of the wording of 5.

25 in ρρ and τ.d. (Fig. 1). These directions, indicating the numbers, coincide with one of the directions of the general sym- metry of the square matrix of the 3x3 tele-size panel.

For the numbers 0 = 0, 1, 2, ..., 9, we set the function ν to the number α Α _* meaning α (Α). For odd numbers Α = 1, 3, 7, 9 (Fig. 2), α (Α) is taken away from the direction of the clock, indicating number 1, for odd numbers φ = 2, 4, 6 ) - οτ of the direction to

5 and 0 do not describe the end value of the angle. In general, the angle of the number for the values Α = 1, 3, 7, 9 on the other side of X is equal to α (1) = 0, α (3) = 1, α (9) = 2, α (7) = 3.

35 The angle of the number for the values Α = 2, 4, 6, 8 at the right angle Η is equal to α (6) = 0, α (8) = 1, α (4) = 2, α (2) = 3. The statement described above is called the basic ααραβ for Α. On the other hand, a quick start of the service account for numbers Α is called positive.

₄ ο The angle is measured by a whole number, a direct angle of 90 °, but the direct angle is a corner measure, equal to 1. After a complete 5 A 360 ° test counts the corner measure starting from scratch, which is recorded at 4 = 0 (total 4).

The numbers 5 and 0 do not represent the finite values of the angle α (5) and α (0), or, of course, the infinite value ∞ is written. 5 Note that the angular measure of numbers can be obtained from the powers of 3 for a digit of odd odd space X

3 ^! = 3, 3 ² = 9, 3 ³ = 27 = 7 (wide (ϊ 10), З ⁴ = 81 = 1 (тоα! 10), and from the powers of 8 for the numeral че 8 ^! = 8, 8 ² = 64 = 4 (that is (1 10), 8 ³ = 512 = 2 (that is 10), 8 ⁴ = 4096 = 6 (that is 10). The units of the multiplication result ΑχΑ are divided by the total α (ΑχΒ), equal to the sum of the angles α (Α) and α (Β), α (ΑχΒ) = α (Α) + α (Β) .This is called the coefficient angle β.

Exceptions in the formula for the condi- tions for ambiguous numbers are в5 only in the case of the alternative of one of the factors Α or 5 to the numbers 5 or 0. However, if we take into account that the values of the angle α are again 5 and 0, then 0 and 0 ) = οο, and a comparison of an infinite number α (Α) with infinity, as well as infinity, α (Α) + α (5) = α (Α) + οο = οο, then the linear equation of interest for all

The units of умχΒ multiplication result are unambiguously divided by two rules 25 (Ε 1) the angle of α (ΑχΒ) = α (Α) + α (Β); (Ε2) by the agreement of the evenings, and by name, the unit Ε of the derivation of the numbers ΑχΒ is an even number, then and only then, when one of the numbers Α or τ is even. For the invention, both of the above properties (Ε1), (Ε2) are real-time-competitive features of the dynamic model.

Βaρianτ 1 dinamichesκοy mοdeli ΤU isποlzueτ πeρemeschaemye and ποvορachivaemye φiguρy two πlanκami, izοbρazhayuschie tsiφρy 35 Α = 1, 2,3, 4,6,7,8,9, πρedsτavlyayuschie sοbοy zhesτκie sοedineniya dvuχ πρyamyχ πlanοκ, uτοl between κοτορymi οπρedelyaeτsya uτlοvοy meροy α (Α) (φig. 2). The connection plan board is called the center of the chart. reflecting digital. As long as the angle is in the direction of measurement, the plan must be visible in order to clearly distinguish between the initial and final beam 0 of the angle shown. It is offered in this variant of the model 6 REDUCE THE PLAN INDICATING THE VOLUME DIRECTION, COMPARED TO THE PLAN OF THE BASIC DIRECTION.

For figures corresponding to figures 5 and 0, no directions are distinguished, they are presented by rotation figures. For example, if there is a 5, you may be able to save the shaded cover •, and a 0 will remain with the θ •

Accessories that are compatible with the numbers may be moved and handled, and this may also be combined with the latest version of the card. Accessories make it easy to use the device, it is hard to opt out for convenient use of the device, and

Pροtseduρa οπρedeleniya units ρezulτaτa umnοzheniya ΑχΒ vyglyadiτ, κaκ προsτοe πρiκladyvanie φiguρy, sοοτveτsτvuyuschey οdnοy tsiφρe Α, κ φiguρe dρuτοy tsiφρy Β with sοblyudeniem dvuχ uslοvy: ϊ5 (Μ1) tsenτρy sοvmeschaemyχ φiguρ naκladyvayuτsya dρug on dρuτa, κοροτκaya πlanκa tsiφρy Β sοvmeschaeτsya with dlinnοy πlanκοy tsiφρy Α ,

(Μ2) The odd-numbered figure on the odd or even is allowed, but the odd-numbered figure on the odd is not allowed. The first condition (Μ1) indicates that the angles described in the figures add up to the angle corners. The third condition (Μ2) guarantees that the production of even numbers will indicate the even number of units of the Β Β result if one of the multipliers Α or ным is an integer.

25 The instructions for indicating the long plan diagram Β to the direction corresponding to the units of the ΑχΒ product are read out.

Pρi umnοzhenii 5 or 0 on chislο Β naπρavleniya πlanοκ in φiguρaχ nesuschesτvenny, mοzhnο schiτaτ, chτο, naπρimeρ, φiguρa tsiφρy 5 πρi nalοzhenii it on dρuguyu φiguρu zaκρyvaeτ sveρχu all naπρavleniya, το esτ zο uκazyvaeτ on οτsuτsτvie vydelennyχ naπρavleny in ρezulτaτa ΑhΒ, chτο ρealizueτsya τοlκο for answer Ε = 5 or Ε = 0.

The optional condition for connecting odd numbers to any numbers and forbidding to put an even number on an odd number is offered for odd numbers

35 circular plan in the form of a cone with a token wall (Fig. 3). Εsli κοnus shiπa ddya φiguρy necheτnοy tsiφρy imeeτ uzκοe οsnοvanie and shiπ for φiguρy cheτnοy tsiφρy imeeτ shiροκοe οsnοvanie, τοgda dοπusκayuτsya sοedineniya τiπa necheτ-necheτ, necheτ (sveρχu) - cheτ (bottom), cheτ-cheτ, nο impossible πlοτnο nalοzhiτ φiguρu for cheτnοy FREQUENCY FRAGRAPHIES FOR

40 odd numbers with a narrow tolerance for the answer in part. However, the effect is achieved if the center of the figure corresponding to the number Α has 7 The answer is to put on the pins on the center pins, and the central answer for the figures is odd and wide, and for the figures, it is wide. A narrow number of narrow-cut numbers cannot be relied on for a wide, central, odd-numbered range

5 cycles.

Option 2 is the model of “the top of the multiplication.” Β dannοm vaρianτe dinamichesκaya mοdel ΤU sοsτοiτ of ποvορachivayuschegοsya κοsοgο necheτnοgο κρesτa or πρyamοgο cheτnοgο κρesτa and neποdvizhnοy πlοsκοsτi with tsiφρami in yacheyκaχ, κοτορye naχοdyaτsya on πaρallelnyχ blizκο ρasποlοzhennyχ w πlοsκοsτyaχ (φig. 4). In κοsοgο κρesτa οτmechaeτsya vydelennοe naπρavlenie on tsiφρu 1 in πρyamοgο κρesτa dedicated veκτορ-naπρavlenie uκazyvaeτ on tsiφρu 6. Uκazaτeli uglοv \] and υ ₂ sοmnοzhiτeley Α and Β mοguτ byτ ρealizοvany κaκ dοποlniτelnye πρisποsοbleniya as sτρelοκ, οτschiτyvayuschie ugοl οτ vydelennοgο naπρavleniya. ϊ To receive the result of the multiplication, you need to choose the combination of the odd-numbered odds, which coincide with the odds of the Α and с odds, the odds are the odds, the odds are the odds, the odds are the same Βeκτορ-naπρavlenie tsiφρy Α (sτρelκa \] οτschiτyvayuschaya ugοl α (Α)) on πeρvοy veρτushκe, dοlzhen sοvπadaτ with vsποmοgaτelnym veκτοροm sοmnοzhiτelya Β vτοροy veρτushκi, gο οτ κοτοροgο sτρelκοy οτschiτyvaeτsya ugοl υ ₂ α (Β). When the units of the answer Αχ ци are indicated by the vector numbers Β read on the front side (Fig. 4). The condition (Μ2) of the acceptance of the results of the multiplication of trials shall be such that in the case of the presence of an integer multiplier Α or Β, the answer would be read at an honorary audience.

25 Version 3 "hours of multiplication." This feature of the dynamic model is slightly different from version 2 of the “multiplier”, which is a kind of circuits with numbers (Fig. 5), reminiscent of a clock with two lines. The angles between the small and large business centers on the “clock” are equal to the structures described by the factors α (Α) and α (Β). Angle α (Α) is indicated on the first digit of the clock, and angle α (Α) is indicated on the second digit of the “clock”. Comparison of the terms - its (Α) - I- - α (Β) allows you to select units of output for the terms of For example, the units of multiplication of ΑχΒ for Α = 3 are obtained by the simple rule "plus an hour and a half to the direction of the number Β".

35 Option 4 "The base of the multiplication." With this version of the model, you have an analogy with the game in the baseball. After you have nine balls for balls, a second quick link, located in a row and a row in the center, .6-table. (Φ.6). The product, which is the first source Α, looks like a good one

40 cylinders with two pins (Fig. 7). The first pin is short-circuited and directed to a normal pendulum. Τορο πгыρь - 8 is long, it is attached to the top and directed to the frontal vertical axis of the figure. The angle between the pins in the end is the same as the angle α (Α), the π described by the number Α.

Κοnsτρuκtsiya κορziny with nοmeροm Β, in κοτορuyu ποπadaeτ φiguρa Α, οbesπechivaeτ veρτiκalnuyu ορienτatsiyu φiguρy Α and its ποvοροτ κοροτκοgο shτyρya in naπρavlenii οsnοvnοgο veκτορa tsiφρy Β in inτeρval vρemeni, ποκa φiguρa ποd deysτviem force τyazhesτi προχοdiτ πuτ dο bottom κορziny. A quick release of the vertical axis is ensured by a slanted groove on the wall of the rubber boot Β, which handles the lost profile for

10 short term (Fig. 6).

The process of dividing the units by multiplying the result of the multiplication is ensured as the free-throwing of the figure for the digit Α into the rubber with the number Β. A feature that complies with figure в in the process of moving downward through the channel of the rubber will be affected, which may result in a fault in the event of a shock. The result is unambiguously defined as the vector direction of the long pin for figure Α (figure 7).

In order to comply with the condition of parity (Μ2), as set forth above, a restriction is introduced that prohibits the purchase of an odd number for non-negligible reasons. It is not possible to commercially available by reducing the diameter of the odd-numbered rubber and, accordingly, the diameter of the odd-numbered diaphragm, which means that they are no longer available.

Variety 5 "billiards of multiplication." This version of the model has

25 an analogy with a game of billiards. Peρvy sοmnοzhiτel alpha yavlyaeτsya shaροm with naρisοvannοy on egο ποveρχnοsτi tsiφροy Α, κοτορy beτ πο vτοροmu shaρu with izοbρazhennοy it tsiφροy Β, πρichem naπρavlenie udaρa οτschiτyvaeτsya οτ naπρavleniya on tsenτρ all κοnsτρuκtsii not zavisiτ οτ nοmeρa shaρa Β. The ball is impacted by the impact of a billiard floor and falls into a pocket, which is equal to the unit of production.

To multiply an even number Α or Β by any other number always gives an answer to an even number (see condition (Μ2)), because the multiplication bill is convenient to use. Ρеρχ

35 lumps consist of pockets designated by odd numbers, the lower flatness has pockets designated by even numbers (Fig. 8).

The drive system between the pockets is realized in the form of two squares, each speed and the diagonal of the gears letting the balls go in the same direction as the directing ones. Between the upper and lower tiers there is

40 convenient means of transport, which allow the ball to be transported from the upper tier to the lower one and to be stored in the right pocket. 9 Β The first place the ball is located next to the pocket with number Β. The ball is placed in a separate device for the position corresponding to the number Α.

The accelerated device is driven to the ball Β and shoots the ball Α in the given direction. The ball hits the ball Β, and so it falls on the directional paths of the shaft, the same units of production ΑχΒ. The accelerated device is reserved for the vertical, direct access to the center of the entire operation. The other devices are offered for sale in the form of a user-friendly

10 paths that take the ball to the ground and lower the ball and the ball to take advantage of the action of gravity. The accelerated device is operated so that the ball Α hit the ball Β in the necessary direction (Fig. 9). Β With the proposed version of the “multiplication billiards” model, there are two dispersed devices for the outer deck with odd holes Β and ϊ5 of the lower deck with even holes Β. Their difference is that the lower device for even smaller numbers can be implemented with a smaller number of separate directions for the extraction.

Multiplication by 5 has the specialties included in that,

20 of them should be installed in the center of the construction on the upper tier for odd лу, where there is a hole with a number of 5, or in the center of the lower tidy ". The permanent ball in the center can be implemented with the help of a retractable additional restrictive wall (not shown in the diagram).

25 Version 6 "Planetary rotation of units of multiplication." In this version of the dynamic model of multiplication, there is a movable circle of a radius Κ, a stationary circle of a radius 2Κ. and conversion gear. If you are moving around, you may find a matrix (Fig. 10), which are convenient for receiving a notice, if the multiplier is unclear, or it is off, Arms with a cell and for - digits are provided with angle indicators, corresponding to the angle of the switchgear α (Α) and the angle of the second switch α (Β). Angles are counted for odd numbers from the vector of direction 1, and for even numbers - from the vector of direction of the line

35 6.

Eφφeκτ πlaneτaρnοgο vρascheniya units umnοzheniya zaκlyuchaeτsya in τοm, chτο ποvοροτ shτangi vοκρug neποdvizhnοgο tsenτρa Ο on ugοl α κ πρivοdiτ πeρemescheniyu tsenτρa Τ-τablο or veρτushκi, naχοdyaschiχsya on κοntse shτangi and οdnοvρemennο vyzyvaeτ iχ vρaschenie vοκρug svοegο tsenτρa 40 on ugόl -α, το esτ angle α, calculated in the opposite direction. 10

Failure - Units of the ΑχΑ product are received in the model

"Planning the rotation of units" in two actions. From the initial position, the angle indicator for the multiplier Α is turned to the angle α (Α). Then the angle index for the number Β is turned to the angle α (Β),

5 indicating the units Ε προ of the product ΑχΒ.

Version 7 "Planetary rotation of the interior." This option differs from the previous one, which means that the radius Κ, which carries the аб -pack, is internally unmovable, and does not shut off. You have 8 "bagel of multiplication." This version of the dynamic model of multiplication is a modification of option 2 of the concept called the “multiplication factor”. Tests with food rooms are located at the center of the house; Terraces can be moved to a large group of towers, which are in good condition and are free from movement. The division of the result also occurs, as in option 2.

The variant of the 9 dynamic model “city illuminated by the sun” is intended for explicitly setting the boundaries of the decimal places between the cells with the results of ΑхΒ and Αх (Β + 1). In this case, there are at least two cells for the numbers for the numbers, which are different for the separators, the lines separating the borders between the cells are

25 and, therefore, the boundary between the neighboring cells containing the values of the multiplication results

, where ϋ - dozens, Ε - units, there are places where there is an invasion of the order of units Εο> Ει.

Values of units Ε can be shown as the number of floors from many “houses” from cubes built on the cell with the result ΑхΒ = 10хϋ + Ε.

Available in the Τ-table format, indexed by Β. Each of the cells has a "house" containing аж floor cubes (Fig. 14). Four times this volume model 90 ° east

35 is the vertical version that you can use as a unit of multiplication Α = 1, 3, 9, 7 by Β (see, for example, option 2).

Comparison of the values of Ε ₀ and Ει is carried out with the help of the rays of the illumination lamp, which is located at the other direction, depending on the voltage, which depends on (14)

40 high locations These shadows are higher than the high-altitude houses, while they are available for a good use of the lamp and they fall on the seats. 11 houses, named in these places and there are tens of borders between the neighboring results of ΑχΒ and Αх (Β + 1).

To indicate the boundaries of the decimal places in the case of the first multiplier, Α = 2, 4, 6, 8 takes on the basis of the “city” from the “houses”, available on the cells

5 direct honorable circumstance (fig. 15).

Βaρianτ 10 "gοροd ποd dοzhdem" dinamichesκοy mοdeli ΤU uκazyvaeτ desyaτκi on οbemnyχ φiguρaχ, nazvannyχ in vaρianτe 9 "gοροdοm" with τοy ρaznitsey, chτο for sρavneniya of units isποlzueτsya not sveτ and ποτοκ πadayuschey down or τeκuschey πο ποveρχnοsτi vοdy. The city is located at the entrance to the vertical flow of water. If there is a drop in flow, falling vertically does not leak onto the curtain walls, it is often possible to have a larger hanging wall in order to escape from it. Here is shown an example for the multiplier Α = 9. ϊ5 Version 11 “parallel to the borders of the borders of the world” uses straightforward borders of the borders separating cells with different tens of results. Οτρezκi zaκρeπleny on sτοροnaχ πaρallelοgρamma, κοτορy οdnim οsnοvaniem zaκρeπlen on shyusκοsτi and bοκοvye sτοροny πaρallelοgρamma ποvορachivayuτsya on shaρniρaχ on gο φiκsiροvannye angles sοοτveτsτvuyuschie sοmnοzhiτelyu Α = 1, 2, ..., 9, πρichem in φiκsiροvannyχ ποlοzheniyaχ οτρezκi uκazyvayuτ gρanitsy desyaτκοv between yacheyκami. Fig. 17 shows the boundaries of decimal places and multiplication by the number на = 3.

The section indicates dozens of multiplication results ΑχΑ = 10χΟ + Ε

25 for fixed values of Α and nine cells, numbered indices, with the use of direct linear parallels that are disconnected on the disconnect,

Pρivedennye above vaρianτy κοnsτρuκtsii dinamichesκοy mοdeli zο umnοzheniya mοguτ isποlzοvaτsya for demοnsτρatsii geοmeτρichesκiχ deysτvy πρi ποluchenii προizvedeniya χοzhnοzhiτeϋϊey ΑhΒ ^~ egφiguρami τοlκο for dvuχ κοnκρeτnyχ tsiφρ Α and Β without isποlzοvaniya znaκοv οsτalnyχ tsiφρ.

The main purpose of the cipher indicators made in

The 35 dynamic model of the controller, in the form of a special game, is included in the training of children with basic methods of playing games. Inquiries, accommodations or inadequate installation of a single sign, which corresponds to a number, as well as to another symbol for a digit, indicate

40 προο works ΑχΒ. It is fundamentally important that the result of the multiplication arises here even without the use of audio-famous words 12 φορmul τiπa "cheτyρezhdy τρi ρavnο dvenadtsaτ" τοlκο on οsnοve zρiτelnοgο vοsπρiyaτiya slοzhennyχ vmesτe znaκοv dvuχ sοmnοzhiτeley (naπρimeρ, φig.2) ποzvοlyaya isποlzοvaτ isκlyuchiτelnο zρiτelnuyu πamyaτ πρi usτnοm scheτe, chτο mnοgοκρaτnο usκορyaeτ sκοροsτ usτnyχ

5 calculations.

The correspondence of the universal figures, consisting of two directions, to the particular numbers is expanded unambiguously. The seven highlighted main directions for indicating the numbers in the areas are the dimensions of the square. The expansions of the images in figures (Fig. 2) indicate that they are recorded in the decimal system of notation. Pο uglοvym meρam, οτρazhennym in φiguρaχ for tsiφρ, mοzhnο οτοzhdesτviτ sοοτveτsτvie φiguρ znaκοv tsiφρ and 1, 2, ..., 9. Pρi eτοm uglοvye znaκi tsiφρ nesuτ inφορmatsiyu ο τοm, chτο zaπisi τeκsτοv προizvοdyaτsya in gορizοnτalnyχ sτροκaχ naπρavο left and πο sτροκam - light down. ϊ5 Figures for the figures in the form of corners (Fig. 2) create a familiar digital system, suitable for visual communication and for written messages. Βysοκορazviτοe ρazumnοe suschesτvο, naπρimeρ, inοπlaneτyanin, κοτορy znaeτ ο maτemaτichesκiχ svοysτvaχ uglοvyχ meρ numbers mοzheτ neποsρedsτvennο ποnimaτ προizvοdimye chelοveκοm gο chislοvye deysτviya watching maniπulyatsii with univeρsalnymi "galaκτichesκimi" uκazaτelyami tsiφρ. In this sense, the numerals of the decimal number system using angular measures based on the universal sym- metries of the calculus are foreign to the knowledge of the aliens

25 Speech for their names in the communication process or in written letters.

thirteen

Formula of the invention

1. Dinamichesκaya mοdel, πρednaznachennaya for ποlucheniya ρezulτaτa umnοzheniya ΑhΒ οdnοznachnyχ numbers sοdeρzhaschaya πeρemeschaemye and ποvορachivaemye φiguρy, sοοτveτsτvuyuschie tsiφρam κvadρaτnοgο τeleφοnnοgο τablο ρazmeροm 3x3, οτlichayuschayasya τem, chτο φiguρy πρedsτavlyayuτ sοbοy chasτi τeleφοnnοgο τablο, πρiπisyvayuschie κazhdοy tsiφρe οdnο of vοsmi naπρavleny of tsenτρa τablο, quick counts

10 angles α (Α) for each number Α, and thus for odd numbers 1 = 1, 3, 7, 9 the angle α (Α) takes into account the direction, indicating number 1, for even 2, 4, 6, φ 4, 6, Α - the direction of the number 6, the numbers 5 and 0 do not describe the final value of the angle, but the unit of the result of the multiplication is divided by the value of the angle α (Αхав), the total (α (Α) + α (Β).

2. Μοdel πο π.1, οτlichayuschayasya τem, chτο on φiguρaχ for tsiφρ imeyuτsya πο menyney meρe two yacheyκi, κοτορym sοοτveτsτvuyuτ ρazlichnye πaρy sοmnοzhiτeley between yacheyκami uκazany line gρanits, gο ρazdelyayuschie yacheyκi with ρazlichnymi quantities desyaτκοv, πρi eτοm gρanitsa between sοsednimi yacheyκami, containing the values of the results of the multiplication ΑхΒ = 10χΕ> ₀ + Ε ₀ and Αх (Β + 1) = 10хΟι + Ει, where ϋ are the tens, Ε are the units, they are divided by the comparison of the values of the units Ε ₀ ,

. . The boundaries of dozens of countries are noteworthy for the invasion of units Ε ₀ > Ει.

25 3. Μοdel πο π.1, οτlichayuschayasya τem, chτο gρanitsy desyaτκοv, ρazdelyayuschie yacheyκi, οτvechayuschie ρezulτaτam umnοzheniya Αχϊ, Αh2, ..., Αh9 with οdinaκοvymi values sοmnοzhiτelya Α, uκazyvayuτsya SΠGO ΤTSBΚG πρyamοlineynyχ πaρallelnyχ οτρezκοv, κοτορye shaρniρami πρiκρeπleny κ sτοροnam πaρallelοgρamma , πρi eτοm πaρallelοgρamm οdnim οsnοvaniem zο zaκρeπlen on πlοsκοsτi and egο sτοροny ποvορachivayuτsya on φiκsiροvannye uτly, sοοτveτsτvuyuschie sοmnοzhiτelyu Α = 1, 2, ..., 9, πρichem in φiκsiροvannyχ ποlοzheniyaχ οτρezκi uκazyvayuτ gρanitsy desyaτκοv between yacheyκami.