US3645440A - Calculating instrument - Google Patents

Calculating instrument Download PDF

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US3645440A
US3645440A US3645440DA US3645440A US 3645440 A US3645440 A US 3645440A US 3645440D A US3645440D A US 3645440DA US 3645440 A US3645440 A US 3645440A
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wheel
combination
symbols
carrier
digit
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Karola Thevis
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SCHILDKROET AG
SCHILDKROT AG VORM RHEINISCHE GUMMI und CELLULOID FABRIK
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SCHILDKROET AG
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Priority to DE19681772896 priority Critical patent/DE1772896B2/en
Priority to DE19681803134 priority patent/DE1803134A1/en
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    • GPHYSICS
    • G09EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09BEDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
    • G09B19/00Teaching not covered by other main groups of this subclass
    • G09B19/02Counting; Calculating

Abstract

A calculating instrument for use by children wherein a dial disk indexes one of two digit wheels and the one wheel indexes the other wheel. The wheels are mounted in a housing behind windows each of which exposes a single digit on the respective wheel. Each digit on the other wheel represents a numerical value 10 times the value of a digit on the one wheel and the wheels drive endless belts respectively having rows of unit symbols and decade symbols. A third digit wheel is indexed in response to successive manipulations of the dial disk when the instrument is set to perform a multiplication or division. The digits of the third wheel represent a series of multiplicands or quotients.

Description

Patented Feb. 29, 1972 8 Sheets-Sheet 1 INVENTOR. r'o
"H ml 4 Writ- Patented Feb. 29, 1972 8 Sheets-Sheet a I uvmvron .21 1 A Patented Feb. 29, 1972 8 Sheets-Sheet 5 Fig.3
iii-ll REE I IL INVENTOR. V 2r a 2 $24;
Patented Feb. 29, 1972 8 Sheets-Sheet 4 lnl R m m m Patented Feb. 29, 1972 8 Sheets-Sheet 6 INVENTOR.
AHA A Patented Feb. 29, 1972 8 Sheets-Sheet 8 Fig.9 148 as 9' e5 1 I CALCULATING INSTRUMENT BACKGROUND OF THE INVENTION The present invention relates to calculating instruments in general, and more particularly to improvements in calculating instruments which can be utilized by children to perform simple arithmetical processes, such as addition, subtraction, multiplication and/or division.
At the present time, the simplest calculating instrument is the abacus wherein l rows of beads are strung on horizontal wires which are mounted in a frame. Such instruments are used by children and by adults. In learning the rudiments of arithmetic, the child pushes the beads along the respective wire, to the right in order to perform an addition and to the left in order to perform a subtraction. A drawback of such instruments is that the child is not visually apprised of the relationship between the numerical expressions in a problem and the number of beads at the leftor right-hand side of the frame. Moreover, the abacus is not a satisfactory instrument to apprise children of the importance and meaning of decimals. Still further, the result of a calculation with the abacus does not appear in the form of a concrete number or a set of numbers, i.e., the child must count the number of beads at the one and/or the other side of the frame in order to arrive at a desired result, Finally, the result of an arithmetical process is determinable only while the frame is held in a position in which the beads cannot slide along the respective wires so that the entire operation must begin anew if the instrument is accidentally shaken in the course of a given operation.
SUMMARY OF THE INVENTION instrument which is particularly suited to apprise children of the meaning and importance of decimal points, especially of the relationship between unit symbols, decade symbols and/or "hundreds symbols, and which furnishes numerical expressions of the results of various arithmetical processes, for example, of the two basic operations (addition and subtraction) or of all four basic operations (addition, subtraction,
multiplication and division).
A further object of the invention is to provide a calculating instrument which can furnish numerical expressions of ultimate results of basic arithmetical processes as well as intermediate results of such processes, and which enables the user to follow the operation not only in the terms of numbers but also in the terms of unit symbols, decade" symbols and, if necessary, hundreds symbols.
An additional object of the invention is to provide a calculating instrument whose construction is simple so that it can be understood by a child of average intelligence whereby the child can readily learn the meaning of basic mechanical movements including those performed by dial disks, wheels, levers, pawls, links, knobs, endless bands or the like.
Still another object of the invention is to provide an instrument which is constructed and assembled in such a way that its manipulation is interesting to the user so that a child is not bored while performing various calculations and that the child is or need not be fully aware of the educational value of the instrument.
An ancillary object of the invention is to provide an instrument which enables the user to record the result of a mentally performed calculation and to thereupon compare such recorded result with the result furnished by the instrument.
Still another object of the invention is to provide an instrument which is not only educational and entertaining but is further designed in a way to present a challenge to an interested child, for example, by permitting recordal of a mentally performed calculation and for concealment of numerical expressions furnished by the instrument prior to completion of a mechanical calculation.
An additional object of the invention is to provide a calculating instrument which enables the user to understand the meaning of signs which denote the basic arithmetical operations and which is compact and simple enough to be readily transported between home and school and to be capable of mass-production at a reasonable cost.
A further object of the invention is to provide a calculating instrument which enables the user to follow the progress of an arithmetical process, not only with the eyes but also with the ears, to thus enable the user to learn how to concentrate during calculation and to even more readily comprehend the meaning of addition, subtraction, multiplication and/or divisron.
The invention is embodied in a calculating instrument, particularly for use by children, which in its simplest form enables the user to perform additions and subtractions. The instrument comprises carrier means including at least one wheelshaped or belt-shaped carrier provided with a sequence of symbols (in the form of digits or unit or multiple-unit symbols) and being movable between a plurality of positions in each of which at least one of its symbols assumes a predetermined position to represent a numerical expression which can be readily seen through a window or aperture of the housing, and moving means (such as a dial disk, a finger flange, a reciprocable slide or a pivotable lever) for moving the carrier through a desired number of unit increments each of which corresponds to placing of at least one different symbol into the predetermined position.
In accordance with a presently preferred embodiment, the housing of the instrument accommodates at least two coaxial digit wheels each of which carries a row of symbols in the form of digits including two sets of digits 0 to 9. The moving means preferably comprises a dial disk which is rotatable in two directions and indexes or increments one of the digit wheels. The other digit wheel is indexed by the one digit wheel when the latter is indexed through a predetermined angle, namely, through an angle which is 10 times a unit angle necessary to move a given digit on the one wheel away from and to place the next-following digit into registry with the corresponding window.
The improved instrument can be designed to perform additions, subtractions, multiplications and divisions. It is then provided with a third digit wheel whose digits represent a series of multiplicands or quotients. The third digit wheel can be indexed by the dial disk.
The novel features which are considered as characteristic of the invention are set forth in particular in the appended claims. The improved calculating instrument itself, however, both as to its construction and its mode of operation, together with additional features and advantages thereof, will be best understood upon perusal of the following detailed description of certain specific embodiments with reference to the accompanying drawing.
BRIEF DESCRIPTION OF THE DRAWING FIG. 1 is a schematic plan view of a calculating instrument which embodies one form of my invention and is designed to perform additions and subtractions;
FIG. 2 is a sectional view as seen in the direction of arrows from the line II-II of FIG. I;
FIG. 3 is a plan view of the interior of the housing in the calculating instrument of FIG. 1, with certain parts omitted and with certain parts shown in section;
FIG. 4 is a transverse sectional view substantially as seen in the direction of arrows from the line IVIV of FIG. 1;
FIG. 5 is a fragmentary sectional view as seen in the direction of arrows from the line V-V of FIG. 4;
FIG. 6 is a schematic plan view of a portion of a second calculating instrument which is provided with record receiving means enabling the user to jot down mentally or mechanically determined results of arithmetical processes;
FIG. 7 illustrates the structure of FIG. 6 and the dial disk, with certain parts shown in different positions;
FIG. 8 is a schematic plan view of parts in the housing of a third calculating instrument which can perform four different arithmetical processes;
FIG. 9 is a plan view of the instrument shown in FIG. 8; and
FIG. 10 is a transverse sectional view as seen in the direction of arrows from the line X-X of FIG. 9.
I DESCRIPTION OF THE PREFERRED EMBODIMENTS Referring first to FIGS. 1 to 5, there is shown a calculating instrument having a main support or housing 1 which need not be closed from below (see FIG. 2) and whose top wall or panel la supports a rotary dial disk 3 having fnger holes 2. The wall In is further formed with two elongated apertures 4, 5 to respectively permit observation of unit symbols and decade symbols, and with two relatively small windows 6, 7 which permit observation of symbols in the form of digits provided on two symbol carriers here shown as digit wheels 19, 39 mounted in the interior of the housing 1. The wall la is further formed with a short arcuate slot 8 for the indexor pointer of a motion transmitting lever 9 which can be moved between two end positions to respectively register with an addition or plus sign and a subtraction or minus sign. A longer second arcuate slot 10b is adjacent to the periphery of the dial disk 3 and accommodates a portion of an outwardly extending stop 10 which overlies the dial disk 3 and is movable by finger pressure from the solid-line neutral position to two end positions which are-shown by broken lines and are denoted by numerals 11 and 12. A spring 10a is connected to the housing 1 and to the stop 10 to urge the latter to the solid-line neutral position. Such mounting of the stop 10 renders it possible to avoid the representation of a zero position.
The dial disk 3 can be rotated in a clockwise direction (arrow 13) or in a counterclockwise direction (arrow 14); it is rotated in a clockwise direction when the index of the lever 9 registers with the plus sign and in a counterclockwise direction when the index registers with the minus sign. The plus and minus signs are shown as being applied directly to the outer side of the wall la. The lever 9 is connected with a number wheel 15 (see FIG. 4) which is located below the wall In and has two sets of equidistant numbers, namely, the counterclockwise applied numbers I to 10 observable in FIG. 1 through the finger holes 2, and the clockwise applied numbers "1 to 10 indicated on the number wheel 15" of FIG. 9 by dots. The numbers of the two sets alternate with each other and the angular displacement of the wheel 15 in response to movement of the index on the lever 9 from registry with the plus sign into registry with the minus sign on the wall la suffices to move the set of dotted numbers into registry with the finger holes 2. The other set of numbers is then concealed behind the wall la which is provided with holes each registering with one of the finger holes 2. That position of the lever 9 in which its index registers with the minus sign on the wall 10 is indicated in FIG. 1 by broken lines, as at 16. When the lever 9 assumes the position 16 of FIG. 1-, the solidlinenumber 1 directly to the right of the stop 10 (solid-line position) is replaced by the dotted number 10"; the number 2 of FIG. 1 is replaced by the dotted number 9; the number 3" of FIG. 1 by the dotted number 8", and so forth. If the dial disk 3 is then rotated in a counterclockwise direction (arrow 14), a
is inserted into one of the finger holes 2 and the disk is then the end position 11. When the finger is removed from the finger hole 2, the stop It) automatically returns to its neutral position under the action of the spring 10a but the dial disk 3 remains in the newly selected position. The distance between the neutral position and the end position 11 or 12 of the stop 10 corresponds to the distance between two successive numbers of either set of numbers on the number wheel 15.
FIG. 4 shows that the dial disk 3 is coaxial with and secured to a first bevel gear 17 which forms part of a transmission further including a second bevel gear 18 which indexes the first digit wheel 19. The latter is accommodated in the interior of the housing 1 and its axis is preferably normal to the axis of the dial disk 3. The wheel 19 is provided with a finger flange 20 having 20 lugs or teeth and with a cylindrical hub 204 which is adjacent to the finger flange 20 and is provided with two groups of digits 0" to 9 which form a single row in line with the window 6. The hub 20a can be omitted if the two groups of digits are provided on an endless symbol carrier belt or tape 23 which is trainedover and driven by the digit wheel 19. The means for driving the belt 23 comprises a sprocket 21 whose teeth can enter perforations 22 (see FIG. 2) of the belt 23. The latter is further trained over a pulley 24 which is rotatable in the housing 1.
The calculating instrument is provided with a yieldable detent device for the digit wheel 19. This detent device is shown in FIG. 2 and comprises a roll or ball 26 which is biased by a spring 25 reacting against the housing 1 so that the roll 26 engages the finger flange 20. When the flange 20 is rotated by hand (see FIG. 2 which shows that several lugs of the flange 20 are accessible at the outer side of the wall 1a), the roll 26 ratchets over the lugs of the flange 20 and preferably produces a series of sounds which can be counted to thus enable the user to totalize the number of clicks" and to follow the arithmetical process with his or her ears.
The second digit wheel 39 is coaxial with the digit wheel 19 and is provided with a finger flange 41 several lugs of which are accessible at the outer side of the wall In. A second springbiased detent roll (not shown) cooperates with the lugs of the finger flange 41 to produce characteristic sounds when the digit wheel 39 is rotated. This latter wheel comprises a cylindrical rim or hub 40 provided with two sets of symbols or digits 0 to 9 which form a single row, and a sprocket 42 whose teeth can enter perforations 43 provided in a second endless symbol carrier belt or tape 44 which is trained over the digit wheel 39 and over a pulley 45 in the housing 1. The bias of springs which form part of the detent means is preferably weak so that a child can turn the digit wheel 19 or 39 with a minimum of effort. The finger flanges 20, 41 constitute an optional feature of the calculating instrument because the digit wheels 19, 39 can be indexed by the dial disk 3. An advantage of such finger flanges is that the user can place a digit 0" into registry with the window 6 and/or 7. The feature that the digit wheels 19, 39 are indexible by the dial disk 3 as well as independently of such dial disk enhances the versatility of the calculating instrument.
As shown in FIG. 1, the endless belt 23 is provided with two parallel rows 27, 28 of unit symbols. The two rows are offset with reference to each other as considered in the circumferential direction of the belt 23. The right-hand portion of the aperture 4 is obscured by an opaque mask 29 and the lefthand portion of this aperture exposes in FIG. I a portion of the row 27, namely, four unit symbols. Such symbols may but need not be encircled. The mask 29 overlies five unit symbols of the row 28, such obscured unit symbols being indicated by broken lines. The manner in which the mask 29 can be shifted with reference to the aperture 4 of the wall la will be explained below. Shifting of the mask 29 takes place automatically when the aperture 4 exposes nine unit symbols of the row 27 or 28. Each of the windows 6, 7 exposes a single digit on the hub 20a, 40 respectively.
FIG. 4 illustrates that the body of the digit wheel 19 supports two radially movable entraining or indexing posts or pins 30, 31. These pins are installed in radially extending slots 30a of the digit wheel 19 and are biased outwardly by helical springs 32, 33. The pins 34), 31 are located diametrically opposite each other and constitute two followers which can track the face of a stationary cam 334 mounted in the housing 1. When the digit wheel 19 rotates, the pin 30 or 31 travels along the cam 334 and is caused to move radially inwardly into engagement with the teeth of an indexible motion receiving gear 38 on the second digit wheel 39. The configuration of the face on the cam 334 is shown in FIG. 5; this face comprises two inclined sections 34, 37 flanking a top land or median section 336. When the digit wheel 19 rotates in a clockwise direction, as viewed in FIG. 5, its pin 30 travels along the section 34 and is caused to move radially inwardly (i.e., toward the axis of the wheel 19) whereby its exposed end portion enters the space between the adjoining teeth of the gear 38 to index the digit wheel 39 in a clockwise direction and through an angle of predetermined magnitude. Once the pin 30 moves beyond the top land 336, it travels along the section 37 (under the bias of the spring 32) and is disengaged from the gear 38 so that the digit wheel 39 then remains in its new angular position. When the digit wheel 19 is caused to rotate in a counterclockwise direction, as viewed in FIG. 5, the pin 30 or 31 moves along the section 37, thereupon along the top land 336, and finally along the section 34 to thus increment the digit wheel 39 in a counterclockwise direction. The digit wheel 39 is incremented whenever the hub 20:: of the digit wheel 19 moves a digit 9" beyond the window 6, i.e., whenever this window exposes a (while the dial disk 3 is rotated in a clockwise direction as indicated by the arrow 13 of FIG. 1). When the dial disk 3 is rotated in the direction indicated by arrow 14 (subtraction), the digit wheel 39 is incremented whenever a digit on the hub 20a disappears, i.e., whenever the window 6 begins to expose a digit 9. The pin 30 or 31 then travels from the section 37 toward the section 34 of the face on the cam 334.
The belt 441 which is associated with the digit wheel 39 is provided with a single row 46 of decade symbols which can be observed in the aperture 5. It is clear, however, that the belt 44 carries two rows of decade symbols if the calculating instrument is designed to carry out arithmetical processes which involve addition of numbers to form a sum in excess of 100. The instrument then comprises a third digit wheel (not shown) which is incremented by the digit wheel 39 in the same way as described in connection with indexing of the wheel 39 and which then drives a third symbol carrier tape or belt having a row of hundred symbols. The instrument then also comprises a second mask for the aperture and the wall 1a is then provided with an additional aperture corresponding to the aperture 5 and registering with the row of hundred symbols on the third belt.
The distribution of symbols in the rows 27, 28 and 46 on the belts 29, 44 is such that the number of unit symbols which are observable in the aperture 4 is indicated by the digit which is observable in the window 6, and that the number of decade symbols which are observable in the aperture 5 is indicated by the digit which can be seen in the window 7. In the setting of digit wheels 19, 39 as shown in FIG. 1, the aperture 4 exposes four unit symbols of the row 27 because the user can see a digit 4 on the hub a of the wheel 19. The aperture 5 exposes three decade symbols because a digit 3 on the hub 40 of the wheel 39 is observable in the window 7. It is immaterial whether the digit wheel 19 is rotated in response to rotation of the dial disk 3 or in response to rotation of the finger flange 20.
In accordance with a slight modification which is not shown in the drawing, the calculating instrument of FIGS. 1 to 5 can be provided with a second mask which automatically conceals or exposes a single-decade symbol behind the window 5 when the mask 29 is caused to change its position. The digit wheel 39 is then omitted, together with the pulley 45 and belt 44, but the aperture 4 must be enlarged and the number of unit symbols on the belt 23 must be augmented in such a way that 10 unit symbols can simultaneously appear behind the thus enlarged aperture 4.
The manner in which the mask 29 is shiftable with reference to the wall 1a of the housing 1 is illustrated in FIG. 3. The mask 29 is located directly behind the front wall in and is formed with an elongated opening or slit 48 whose size equals or approximates half the size of the aperture 4. In the solidline position of FIG. 3, the opening 48 registers with the lefthand portion of the aperture 4 and permits observation of selected unit symbols in the row 27. When moved to the broken line position 439, the opening 48 registers with the right-hand portion of the aperture 4 and exposes a seiected number of unit symbols in the row 28. The mask 29 has a lug 29a provided with a pin 59 which extends into m open slot 51a defined by a bifurcated end portion or claw 51 of a shifting lever 52. The other end portion of the lever 52 is turn-able on a fixed pivot 53 and its median portion is formed with a cutout 54 for a fixed shaft 55. A helical spring 56 is coupled to the lever 52 and tends to turn it in a clockwise direction, as viewed in FIG. 3, so that the mask 29 tends to assume its lefthand end position and to maintain its opening 4% in registry with the left-hand portion of the aperture 4. The right-hand end portion of the digit wheel 19 forms a face cam which is provided with axially offset cam face sections 58, 59 and two inclined sections 60. A follower 57 of the lever 52 is biased against the face cam by the spring 56 whereby the mask 29 dwells in the solid-line position of FIG. 3 when the follower 57 engages the section 58 but the mask 29 moves to the other end position (indicated by broken lines) when the follower 57 tracks a section 60 and thereupon engages the section 5'9. The spring 56 automatically returns the lever 52 from the broken line position 61 to the solid-line position of FIG. 3 when the digit wheel 19 is rotated to such an extent that the follower 57 of the lever 52 is adjacent to the section 58. The length of each of the cam sections 58, 59 corresponds to the length of a group of digits 0 to 9 on the hub 20a of the digit wheel 19. The mask 29 is shifted whenever the opening 48 exposes nine unit symbols of the row 27 or 23; such shifting takes place while a single-unit symbol appears behind the opening 418 as soon as the latter changes its position by moving in axial direction of the digit wheel 19. If desired, the instrument can be provided with a device which produces a readily detectable audible signal when the mask 29 is caused to change its position; this is tantamount to indicating that the sum of numbers represented by the unit symbols and decade symbols has been changed by ten. One of two acoustic signal generating devices which can be utilized in the calculating instrument of FIGS. 1 to 5 is indicated schematically in FIG. 3, as at 35%; this device produces an audible signal when the lever 52 moves to the broken line position 61. The provision of such signal generating devices constitutes an optional feature of my invention because at least some audibly detectable signals can be produced by the finger flanges 20, 41 in cooperation with the respective detent devices.
The parts 19, 39, 23, 44 together constitute a carrier assembly which can move selected symbols to predetermined positions in which such symbols can be observed through apertures 4, 5 and windows 6, 7 and represent given numerical expressions. The parts 3, 17, 18, 30, 31, 38, 20 and 41 together constitute a moving assembly which can effect. movements of the carrier assembly to any one of a large number of different positions.
Referring to FIGS. 6 and '7, there is shown a portion of a modified calculating instrument which is provided with means for facilitating a comparison between the mentally determined and recorded sum or result and the result which is indicated by the instrument. A sidewall 10111 of the housing 191 is provided with a slot for a portion of a two-armed digit concealing lever or shutter 62 fulcrumed at 63 and having an arm 63a which can be moved into registry with the windows 106 and 107. The finger flanges 20a, 40 are omitted (see the digit wheels 119, 139 of FIG. 7) to enable the arm 63a to move into and away from registry with the windows 106, 107. It is clear, however, that the housing 101 can be designed in such a way that the wheels 119, 139 may be replaced by wheels 19, 39 if portions of finger flanges on such wheels extend through slots provided, for example, in the end wall 101s of the housing 101.
The right-hand arm of the lever 62 is articulately connected with a transparent shield 65 by means of a link 64. The marginal portions of the shield 65 are guided by suitable rails or 'ways provided on the wall 101a. When the arm 63a registers with the windows 106 and 107, the shield 65 is moved away "from registry with a record receiving or writing pad 66 (or at least with a line of such pad) so that the user can write down the arithmetical operation which is to be performed or which has just been completed. The result of calculation written down on the pad 66 can be compared with the result which is observable in the windows 106, 107 when the lever 62 is thereupon pivoted to the position shown in FIG. 7. The shield 65 then overlies the pad 66 but its arm 63a permits observation of digits 3" and 4 behind the windows 107, 106, respectively. In performing the operation which is written down on the pad 66, the user of the instrument can refer to decade symbols and unit symbols which are observable in the apertures 105 and 104 of the wall 101a. The pad 66 can be replaced with a roll of writing paper mounted in the housing 101 behind a suitable window in the wall 101a so that a line, ready for writing down a series of numerical expressions, is accessible as soon as the lever 62 is moved to the position of FIG. 6. The roll of paper can be advanced automatically in response to movement of the lever 62 from the position of FIG. 7 to the position of FIG. 6 (i.e., counter to the direction indicated by arrow B of FIG. 7).
If desired, the pad 66 can constitute a writing tablet which can be readily wiped clean, either by the user or automatically in response to movement of the shield 65 from the position of FIG. 7 to the position of FIG. 6.
The manner in which the dial disk 3 (shown in FIG. 7) is mounted and coupled to the digit wheel 119 is the same as described for the disk 3 and wheel 19 of FIG. 1.
Referring finally to FIGS. 8 to 10, there is shown a third calculating instrument wherein the dial disk 3 and the .digit wheels 19, 39 are mounted and operated in the same way as described in connection with FIG. 1. In FIG. 8, the front wall 201a of the housing 201 is omitted and the dial disk 3 is indicated by phantom lines. The instrument of FIGS. 8 to can perform four different operations, namely, addition, subtraction, multiplication and division. Addition and subtraction are performed in the same way as described in connection with FIGS. 1 to 5.
The stop 210 is mounted on a lever 67 which forms part of a linkage and is tumable about the axis of the dial disk 3. The lever 67 is articulately connected to a link 68 which latter is pivotally connected to a median portion of a further lever 69. One end of the lever 69 is tumable on a pivot 70 in the housing 201 and its other end carries a pivotable pawl 71 having a bentover pallet or arm 72 which normally engages an abutment 73. The other arm 74 of the pawl 71 is coupled to a spring 75 which urges the pallet 72 against the abutment 73. The spring 75 is connected to the lever 69. When the dial disk 3 is rotated and the users finger moves the stop 210 to the end position 211 or 212, the lever 67 pivots the lever 69 by way of the link 68. The lever 69 turns in a clockwise direction so that the pallet 72 moves beyond the abutment 73. The spring 75 then contracts and moves the pallet 72 against the teeth 76 of a further digit wheel 77 which is rotatable in the housing 201 and has a finger flange 77a some lugs of which extend through a slot in the wall 201a. The angular movement of the lever 69 is terminated when the pallet 72 increments the digit wheel 77 through a predetermined angle. The hub 77b of the digit wheel 77 carries two groups of digits l to 9 which form a single row. One digit is observable behind a window 70 of the front wall 201a. With reference to FIG. 0, the pallet 72 moves downwardly when the stop 210 is moved to the end position 211 or 212. Thus, the lever 69 is always pivoted in the same direction (clockwise, as viewed in MG. 0) irrespective of whether the stop 210 moves to the position 211 or 212. Each movement of the stop 210 to the position 211 or 212 results in such angular displacement of the digit wheel 77 that the hub 77b moves the next-following digit into registry with the window 78.
The manner in which the instrument is to be set prior to carrying out a multiplication or division is illustrated in H6. 9. The purpose of such setting is to enable the user to readily understand the operation which is being performed and to be able to identify such operations by observation of appropriate signs. Indexing of the digit wheel 77 is one indication that the instrument is in the process of carrying out either a multiplication or a division.
For example, if a child is to execute a simple multiplication (5X2), the finger is repeatedly inserted into the finger hole 2 above the number 2, and the dial disk 3 is turned five times in a clockwise direction (arrow 13) to move the stop 210 to the end position 212. The product (10) is observable in the windows 207, 206. The digit behind the window 70 indicates the number of successive incrementations of the digit wheel 77. The digits behind the windows 207, 206 further indicate the intermediate product (e.g., the window 207 will expose the digit 0, the window 206 will expose the digit 8, and the window 70 will expose the digit 4 upon completion of four rotations of the dial disk 3, it being assumed that the wheels 19, 39 and 77 were reset to zero prior to start of the multiplication). Thus, the child can observe the increase of the product from zero to 10, which is a simple and effective way of comprehending the meaning of multiplicand, multiplicator and product.
A division is performed in an analogous way. For example, if the child is to divide 10 by 2, the digit wheels 39, 19 are set in such a way that the windows 207, 206 respectively expose a digit l and a digit 0. The digit wheel 77 is reset to zero (by rotating the finger flange 77a). The lever 9 is moved to the position 16 so that the finger holes 2 register with the dotted numbers of the number wheel 15' and the finger is inserted into the finger hole 2 above the dotted number 2." The disk 3 is thereupon rotated in a counterclockwise direction (arrow 14) to move the stop 210 to the end position 211. This is repeated four times, i.e., until each of the windows 207, 206 exposes a digit 0. The quotient (5) can be seen behind the window 78. The child is thereby apprised of the fact that the division corresponds to repeated subtraction of a divisor from the dividend, and the child also learns that certain dividends cannot be divided with a divisor without a rest. The digit which is observable behind the window 78 apprises the child of the number of subtractions of the divisor (2) from the dividend (10). It will be seen that, while a product must be read behind the windows 207 206, a quotient can be seen behind the window 78.
The instrument of FIGS. 8 to 10 is further provided with arresting or blocking means which prevents rotation of the digit wheel 77 when the user performs an addition or subtraction.
Such arresting means comprises a blocking lever 79 which is tumable on a fixed pivot 00 of the housing 201. The free end of the lever 79 is provided with a projection or tongue 81 which can be moved to the phantomline position of MG. 0 to thereby engage the arm 74 of the pawl 71 on the lever 69. The pawl 71 is then held in a position in which its pallet 72 cannot index the digit wheel 77 when the stop 210 is moved to the end position 211 or 212. The means for pivoting the lever 79 between the solid-line and phantom-line positions of FIG. 8 comprises a modified motion transmitting lever 9' which is pivotably mounted in the housing 201 (pivot 290 in FIG. 10) and extends through a slot 02 of the lever 79. The lever 9' further extends through a slot 83 of the wall 201a and is movable by hand to perform its basic function of turning the dial disk 15. The slot 83 is wider than the slot 8 of FIG. 1; this enables the lever 9' to move to one of four different positions to be respectively adjacent to a plus sign, a minus sign, a multiplication sign (x) and a division sign (z), When the accessible portion of the lever 9 is adjacent to the plus sign or to the minus sign, the tongue 81 of the arresting lever 79 blocks the pawl 71 and prevents indexing of the digit wheel 77 in response to movement of the stop 210 to the position 211 or 212. The tongue 81 is automatically disengaged from the arm 74 of the pawl 71 when the exposed portion of the lever 9 is moved into alignment with the division or multiplication sign. The pawl 71 is then free to index the digit wheel 77 in response to angular displacement of the stop 210 in either direction.
The number wheel 15' is formed with a bifurcated extension 84. having a radially extending slot 85 for the lever 9'. Thus, the wheel 15 is turned in automatic response to movement of the lever 9' in the direction indicated by arrow 13 or 14. The slot 85 permits the lever 9' to move from the plus sign to the multiplication sign or vice versa or to move from the minus sign to the division sign or vice versa. As stated before, the lever 79 maintains its tongue 81 in engagement with the arm 74 of the pawl 71 when the lever 9' is moved from the plus sign to the minus sign or vice versa; however, the lever 79 releases the pawl 71 when the lever 9' is moved from the plus sign to the multiplication sign, from the minus sign to the division sign, from the division sign to the multiplication sign, or from the multiplication sign to the division sign.
The shaft 203 of the dial disk 3 in the instrument of FIGS. 8 to 10 carries a transparent or translucent circular plate 86 provided with a pointer 87 which registers with the number 2 on the number wheel The plate 86 serves as a memory aid in that its pointer 87 indicates the divisor or multiplicator while the user performs a division or multiplication. The plate 86 has an upstanding lug 86a and the shaft 203 has a set of equidistant notches or flutes 88, one for each of the 10 numbers which are observable through the finger holes 2. An elastic pawl 89 of the plate 86 enters the adjoining notch 88 when the pointer 87 is moved into registry with a selected finger hole 2. The notched portion of the shaft 203 constitutes a simple ratchet which cooperates with the pawl 89 to yieldably hold the plate 86 in selected angular position. One of the notches 88 is so positioned that the pointer 87 can be moved to the position 87' of FIG. 9 in which its tip registers with the tip of the stop 210 in the neutral position of the stop.
The plate 86 can be replaced with a suitable mask which is then adjustably fixed to the stop 210 in such a way that it always exposes only one of the finger holes 2. Such mask can also be mounted on the front wall 2010.
A writing pad or notebook 90 is provided on the front wall 201a to permit recordal of several arithmetical operations. The pad 90 preferably comprises a stack of readily separable sheets. lt is further clear that this pad can be replaced with a tablet which is preferably ruled and can be readily wiped clean.
A further shield or mask 92 is mounted behind the front wall 201a and can be shifted by a knob 91 so as to conceal or expose the digits behind the windows 2117, 206. The purpose of this mask is analogous to that of the shutter lever 62 shown in FIGS. 6 and 7, i.e., a child can conceal a sum, quotient or product while attempting to perform a mental calculation. The mentally determined result is then written down on the pad 911 or simply memorized before the mask 92 is moved to the position of FIG. 9 to expose the digits behind the windows 207 and 2116.
If desired, the dial disk 3 can be replaced with a lever which is pivotable with reference to the housing or with a slide which is reciprocable with reference to the housing. The moving assembly then comprises a suitable mechanism for converting pivotal or reciprocatory movements into rotary movements of the digit wheels.
Without further analysis, the foregoing will so fully reveal the gist of the present invention that others can, by applying current knowledge, readily adapt it for various applications without omitting features which fairly constitute essential characteristics of the generic and specific aspects of my contribution to the art.
What is claimed as new and desired to be protected by Letters Patent is set forth in the appended 1. In a calculating instrument, particularly for use by chil dren, a combination, comprising carrier means comprising two carriers each provided with a sequence of symbols and each including a rotary digit wheel, said digit wheels being coaxial with each other and one thereof having indexing means for rotating the other thereof through a single increment in response to rotation of said one wheel through a predetermined number of increments, the symbols of said wheels constituting digits and each of said wheels having a single row of circumferentially extending digits including two groups of digits 0 to 9"; moving means for moving said carriers through a desired number of unit increments in each of which at least one difierent symbol is located in a predetermined position to represent a given numerical expression, said moving means including a finger flange on each of said wheels; and yieldable detent means cooperating with said finger flanges to normally hold said means against rotation.
2. In a calculating instrument, particularly for use by children, a combination comprising carrier means comprising a plurality of indexible wheels including a first and a second wheel each provided with a sequence of symbols including a row of digits extending circumferentially of each wheel; and moving means for moving said wheels through a desired number of unit increments in each of which at least one different symbol is located in a predetermined position to represent a given numerical value, said moving means comprising a first device for indexing said first wheel through increments of predetermined magnitude and a second device for indexing said second wheel through a single increment in response to indexing of said first wheel through a predetermined number of increments, said second device comprising a stationary cam, follower means movably mounted on said first wheel, and motion receiving means provided on said second wheel, said cam being arranged to move said follower means into torque transmitting engagement with said motion receiving means in predetermined angular positions of said first wheel. I
3. In a calculating instrument, particularly for use by children, a combination comprising carrier means including at least one carrier provided with a sequence of symbols and being movable between a plurality of positions in each of which at least one of said symbols assumes a predetermined position to represent a given numerical expression; moving means comprising a rotary dial disk for moving said carrier through a desired number of unit increments in each of which at least one different symbol is located in said predetermined position; a number wheel registering with said dial disk; and adjustable indicating means for pinpointing a selected number on said wheel.
4. In a calculating instrument, particularly for use by children, a combination, comprising carrier means including at least one carrier provided with a sequence of symbols and being movable between a plurality of positions in each of which at least one of said symbols assumes a predetermined position to represent a given numerical expression; moving means for moving said carrier through a desired number of unit increments in each of which at least one different symbol is located in said predetermined position; said moving means comprising a dial disk which is rotatable in two directions and has a group of finger holes; a support for said dial disk; and a number wheel mounted on said support for movement between two positions, said number wheel having a first set of numbers each registering with one of said finger holes in one position of said number wheel and a second set of numbers each registering with one of said finger holes in the other position of said number wheel.
5. A combination as defined in claim 4, wherein said carrier comprises an indexible digit wheel.
6. A combination as defined in claim 4, wherein each symbol of said carrier represents the same numerical value.
7. A combination as defined in claim 4, wherein the symbols of said carrier constitute digits each representing a different numerical expression.
8. A combination as defined in claim 4, wherein the first of said carriers has symbols representing unit values and the second carrier has symbols representing multiple unit values.
9. A combination as defined in claim 8, wherein each symbol of said second carrier represents 10 unit values.
10. A combination as defined in claim 4, wherein said first set of numbers includes a ring of numbers 1-10 running in a clockwise direction and said second set includes a ring of numbers 1-10 running in a counterclockwise direction, the numbers of said first set alternating with the numbers of said second set.
11. A combination as defined in claim 4, further comprising stop means adjacent to said dial disk to arrest the disk by extending into the path of movement of a finger which is inserted into a selected finger hole to rotate said dial disk in one of said directions.
12. A combination as defined in claim 11, wherein said stop normally assumes a neutral position and is yieldable to finger pressure to move through a predetermined distance to either side from said neutral position.
13. A'combination as defined in claim 12, wherein the numbers of said sets on said number wheel are equidistant from each other and wherein the distance between successive numbers of either set corresponds to the extent to which the stop is movable from said neutral position.
14. A combination as defined in claim 4, wherein said carrier comprises a rotary digit wheel and further comprising yieldable detent means for normally holding said wheel against rotation.
15. A combination as defined in claim 4, wherein said carrier means comprises two carriers each of which constitutes a rotary digit wheel having an annulus of symbols including two sets of digits to 9.
16. A combination as defined in claim 4, further comprising means for producing audible signals in response to each incrementing of said carrier.
17. In a calculating instrument, particularly for use by children, a combination comprising carrier means comprising two first carriers each constituting an indexible digit wheel and two second carriers constituting endless belts each'driven by one of said wheels, each of said carriers being provided with a sequence of symbols including a row of digits provided on and extending circumferentially of each of said wheels and at least one row of symbols on each of said belts, one row of symbols including unit symbols and the other row including decade symbols; and moving means for moving said carriers through a desired number of unit increments in each of which at least one different symbol is located in a predetermined position to represent a give numerical value, said moving means including meansfor indexing one of said wheels through increments of predetermined magnitude and means for indexing the other wheel through one increment in response to indexing of said one wheel through 10 increments.
18. A combination as defined in claim 17, further comprising a pair of pulleys, each of said belts being trained over one of said pulleys and the respective digit wheel.
19. A combination as defined in claim 18, wherein each of said belts is provided with a line of perforations and each of respective perforations.
20. A combination as defined in claim 17, further comprising a wall overlying said digit wheels and having a pair of winsaid digit wheels comprises a sprocket whose teeth engage the said belts is provided with two rows of unit symbols and wherein one row of said unit symbols is ofi'set with reference to the other row of unit symbols.
22. A combination as defined in claim 21, further compris ing masking means movable between first and second positions in which it respectively conceals the one and the other row of said unit symbols, and means for moving said masking means between said positions in response to indexing of the corresponding digit wheel through said predetermined number of increments.
23. A combination as defined in claim 22, wherein the means for moving said masking means comprises cam means provided on said last-mentioned digit wheel and shifting means coupled to said masking means and having follower means arranged to track said cam means.
24. A combination as defined in claim 17, further comprising a wall overlying said carriers and having a pair of apertures each permitting observation of a limited number of symbols on one of said belts and a pair of windows each pennitting observation of a single digit on one of said wheels.
25. A combination as defined in claim 24, further comprising shutter means movable to and from a predetermined position in which it conceals the digits behind said windows.
26. A combination as defined in claim 25, further comprising record receiving means to permit recordal of mentally performed calculations and shield means operatively connected with said shutter means to overlie said record receiving means in response to movement of the shutter means away from said predetermined position.
27. A combination as defined in claim 26, wherein said shield means consists at least in part of light transmitting material.
28. In a calculating instrument, particularly for use by children, a combination comprising carrier means comprising a pair of first indexible carriers each provided with a sequence of symbols which include digits, said carriers being movable between a plurality of positions in each of which at least one of said symbols assumes a predetermined position to represent a given numerical expression; a first indexing device actuable to index one of said first carriers through increments of unit length; a second indexing device for indexing the other first carrier by a single increment in response to indexing of said one first carrier through a predetermined number of increments; an additional indexible carrier having digits representing a series of numerical values; and a third indexing device operative to index said additional carrier in response to each actuation of said first indexing device.
29. A combination as defined in claim 28, wherein the digits of said additional carrier represent quotients and multiplicands.
30. A combination as defined in claim 28, wherein said first indexing device comprises a dial disk rotatable in two directions and said additional carrier comprises a rotary digit wheel, said third indexing device comprising means for index ing said digit wheel by one increment in response to rotation of said dial disk in either direction.
31. A combination as defined in claim 30, wherein said lastmentioned means comprises a stop movable from a neutral position and extending into the path of a finger during rotation of said dial disk, and a linkage coupling said stop with said digit wheel.
32. A combination as defined in claim 31, further comprising blocking means actuatable to disengage said linkage from said digit wheel.

Claims (32)

1. In a calculating instrument, particularly for use by children, a combination, comprising carrier means comprising two carriers each provided with a sequence of symbols and each including a rotary digit wheel, said digit wheels being coaxial with each other and one thereof having indexing means for rotating the other thereof through a single increment in response to rotation of said one wheel through a predetermined number of increments, the symbols of said wheels constituting digits and each of said wheels having a single row of circumferentially extending digits including two groups of digits ''''0'''' to ''''9''''; moving means for moving said carriers through a desired number of unit increments in each of which at least one different symbol is located in a predetermined position to represent a given numerical expression, said moving means including a finger flange on each of said wheels; and yieldable detent means cooperating with said finger flanges to normally hold said means against rotation.
2. In a calculating instrument, particularly for use by children, a combination comprising carrier means comprising a plurality of indexible wheels including a first and a second wheel each provided with a sequence of symbols including a row of digits extending circumferentially of each wheel; and moving means for moving said wheels through a desired number of unit increments in each of which at least one different symbol is located in a predetermined position to represent a given numerical value, said moving means comprising a first device for indexing said first wheel through increments of predetermined magnitude and a second device for indexing said second wheel through a single increment in response to indexing of said first wheel through a predetermined number of increments, said second device comprising a stationary cam, follower means movably mounted on said first wheel, and motion receiving means provided on said second wheel, said cam being arranged to move said follower means into torque transmitting engagement with said motion receiving means in predetermined angular positions of said first wheel.
3. In a calculating instrument, particularly for use by children, a combination comprising carrier means including at least one carrier provided with a sequence of symbols and being movable between a plurality of positions in each of which at least one of said symbols assumes a predetermined position to represent a given numerical expression; moving means comprising a rotary dial disk for moving said carrier through a desired number of unit increments in each of which at least one different symbol is located in said predetermined position; a number wheel registering with said dial disk; and adjustable indicating means for pinpointing a selected number on said wheel.
4. In a calculating instrument, particularly for use by children, a combination, comprising carrier mEans including at least one carrier provided with a sequence of symbols and being movable between a plurality of positions in each of which at least one of said symbols assumes a predetermined position to represent a given numerical expression; moving means for moving said carrier through a desired number of unit increments in each of which at least one different symbol is located in said predetermined position; said moving means comprising a dial disk which is rotatable in two directions and has a group of finger holes; a support for said dial disk; and a number wheel mounted on said support for movement between two positions, said number wheel having a first set of numbers each registering with one of said finger holes in one position of said number wheel and a second set of numbers each registering with one of said finger holes in the other position of said number wheel.
5. A combination as defined in claim 4, wherein said carrier comprises an indexible digit wheel.
6. A combination as defined in claim 4, wherein each symbol of said carrier represents the same numerical value.
7. A combination as defined in claim 4, wherein the symbols of said carrier constitute digits each representing a different numerical expression.
8. A combination as defined in claim 4, wherein the first of said carriers has symbols representing unit values and the second carrier has symbols representing multiple unit values.
9. A combination as defined in claim 8, wherein each symbol of said second carrier represents 10 unit values.
10. A combination as defined in claim 4, wherein said first set of numbers includes a ring of numbers 1-10 running in a clockwise direction and said second set includes a ring of numbers 1-10 running in a counterclockwise direction, the numbers of said first set alternating with the numbers of said second set.
11. A combination as defined in claim 4, further comprising stop means adjacent to said dial disk to arrest the disk by extending into the path of movement of a finger which is inserted into a selected finger hole to rotate said dial disk in one of said directions.
12. A combination as defined in claim 11, wherein said stop normally assumes a neutral position and is yieldable to finger pressure to move through a predetermined distance to either side from said neutral position.
13. A combination as defined in claim 12, wherein the numbers of said sets on said number wheel are equidistant from each other and wherein the distance between successive numbers of either set corresponds to the extent to which the stop is movable from said neutral position.
14. A combination as defined in claim 4, wherein said carrier comprises a rotary digit wheel and further comprising yieldable detent means for normally holding said wheel against rotation.
15. A combination as defined in claim 4, wherein said carrier means comprises two carriers each of which constitutes a rotary digit wheel having an annulus of symbols including two sets of digits ''''0'''' to ''''9''''.
16. A combination as defined in claim 4, further comprising means for producing audible signals in response to each incrementing of said carrier.
17. In a calculating instrument, particularly for use by children, a combination comprising carrier means comprising two first carriers each constituting an indexible digit wheel and two second carriers constituting endless belts each driven by one of said wheels, each of said carriers being provided with a sequence of symbols including a row of digits provided on and extending circumferentially of each of said wheels and at least one row of symbols on each of said belts, one row of symbols including unit symbols and the other row including decade symbols; and moving means for moving said carriers through a desired number of unit increments in each of which at least one different symbol is located in a predetermined position to represent a give numerical value, said moving means including means for indexing one of said wheels through increments of predetermined magnitude and means for indexing the other wheel through one increment in response to indexing of said one wheel through 10 increments.
18. A combination as defined in claim 17, further comprising a pair of pulleys, each of said belts being trained over one of said pulleys and the respective digit wheel.
19. A combination as defined in claim 18, wherein each of said belts is provided with a line of perforations and each of said digit wheels comprises a sprocket whose teeth engage the respective perforations.
20. A combination as defined in claim 17, further comprising a wall overlying said digit wheels and having a pair of windows each of which permits observation of a single digit on one of said digit wheels.
21. A combination as defined in claim 17, wherein one of said belts is provided with two rows of unit symbols and wherein one row of said unit symbols is offset with reference to the other row of unit symbols.
22. A combination as defined in claim 21, further comprising masking means movable between first and second positions in which it respectively conceals the one and the other row of said unit symbols, and means for moving said masking means between said positions in response to indexing of the corresponding digit wheel through said predetermined number of increments.
23. A combination as defined in claim 22, wherein the means for moving said masking means comprises cam means provided on said last-mentioned digit wheel and shifting means coupled to said masking means and having follower means arranged to track said cam means.
24. A combination as defined in claim 17, further comprising a wall overlying said carriers and having a pair of apertures each permitting observation of a limited number of symbols on one of said belts and a pair of windows each permitting observation of a single digit on one of said wheels.
25. A combination as defined in claim 24, further comprising shutter means movable to and from a predetermined position in which it conceals the digits behind said windows.
26. A combination as defined in claim 25, further comprising record receiving means to permit recordal of mentally performed calculations and shield means operatively connected with said shutter means to overlie said record receiving means in response to movement of the shutter means away from said predetermined position.
27. A combination as defined in claim 26, wherein said shield means consists at least in part of light transmitting material.
28. In a calculating instrument, particularly for use by children, a combination comprising carrier means comprising a pair of first indexible carriers each provided with a sequence of symbols which include digits, said carriers being movable between a plurality of positions in each of which at least one of said symbols assumes a predetermined position to represent a given numerical expression; a first indexing device actuable to index one of said first carriers through increments of unit length; a second indexing device for indexing the other first carrier by a single increment in response to indexing of said one first carrier through a predetermined number of increments; an additional indexible carrier having digits representing a series of numerical values; and a third indexing device operative to index said additional carrier in response to each actuation of said first indexing device.
29. A combination as defined in claim 28, wherein the digits of said additional carrier represent quotients and multiplicands.
30. A combination as defined in claim 28, wherein said first indexing device comprises a dial disk rotatable in two directions and said additional carrier comprises a rotary digit wheel, said third indexing device comprising means for indexing said digit wheel by one increment in response to rotation of said dial disk in either direction.
31. A combination as defined in claim 30, wherein said last-mentioned means comprises a stop movable from a neutral position and extending into the path of a finger during rotation of said dial disk, and a linkage coupling said stop with said digit wheel.
32. A combination as defined in claim 31, further comprising blocking means actuatable to disengage said linkage from said digit wheel.
US3645440D 1968-07-17 1969-07-15 Calculating instrument Expired - Lifetime US3645440A (en)

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DE19681772896 DE1772896B2 (en) 1968-07-17 1968-07-17 Learning and play device to illustrate arithmetic processes
DE19681803134 DE1803134A1 (en) 1968-10-15 1968-10-15 Learning calculator

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US3645440A true US3645440A (en) 1972-02-29

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AT (1) AT307090B (en)
CH (1) CH517982A (en)
FR (1) FR2013119A1 (en)
GB (1) GB1274037A (en)
SE (1) SE355885B (en)

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EP0125836A2 (en) * 1983-05-06 1984-11-21 O'Malley, Arthur Robert Teaching aid
WO2012017397A3 (en) * 2010-08-03 2012-05-10 Its Mediaservice Gmbh Counting board

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CN107293192A (en) * 2017-06-02 2017-10-24 陈晓纪 The mathematics teaching aid trained for mathematical thinking

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US1214262A (en) * 1914-09-12 1917-01-30 Caesar R Bannihr Computing device.
US1347014A (en) * 1920-07-20 Time-computing apparatus
US2549248A (en) * 1949-05-14 1951-04-17 William H Scott Game scoring device
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US3160345A (en) * 1960-04-22 1964-12-08 Edward C Walsh Manual calculator having multiple rotary inputs
US3507447A (en) * 1968-08-05 1970-04-21 Edward C Walsh Adding machine adapted to be held in one hand

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US939479A (en) * 1907-04-10 1909-11-09 John M Daly Computing-machine.
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EP0125836A2 (en) * 1983-05-06 1984-11-21 O'Malley, Arthur Robert Teaching aid
EP0125836A3 (en) * 1983-05-06 1986-07-02 O'Malley, Arthur Robert Teaching aid
WO2012017397A3 (en) * 2010-08-03 2012-05-10 Its Mediaservice Gmbh Counting board

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SE355885B (en) 1973-05-07
FR2013119A1 (en) 1970-03-27
CH517982A (en) 1972-01-15
GB1274037A (en) 1972-05-10
AT307090B (en) 1973-05-10

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