Device of extracting regularity for a number sequence and the method thereof
11017692 · 2021-05-25
Assignee
Inventors
Cpc classification
G09B5/065
PHYSICS
International classification
G09B5/06
PHYSICS
Abstract
The present invention relates to a method of extracting regularity for an arbitrary number sequence and a device using the same, and especially provides a method and a device for finding regularity for an arbitrary number sequence using objects and computing the number that appears after a certain amount of time or times.
Claims
1. A device of representing regularity of a sequence of numbers to teach a user mathematics, the device comprising: a plurality of objects arranged for the numbers in the sequence, wherein the first number in the sequence is represented by one or more first objects in the plurality of objects and any increase from a previous number in the sequence is represented by the increment of the number of objects in the plurality of objects, wherein the objects are represented with at least one of cubes, spheres, blocks, or combinations thereof, wherein a pattern of the increment of the number of objects in the sequence represents regularity, a number to be appeared after certain numbers of times is represented by using the regularity, and wherein the increment of the number of objects (k) to be all the same, and missing or remaining objects (a) to be represented separately after matching the one or more first objects to the increment of the number of objects, and an n-th number in the sequence is represented as (k*n+a), in case that a dimension recognized through the arrangement is one-dimensional.
2. The device of claim 1, wherein the device of representing regularity of the sequence of numbers is one of a math learning device, a game device, or a content player.
3. The device of claim 1, wherein the device of representing regularity of the sequence of numbers is made into a book, a toy or a teaching material containing a flat image, a stereoscopic image or an animation, by using any material including paper, wood, plastic, metal, or combinations thereof.
4. A device of representing regularity of a sequence of numbers to teach a user mathematics, the device comprising: a plurality of objects arranged for the numbers in the sequence, wherein the first number in the sequence is represented by one or more first objects in the plurality of objects and any increase from a previous number in the sequence is represented by the increment of the number of objects in the plurality of objects, wherein the objects are represented with at least one of cubes, spheres, blocks, or combinations thereof, wherein a pattern of the increment of the number of objects in the sequence represents regularity, a number to be appeared after certain numbers of times is represented by using the regularity, and wherein the objects are divided in half or stacked in two folds, so that the objects are rearranged with increases by two objects in the sequence with a thickness (k) of the half objects (k=½) or the stacked objects (k=2), respectively, and result in a multiple (k) of a square (n{circumflex over ( )}2), and missing or remaining objects (a) after matching the square, and thus an n-th number in the sequence is represented as (k*n{circumflex over ( )}2)+a, in case that a dimension recognized through the arrangement is two-dimensional.
5. The device of claim 4, wherein the device of representing regularity of the sequence of numbers is one of a math learning device, a game device, or a content player.
6. The device of claim 4, wherein the device of representing regularity of the sequence of numbers is made into a book, a toy or a teaching material containing a flat image, a stereoscopic image or an animation, by using any material including paper, wood, plastic, metal, or combinations thereof.
7. A method of representing regularity of a sequence of numbers to teach a user mathematics, the method comprising: arranging a plurality of objects for the numbers in the sequence, wherein the first number in the sequence is represented by one or more first objects in the plurality of objects and any increase from a previous number in the sequence is represented by the increment of the number of objects in the plurality of objects, wherein the objects are represented with at least one of cubes, spheres, blocks, or combinations thereof; and representing regularity with a pattern of the increment of the number of objects in the sequence, a number to be appeared after certain numbers of times by using the regularity, wherein the increment of the number of objects (k) to be all the same, and missing or remaining objects (a) to be represented separately after matching the one or more first objects to the increment of the number of objects, and an n-th number in the sequence is represented as (k*n+a), in case that a dimension recognized through the arrangement is one-dimensional.
8. The method of claim 7, wherein the method of representing regularity of the sequence of numbers is operated by one of a math learning device, a game device, or a content player.
9. The method of claim 7, wherein the method of representing regularity of the sequence of numbers is realized on a book, a toy or a teaching material containing a flat image, a stereoscopic image or an animation using any material including paper, wood, plastic, metal, or combinations thereof.
10. A method of representing regularity of a sequence of numbers to teach a user mathematics, the method comprising: arranging a plurality of objects for the numbers in the sequence, wherein the first number in the sequence is represented by one or more first objects in the plurality of objects and any increases from a previous number in the sequence is represented by the increment of the number of objects in the plurality of objects, wherein the objects are represented with at least one of cubes, spheres, blocks, or combinations thereof; and representing regularity with a pattern of the increment of the number of objects in the sequence, a number to be appeared after certain numbers of times by using the regularity, wherein the objects are divided in half or stacked in two folds, so that the objects are rearranged with increases by two objects in the sequence with a thickness (k) of the half objects (k=½) or the stacked objects (k=2), respectively, and result in a multiple (k) of a square (n{circumflex over ( )}2), and missing or remaining objects (a) are represented after matching the square, and an n-th number in the sequence is represented as (k*n{circumflex over ( )}2)+a, in case that a dimension recognized through the arrangement is two-dimensional.
11. The method of claim 10, wherein the method of representing regularity of the sequence of numbers is operated by one of a math learning device, a game device, or a content player.
12. The method of claim 10, wherein the method of representing regularity of the sequence of numbers is realized on a book, a toy or a teaching material containing a flat image, a stereoscopic image or an animation using any material including paper, wood, plastic, metal, or combinations thereof.
Description
DETAILED DESCRIPTION
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DETAILED DESCRIPTION
(8) Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. Like reference symbols in the drawings denote like elements. Also, specific structural and functional descriptions for embodiments of the present invention are presented for purposes of describing embodiments of the present invention only, and unless otherwise defined, all terms used herein, including technical or scientific terms have the same meaning as commonly understood by those of ordinary skill in the art to which the present invention belongs.
(9) In the present invention, an object (cube) is used to extract regularity of a sequence of numbers and the cube is preferably a regular hexahedron. Basically, cubes having the same size are arranged to derive regularity. However, in order to find regularity, the cubes can be divided at a certain rate such as ½ or ¼. However, the basic shape used for the arrangement of the cubes for an arbitrary sequence is preferably a regular hexahedron. In the case where a multi-dimensional array is further required, it is possible to divide the cubes at a predetermined ratio. On the other hand, finding regularity of a number sequence using an object of the present invention does not necessarily require the use of cubes. Therefore, a figure having a certain shape or an object belongs to the scope of the present invention if it can be arranged in a geometrical manner according to the method of the present invention to induce regularity.
(10) Also, the technical scope of the present invention may apply to a book, a toy, or a teaching material containing a flat image, a stereoscopic image or an animation made of any material including paper, wood, plastic, metal or a combination thereof according to the method of the invention. It should be understood that a product simply modified by those skilled in the art is also within the scope of the present invention.
(11) In addition, the object used in the present invention may be any object or figure including a cube, a sphere, an arbitrary shape and a block.
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(13) As shown in
(14) In other words, the service provider implements a technology for extracting regularity of a sequence of numbers using objects (cubes) through a service support platform 10 as a core program, and uses it to create various application programs (game contents, contents, lecture contents) and supplies the user with the program, which the user can download and use. Devices that can download or stream application can be mobile phones, tablets, PCs, laptop computers, televisions, dedicated learning tools or memories (USB, SSD memory, etc.). The device can execute the program that can find regularity of a sequence of numbers through the application by executing the downloaded or streamed application.
(15) The service support platform 10 according to the present invention can generate and provide various games, contents, and learning programs to which a technique of extracting regularity of numbers is applied by using objects (cubes). It is also possible to adjust the difficulty level according to the user's age and level in various versions, or to instruct the learning or game by keeping the result of the process of learning or playing the game by the user.
(16) Here, the game can provide a variety of numbers, including providing a learning as a game, and it is also possible to provide a quiz form to extract a specific sequence number or a post-sequential result of the sequence, and to perform a game through a character.
(17) In addition, the contents according to the present invention may include various contents such as learning contents, game contents, or problem-solving contents using a technique of extracting regularity of numbers using objects (cubes).
(18) In addition, the service support platform 10 provides an operating environment for various kinds of devices consumed by a user, and also includes an update for various games or learning contents provided by a service provider and maintains user information and etc.
(19) Each cube device includes a user interface 130 including a wired/wireless communication interface (or network interface), a speaker, a microphone, a display, and the like and a memory (e.g., HDD, SSD, USB, etc.) inside or outside the cube device.
(20) Meanwhile, the present invention can be applied to a device for extracting regularity of a number sequence by using objects (cubes) is made into a book, a toy, or a teaching material containing a flat image, a stereoscopic image or an animation using any material including paper, wood, plastic, metal, or combinations thereof. Therefore, in the present invention, the term device may be various types of products manufactured as described above.
(21) The object (cube) of the present invention can be made of various materials, and it is possible to make a book using a manufactured object (cube), a toy, a teaching material, or an experiential apparatus for applying the regularity according to the present invention to real life. And all of these processes can be made into images. The image includes a plane image and a stereoscopic image, and these images can be reproduced in an animation form.
(22) Hereinafter, a structure of a device for providing various kinds of contents to various kinds of devices and a detailed structure thereof will be described by using a method of extracting regularity for a sequence of numbers using objects (cubes).
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(24) As shown in
(25) The memory 120 may include information on a program for a process of finding regularity by using objects (cubes), the rule information, the graphic information, the sound information and the object (cube) information necessary for the processor 110 to operate.
(26) The processor is a term that is mainly used when the device of the present invention is in the form of an electronic device. But if the method of the present invention is realized using a book, a toy, an experiential apparatus, a flat image, a stereoscopic image, an animation or a teaching material containing a flat image, a stereoscopic image or an animation, it should be considered that it contains the above processor.
(27) And if a method of extracting regularity for an arbitrary sequence according to the present invention is implemented in the device, it should be recognized that it also includes technical features for the object arrangement unit 111 and the regularity extraction unit 113 in the processor of the present invention.
(28) In addition, in the embodiment of the present invention, various information that can be perceived by humans can be provided for the process of finding the regularity of a sequence of numbers by using objects (cubes). The information includes text, video (image), alphabets, sounds (including voice, music, etc.), pulse signals, tactile signals, stimulus signals, and the like. These signals allow the human to recognize the process of finding the regularity of the numerical sequence using objects (cubes) in visual, tactile, auditory sense and perception and the information is output singly or in a combined form of plural information.
(29) The user interface 130 also serves as an interface for receiving a specific input (e.g., a sequence of numbers) from a user or providing a variety of display results using objects (cubes). That is, a user can input information on a sequence of numbers by various methods such as voice, touch, input using a touch pad or keyboard and code. The output can also be graphically output to the display, or output as text, symbols, audible or tactile signals. In the present invention, an input method and an output method are not limited to those listed above. That is, there is no limitation on the input method or means, the output means, or the method.
(30) As a result, the process of extracting regularity of a sequence of numbers according to the present invention can be transmitted using the brain waves so that the user can recognize them naturally.
(31) In addition, the network interface 140 provides a means for the cube device 100 to operate by being connected to the network and receiving services remotely and to communicate with each other among the cube devices. It also makes it possible to update the contents of the service through the platform. Also, the network interface includes a wired and wireless communication interface and a combination thereof is also possible.
(32) Next, the method of extracting regularity of a sequence of numbers using objects (cubes) of the present invention is executed in the processor 110 and the corresponding program can be stored in the memory 120.
(33) Hereinafter, a method of extracting regularity of a sequence of numbers using objects (cubes) in the processor will be described in detail.
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(35) As shown in
(36) Here, the processor 110 may further include an input signal converter (not shown) for receiving various inputs and converting the received signals into signals suitable for use in the device in addition to the object arrangement unit 111, the dimension recognition unit 112 and the regularity extraction unit 113. And it may further include an output signal converting unit (not shown) for converting the output into a form selected in advance for graphics, sound, text, and the like and outputting it. And it may further include a storage interface unit (not shown) for storing the data in DB 120.
(37) Hereinafter, a process of arranging the input sequence of numbers, recognizing the dimension and extracting the regularity will be described with reference to the following drawings.
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(39) Here, the case where the sequence of numbers is 1) 2, 4, 6, 8, . . . and 2) 3, 5, 7, 9, . . . are described first with the following example (refer to
(40) First, the object arrangement unit 111 arranges, rearranges, or combines objects (cubes) corresponding to the number of numbers for the arbitrary numbers input through the sequence input unit 131.
(41) Here, a sequence for arbitrary numbers is the sequence such as simply 1, 3, 5, 7, . . . 2, 4, 6, 8, . . . . According to this sequence, the objects (cubes) are arranged in a horizontal direction by the number of the first number and then, the objects (cubes) corresponding to the sum of the first number and the next number are arranged in the horizontal direction. In this way, the objects (cubes) are arranged repeatedly enough to grasp the overall pattern of the sequence. (Three to six times may be sufficient).
(42) It is easy to judge the increase of the number by vertically rearranging the objects (cubes) arranged in the horizontal direction as the corresponding number. Of course, they may be arranged in the vertical direction at one time.
(43) Next, the dimension recognition unit 112 analyzes a pattern of a sequence of numbers according to the number of objects (cubes) arranged in the vertical direction, recognizes it as a one-dimensional sequence if the objects (cubes) are increased or decreased identically and recognizes it as a multi-dimensional sequence if the objects (cubes) are increased or decreased differently.
(44) If the sequence recognized in this manner is one-dimensional, the regularity extraction unit 113 performs the following operations.
(45) That is, if the sequence is 1) 2, 4, 6, 8, . . . , the n-th outgoing number is 2*n and if the sequence is 2) 3, 5, 7, 9, . . . , the n-th outgoing number is 2*n+1. In other words, if the sequence of numbers is 2, 4, 6, 8, . . . , the number of objects (cubes) to be incremented is 2 and it is simple that the n-th output is 2*n. If the sequence is 3, 5, 7, 9 . . . , the number that appears at the beginning is 3, so if 2 is set to the initial value, 1 is left. The number remaining or missing from the initial value is separately recorded and that value is added to the result. That is, it becomes 2*n+1. Of course, in the case of 1, 3, 5, 7, 9, . . . the n-th number becomes 2*n−1.
(46) In general, 1) if the sequence of numbers is 1, 2, 4, 6, . . . , the n-th outgoing number is k*n (where k is the number of objects (cubes) to be incremented or decreased), 2) if it is 3, 5, 7, 9, . . . , it becomes k*n+a (where k is the number of objects (cubes) to be incremented or decreased, and a is the number of objects (cubes) missing or remaining. If there are no missing or remaining objects (cubes) from (k*n+a) cubes, it becomes k*n.
(47) Therefore, if the number sequence is one-dimensional and is 1, 4, 7, 10, . . . , the numbers are increased by 3, and since there is one object (cube) in the beginning and not enough 2 objects (cubes) compared to increasing by 3, the n-th outgoing number is 3*n−2 (see
(48) If the number array is 1, 4, 9, 16, . . . , the number increases or decreases by 1, 3, 5, 7, etc. and does not increase by the same size of number. In this case, it is necessary to determine the sequence as two-dimensional and extract the regularity of it.
(49) In conclusion, the present invention extracts the regularity of the numbers according to the dimension recognized from the arranged objects (cubes), and recognizes the number that appears after a certain amount of time or times from the regularity.
(50) When the recognized dimension is one-dimensional in particular, the objects (cubes) are arranged to be the same vertically and the number of the first objects (cubes) is matched, and then the objects (cubes) (a) are separately recorded in the case where there are objects (cubes) or no objects (cubes) missing or remaining. The number of n-th cube is calculated from the result. (=k*n+a). Here, if a=0, the number of all the vertically arranged objects (cubes) are the same. If a is positive (a>0), it means that the number of the first objects (cubes) is larger than the number of objects (cubes) increased or decreased. If a is negative (a<0), the number of the first objects (cubes) is smaller than the number of objects (cubes) increased or decreased.
(51) If the number of objects (cubes) to be increased or decreased is not constant and increases more and more when the dimension recognition unit 112 analyzes the pattern of the sequence of numbers, it is required to recognize it as a multidimension and extract regularity accordingly.
(52) Hereinafter, the operation of the regularity extraction unit 113 for extracting the regularity in the case where the sequence is multidimensional will be described.
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(54) In the case of 1, 4, 9, 16, . . . , since the increase or decrease of the number of rearranged results is 1, 3, 5, 7, . . . , if the number of the object (cube) is initially 1, it is 1. If three (3) are increased here, the increased three surround the one object (cube). In case of 5 more objects (cubes), one more surround makes a 2×2 object (cube) surrounded by three objects (cubes) a 3×3 object (cube). In this way, 7 more objects (cubes) make a 4×4 object (cube). For this sequence, we can see that the n-th number is the square of n (=n{circumflex over ( )}2).
(55) In the case of
(56) Next, a three-dimensional case will be described as an example.
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(58) In this case, once the sequence is rearranged, the number of objects (cubes) increases by 2, 6, 10, . . . . When they are rearranged in pairs, they are arranged in pairs of 1, 3, 5, 7, . . . . This can be arranged in a square in pairs, so the n-th number is 2*(n{circumflex over ( )}2). Here, it is k=2 when the two objects (cubes) are combined in pair, and a generalized expression is described as k*(n{circumflex over ( )}2).
(59) In other words, when the recognized dimension is two-dimensional, the objects (cubes) are arranged in the form of 1, 3, 5, 7, 9, . . . and the objects (cubes) are divided in halves so as to make a difference by two or stacked in two to extract the thickness (k). The number of n-th cubes (=k*n{circumflex over ( )}2) can be calculated by cutting out the remainder so that the sequence has a pattern such as 1, 3, 5, 7.
(60) From this regularity, it is possible to recognize, predict or calculate the number after a certain amount of time or times.
(61) A method of finding the regularity of an arbitrary sequence by describing the calculation method as a flowchart will be described as follows.
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(63) As shown in
(64) Next, objects (cubes) as the sequence of numbers are arranged in the horizontal direction (S120). The object (cube) is rearranged vertically according to the arranged numbers (S130). This process is performed through the object arrangement unit 111 and is a process of arranging objects (cubes) for any given arranged numbers. This process further includes rearranging vertically in addition to arranging horizontally the objects (cubes) corresponding to the input sequence, it is easy to see how much the corresponding sequence increases through rearrangement.
(65) Then, the dimension is recognized from the arranged objects (cubes) (S140). According to the dimension of the input sequence of numbers (S150), if the dimension is one-dimensional, the regularity is extracted through the processes of S160 and S170, and the n-th emerging number is recognized, predicted or calculated.
(66) That is, in the case of one dimension, the number of vertically rearranged objects (cubes) is set to be equal to k, and if the number of the first objects (cubes) is not k, the number of the objects (cubes) is set to k first and count the number of missing or remaining and record it separately as a. (S160). Next, when the number of the n-th object (cube) is calculated, k*n+a is obtained (S170).
(67) Next, the case where the dimension determined at S150 is a multidimensional higher than one dimension will be described. In the case of the one-dimensional case, if vertically arranged objects (cubes) are in the form of 1, 3, 5, 7, . . . the number of the n-th object (cube) is n{circumflex over ( )}2. Also, when vertically arranged objects (cubes) are arranged in the form of 1, 2, 3, 4, . . . , half objects (cubes) are arranged as an array like 2, 4, 6, . . . , and the top half n blocks are kept in advance. The n{circumflex over ( )}2 sequence of (½) are derived from the remaining 1, 3, 5, and 7, . . . arrays. Therefore, the n-th number is (n/2)+(n{circumflex over ( )}2)/2.
(68) On the other hand, if vertically arranged objects (cubes) are 2, 6, 10, . . . , the number of n-th object (cube) is 2*(n{circumflex over ( )}2). Therefore, generalizing these results is described as k*(n{circumflex over ( )}2) (S180).
(69) On the other hand, extracting regularity for an arbitrary sequence using objects (cubes) can graphically output a process of inputting and arranging a sequence of numbers, recognizing a dimension, and extracting regularity in the various forms such as text, image (image), number, alphabet, sound (including voice and music), pulse, tactile and stimulus signal. These signals allow the human to recognize the process of finding the regularity of the numerical sequence through the objects (cubes) by using visual, tactile, auditory sense and perception, and single or plural information in combination may be provided to humans.
(70) Also, it is possible to allow the user to interactively recognize the progress of the process of extracting the regularity of the input sequence using the objects (cubes) or to automatically recognize the process with a time delay. This process means that a variety of expression methods can be used when a regularity extraction method for a sequence of numbers according to the present invention is specifically made to an application program.
(71) That is, the present invention may output a process of finding the regularity of the sequence input as an audible signal and allow the user to recognize the process. In addition, it is also possible to output the tactile sense or perception. Outputting the extraction process can be performed through visual, tactile, auditory, perception, or a combination thereof, and does not limit the specific method.
(72) In the present invention, it goes without saying that the technique of extracting the regularity of numbers using objects (cubes) can be operated by a mathematical learning device, a game device, a content player, a storage device storing computer program or source codes for executing a computer program.
(73) As described above, the present invention relates to a method of finding regularity of an arbitrary sequence by using objects (cubes). By using objects (cubes), it is possible to find out the regularity of an arbitrary sequence and easily calculate the number of the sequence after a certain amount of time or times in the sequence and understand the concept of number arrangement. In addition, it is possible to easily find the regularity of the sequence in a specific application field, thereby helping solve the problem of the field. The present invention allows anyone to get familiar with numbers by providing a device, a learning tool, a computer program, a game tool, a content that implements a method of finding regularity of a sequence of numbers and to solve problems easily by finding the concept and the arrangement and order of the numbers.
(74) While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. Each component of the present invention may be changed or modified within the technical scope of the present invention to achieve the same objectives and effects.
(75) While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is clearly understood that the same is by way of illustration and example only and is not to be taken in conjunction with the present invention. It will be understood that various changes and modifications may be made by those skilled in the art without departing from the spirit and scope of the present invention.