Patent Publication Number: US-2015064667-A1

Title: Visual teaching tool and method for determining the result of digit multiplication based-on diagram rotation and transition path

Description:
STATEMENT OF NO NEW MATTER 
     The applicant states that the substitute specification as well as this revised specification contains no new matter. 
     TECHNICAL FIELD 
     The present invention is generally relevant to a teaching tool for digit multiplication, specifically, a visual teaching tool and method for determining the result of digit multiplication based-on diagram rotation and various transition path(s). 
     BACKGROUND 
     The prior art discloses that mathematics teaching devices, in particular those intended to teach “times tables” or multiplication tables, are well known. These devices usually involve an article upon which the multiplication tables are reproduced in their entirety, and require the student using the device to “cross reference” one number against another, and note the product of those two numbers. 
     In each device, the numbers are arranged in a grid pattern, and the student is expected to follow one number across, horizontally (an “X” axis) and another number down, vertically (a “Y” axis), to locate the answer (product) of the problem posed. In one manifestation, this process involves the use of wooden (or similar material) pegs which are place at the location of the numbers for which a product is sought, while a third peg is then placed at the intersection of the two numbers, which is the product. Another manifestation substitute&#39;s transparent material strips for the pegs, and locates the product at the place where the two strips cross one another, the answer being visibly apparent through the two strips. 
     Unfortunately, these devices and their methods of use all require that the user of the device be looking at the device, with the answer readily apparent, during the process of determining an answer to the problem posed. There is, by the very design of these devices, a built in encouragement to “cheat” and disclose the answer without having actually thought about it. 
     Besides, teachers and educators have devised and tested many methods and techniques for teaching multiplication tables to elementary school students. Examples include typed or printed sheets of the multiplication tables, display cards with the equation printed on one side and the answer on the opposite side, and teaching methods an illustrated in recent text books often referred to as “modern math,” such techniques being generally tedious and boring to the student. So, that mental enforcement of the multiplication tables is usually accomplished only after long and continuous use of the multiplication tables after progressing to more difficult problems thereby resulting in a slow and gradual understanding of the multiplication process. 
     Accordingly, there is an obvious need for a simple training device that will teach elementary school students and provide a thorough appreciation and understanding of the multiplication process. Thus, the invention&#39;s method is proposed. 
     SUMMARY OF THE INVENTION 
     To address the above shortcomings, a visual teaching tool for digit multiplication is proposed for determining the result of digit multiplication based-on diagram rotation and various transition path(s). 
     One feature of the invention is method for determining the result of digit multiplication by a computing device, comprising: selecting one of three types of visual teaching tools including first type of visual teaching tool, second type of visual teaching tool and third type of visual teaching tool, by the computing device; wherein the first type of visual teaching tool has a 3×3 array nodes with nine digits (1, 2, 3, 4, 5, 6, 7, 8, 9) in the 3×3 array nodes respectively and a tenth node with digit 0 therein, digits (1, 3, 7, 9) locate on its corner of the 3×3 array nodes, and adjacent number order nodes of the 3×3 array nodes are associated with each other via first transition paths; wherein the second type of said visual teaching tool has two 2×2 array nodes with four digits (2, 4, 6, 8) on its corner of each of the 2×2 array nodes and a fifth node and a tenth node with digit 0 therein respectively, and adjacent number order nodes of the two 2×2 array nodes are associated with each other via second transition paths; wherein the third type of the visual teaching tool has four corners nodes with digit 5 therein respectively, a center node with digit 0 therein and a sixth node with digit 0 therein, and each of the four corners nodes is transited from/to the center node with each other via third transition paths. If the first type of visual teaching tool or the second type of visual teaching tool is selected, then rotating the first type of visual teaching tool or the second type of visual teaching tool to determine an initial node by the computing device, wherein digit in the initial node is defined as a multiplicand, and thereby transferring the multiplicand from digit 1 to digits 3, 7, or 9, or transferring the multiplicand from digit 2 to digits 4, 6, or 8. Then, proceeding number (PN) of the first transition paths, the second transition paths or the third transition paths reaching to an object node is determined to obtain a multiplier equal to the PN plus 1 by the computing device such that product value of the multiplicand and the multiplier has a unit place equal to a digit in the object note, and a tens place equal to a number of transition paths for carrying. 
     As above described, nine digits (1, 2, 3, 4, 5, 6, 7, 8, 9) locate and fix in node (1, 1), node (1, 2), node (1, 3), node (2, 1), node (2, 2), node (2, 3), node (3, 1), node (3, 2), node (3, 3) respectively of the 3×3 array nodes, wherein the four digits (2, 4, 6, 8) locate and fix in node (1, 1), node (1, 2), node (2, 1), node (2, 2) respectively of the 2×2 array nodes. 
     According an aspect, node transition orders of the first type of visual teaching tool are as follows: 1 st  node (1, 1) proceeding to 2 nd  node (1, 2) via transition path 1, 2 nd  node (1, 2) proceeding to 3 rd  node (1, 3) via transition path 2, 3 rd  node (1, 3) proceeding to 4 th  node (2, 1) via transition path 3, 4 th  node (2, 1) proceeding to 5 th  node (2, 2) via transition path 4, 5 th  node (2, 2) proceeding to 6 th  node (2, 3) via transition path 5, 6 th  node (2, 3) proceeding to 7 th  node (3, 1) via transition path 6, 7 th  node (3, 1) proceeding to 8 th  node (3, 2) via transition path 7, 8 th  node (3, 2) proceeding to 9 th  node (3, 3) via transition path 8, and 9 th  node (3, 3) proceeding to said tenth node via transition path 9. 
     Besides, node transition orders of the second type of visual teaching tool are as follows: 1 st  node (1, 1) proceeding to 2 nd  node (1, 2) via transition path 1, 2 nd  node (1, 2) proceeding to 3 rd  node (2, 1) via transition path 2, 3 rd  node (2, 1) proceeding to 4 th  node (2, 2) via transition path 3, 4 th  node (2, 2) proceeding to 5 th  node via transition path 4. 
     Again, node transition orders of the third type of visual teaching tool are as follows: node (1, 1) proceeding to said center node via transition path 1, said center node proceeding to node (1, 2) via transition path 2, node (1, 2) proceeding to said center node via transition path 3, said center node proceeding to node (2, 2) via transition path 4, node (2, 2) proceeding to said center node via transition path 5, said center node proceeding to node (2, 1) via transition path 6, node (2, 1) proceeding to said center node via transition path 7, and said center node proceeding to node (1, 1) via transition path 8, and node (1, 1) proceeding to said sixth node via transition path 9. 
     The degree of rotating is 90, 180 or 270. The first transition paths, the second transition paths and the third transition paths are divided into two types, the first type of transition paths are for carrying, and the second type of transition paths are for NOT-carry. 
     According to another aspect, the invention provides a computing device-readable medium including instructions which, when executed by computing device, cause the computing device to perform above-mention steps. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The attached specifications and drawings outline the preferred embodiments of the invention, including the details of its components, characteristics and advantages. 
         FIG. 1  shows a block diagram of an embodiment of a computing device for implementing an embodiment of a method according to the invention; 
         FIG. 2  shows the first type of visual teaching tool according to one embodiment of the invention; 
         FIGS. 3   a  and  3   b  show the second type of visual teaching tool according to one embodiment of the invention; 
         FIG. 4  shows the third type of visual teaching tool according to one embodiment of the invention; 
         FIG. 5  shows the 1 st  type of visual teaching tool with clockwise rotating 90 degrees; 
         FIG. 6  shows the 1 st  type of visual teaching tool with counter-clockwise rotating 90 degrees; 
         FIG. 7  shows the 1 st  type of visual teaching tool with rotating 180 degrees 
         FIGS. 8   a  and  8   b  show the 2 nd  type of visual teaching tool with clockwise rotating 90 degrees; 
         FIGS. 9   a  and  9   b  show the 2 nd  type of visual teaching tool with counter-clockwise rotating 90 degrees; 
         FIGS. 10   a  and  10   b  show the 2 nd  type of visual teaching tool with rotating 180 degrees; 
         FIGS. 11   a ,  12   a  and  12   b , and  14   a  show a non-rotate diagram configuration of the 1 st  type of visual teaching tool, 2 nd  type of visual teaching tool and 3 rd  type of visual teaching tool, respectively; 
         FIGS. 11   b ,  13   a  and  13   b , and  14   b  show a digits configuration of the 1 st  type of visual teaching tool, 2 nd  type of visual teaching tool and 3 rd  type of visual teaching tool, respectively. 
     
    
    
     DETAILED DESCRIPTION 
     Next, the preferred embodiments of the invention are described in further detail. Notably, however, the preferred embodiments are provided for illustration purposes rather than for limiting the use of the invention. The invention is also applicable in many other embodiments besides those explicitly described, and the scope of the invention is not expressly limited except as specified in the accompanying claims. 
     The invention provides a visual teaching tool for digit multiplication to determine the result of digit multiplication based-on diagram rotation and various transition path(s) by a computing device, without transitional multiplication table or times table. 
       FIG. 1  shows a block diagram of an embodiment of a computing device for implementing an embodiment of a method according to the invention. The computing device includes computer, smart phone or tablet. The computing device  100  includes a processor  101 , a storage device  102 , an operating system (OS)  103 , a memory  104 , a display  106 , interfaces  107  and a visual teaching tool generating module  108 . The storage device  102 , the operating system (OS)  103 , the memory  104 , the display  106 , the interfaces  107  and the visual teaching tool generating module  108  are coupled to the processor  101 . Examples of the storage device  102  include hard drive (HD), SD or EPROM. The processor  101  may be implementing programs to encode or decode data. The memory  104  contains data  105 . The display  106  may include a liquid crystal display (LCD), a plasma display, a cathode ray tube (CRT) display, or any other display technology, for displaying information or content to a user. The interfaces  107  include for example audio/video (A/V) interface, mouse interface, keyboard interface, USB interface . . . etc. The visual teaching tool generating module  108  is capable of generating a visual teaching tool for digit multiplication. 
     The proposed method for digit multiplication of a multiplicand and a multiplier based-on diagram rotation and various transition path(s) to obtain a product value is capable of performing by the computing device  100 . 
     The proposed method for digit multiplication of a multiplicand and a multiplier based-on diagram rotation and various transition path(s) to obtain a product value is described further below. 
     (1). Determine Multiplicand: 
     First, one of three types of visual teaching tools is selected. The three types of visual teaching tools are generated by the visual teaching tool generating module  108 , and displaying on the display  106 . An initial node on one of the four corners is determined based on the selected one of three types of visual teaching tools. The digit in the initial node is the multiplicand (or multiplier as “commutative law”). The multiplicand and the multiplier can be changeable with each other. 
       FIG. 2  shows the first type of visual teaching tool. The first type of visual teaching tool has a 3×3 array nodes with nine digits (1, 2, 3, 4, 5, 6, 7, 8, 9) in their nodes, respectively, and the tenth node with digit 0 therein. Thus, the first type of visual teaching tool consists of ten digits (1, 2, 3, 4, 5, 6, 7, 8, 9, 0), ten nodes and nine transition paths. Nine digits (1, 2, 3, 4, 5, 6, 7, 8, 9) locate and fix in node (1, 1), node (1, 2), node (1, 3), node (2, 1), node (2, 2), node (2, 3), node (3, 1), node (3, 2), node (3, 3), respectively. Such nodes are defined by (column, row) node. The 3×3 array nodes have four corners. Four digits (1, 3, 7, 9) locate on its corner of the 3×3 array nodes. Each digit corresponds to a node. Nine digits correspond to nine nodes, respectively. The adjacent number order nodes of the nine nodes are associated with each other via a transition path to form a node string. The node string is a bend string. The transition order is from the initial node to the terminal node. The former node is transited to the next node via the transition path. For example, the node transition orders are as follows: 1 st  node (1, 1) proceeding to 2 nd  node (1, 2) via the first transition path; 2 nd  node (1, 2) proceeding to 3 rd  node (1, 3) via the second transition path; 3 rd  node (1, 3) proceeding to 4 th  node (2, 1) via the third transition path; 4 th  node (2, 1) proceeding to 5 th  node (2, 2) via the fourth transition path; 5 th  node (2, 2) proceeding to 6 th  node (2, 3) via the fifth transition path; 6 th  node (2, 3) proceeding to 7 th  node (3, 1) via the sixth transition path; 7 th  node (3, 1) proceeding to 8 th  node (3, 2) via the seventh transition path; and 8 th  node (3, 2) proceeding to 9 th  node (3, 3) via the eighth transition path. In this example, an initial node is node (1, 1). The digit in the initial node is defined as the multiplicand. So, the multiplicand is 1. That is, the multiplicand of the first type of visual teaching tool is 1. Additionally, node (3, 3) is proceeding to the tenth node with digit 0 via the ninth transition path (last path). The digit in the tenth node is fixed as digit 0. The (tenth) node with digit 0 is terminal (end) node. 
       FIGS. 3   a  and  3   b  show the second type of visual teaching tool. The second type of visual teaching tool has two 2×2 array nodes with four digits (2, 4, 6, 8) in their nodes, respectively, and the fifth node with digit 0 therein. Thus, the second type of visual teaching tool consists of five digits (2, 4, 6, 8, 0), ten nodes and eight transition paths. For example, the two array nodes are parallel arrangement, and the two array nodes are identical. The first array nodes show in  FIG. 3   a , and the second array nodes show in  FIG. 3   b . Four digits (2, 4, 6, 8) locate in node (1, 1), node (1, 2), node (2, 1), node (2, 2), respectively. Such nodes are defined by (column, row) node. The 2×2 array nodes have four corners (which allocation may be the same as the four corners of the first type of visual teaching tool). Four digits (2, 4, 6, 8) locate on its corner of the 2×2 array nodes. Each digit corresponds to a node. Four digits correspond to four nodes, respectively. The adjacent number order nodes of the four nodes are associated with each other via a transition path to constitute a node string. The node string is a bend string (like a “duck” or letter “Z”). The transition order is from the initial node to the terminal node. The former node may be transited to the next node via the transition path. For example, the node transition orders are as follows: 1 st  node (1, 1) proceeding to 2 nd  node (1, 2) via the first transition path; 2 nd  node (1, 2) proceeding to 3 rd  node (2, 1) via the second transition path; 3 rd  node (2, 1) proceeding to 4 th  node (2, 2) via the third transition path. In this example, an initial node is node (1, 1). The digit in the initial node is defined as the multiplicand. So, the multiplicand is 2. That is, the multiplicand of the second type of visual teaching tool is 2. Additionally, node (2, 2) is proceeding to the fifth node with digit 0 via the fourth transition path (last path). The digit in the fifth node is fixed as digit 0. The (fifth) node with digit 0 is terminal (end) node. The sixth to tenth nodes are the same as the first to fifth nodes. 
       FIG. 4  shows the third type of visual teaching tool. The third type of visual teaching tool has four corners nodes, such as 2×2 array nodes, with digits 5 in their nodes, respectively, and a center node with digit 0 therein. Thus, the third type of visual teaching tool consists of two digits (0, 5), six nodes and nine transition paths. Digit in node (1, 1), node (1, 2), node (2, 1), and node (2, 2) is the same as 5. The node on the four corners is transited from/to the center node with each other via two transition paths, respectively. The transition order is from the initial node to the terminal node. On one embodiment, number and/or order of the transition paths in visual teaching tool may be default without counting. For example, the node transition orders are as follows: node (1, 1) proceeding to the center node via the first transition path; the center node proceeding to node (1, 2) via the second transition path; node (1, 2) proceeding to the center node via the third transition path; the center node proceeding to node (2, 2) via the fourth transition path; node (2, 2) proceeding to the center node via the fifth transition path; the center node proceeding to node (2, 1) via the sixth transition path; node (2, 1) proceeding to the center node via the seventh transition path; and the center node proceeding to node (1, 1) via the eighth transition path. In this example, an initial node is node (1, 1). The digit in the initial node is defined as the multiplicand. So, the multiplicand is 5. That is, the multiplicand of the third type of visual teaching tool is 5. Additionally, node (1, 1) is proceeding to the sixth node with digit 0 via the ninth transition path (last path). The digit in the sixth node is fixed as digit 0. The (sixth) node with digit 0 is terminal (end) node. In other words, the initial node proceeds to the terminal node. The digit in the last node is always 0. 
     More specific, 1 st  type of visual teaching tool has 4 digits (1, 3, 7, 9) on its corner, 2 nd  type of visual teaching tool has 4 digits (2, 4, 6, 8) on its corner and 3 rd  type of visual teaching tool has digit 5 on its corners. The initial node is always appearing on the corner. So, if multiplicand is 4, the 2 nd  type of digit should be chosen. 
     The initial node is determined by rotating visual teaching tool. After rotating, digits in nodes are not changed. Then, digit in the new initial node is the multiplicand. For example, the 1 st  type of visual teaching tool has to transform 90 degrees (clockwise rotation) to see digit 3 appearing on its 1 st  (initial) node, show in  FIG. 5 . So, the multiplicand is 3. In an example, the 1 st  type of visual teaching tool is transforming 90 degrees (counter-clockwise rotation; or clockwise rotation 270 degrees) to see digit 7 appearing on its 1 st  (initial) node, show in  FIG. 6 . So, the multiplicand is 7. In another example, the 1 st  type of visual teaching tool is transforming 180 degrees to see digit 9 appearing on its 1 st  (initial) node, show in  FIG. 7 . So, the multiplicand is 9. Similarly, the 2 nd  type of visual teaching tool has to transform 90 degrees (clockwise rotation) to see digit 4 appearing on its 1 st  (initial) node, show in  FIGS. 8   a  and  8   b . So, the multiplicand is 4. In an example, the 2 nd  type of visual teaching tool is transforming 90 degrees (counter-clockwise rotation) to see digit 6 appearing on its 1 st  (initial) node, show in  FIGS. 9   a  and  9   b . So, the multiplicand is 6. In another example, the 2 nd  type of visual teaching tool is transforming 180 degrees to see digit 8 appearing on its 1 st  (initial) node, show in  FIGS. 10   a  and  10   b.    
     In one embodiment, the visual teaching tool consists of a digits configuration and a diagram configuration. When the diagram configuration is overlapping on the digits configuration, each digit on the digits configuration locates in the corresponding node of the diagram configuration, respectively. The digits on the digits configuration are still fixed in rotation operation and after rotating. Only the diagram configuration can be rotated. The diagram configuration consists of all nodes and all transition paths. When rotating, the digit 0 is/are rotated together. After rotating, digits of the digits configuration still locate in the nodes of the rotated diagram configuration, respectively. The shape or image (such as circle) of each node of the diagram configuration can be rotated and it still looks the same after rotating. If the diagram configuration (1 st  layer) and the digits configuration (2 nd  layer) are different two layers, then rotating the 1 st  layer of the visual teaching tool to determine that the digit in the initial node (1 st  appearing number) is the multiplicand. For example, 1 st  layer of the 1 st  type of visual teaching tool has to transform 90 degrees to see 3 or 7 appearing on its 1 st  node. Also, if multiplicand is one of digits (1, 2, 5), the 1 st  layer of the visual teaching tool does not rotate as the 1 st  number is already appeared (on the initial node).  FIGS. 11   a ,  12   a  and  12   b , and  14   a  show a non-rotate diagram configuration of the 1 st  type of visual teaching tool, 2 nd  type of visual teaching tool and 3 rd  type of visual teaching tool, respectively. The multiplicand is digits 1, 2, 5, respectively.  FIGS. 11   b ,  13   a  and  13   b , and  14   b  show a digits configuration of the 1 st  type of visual teaching tool, 2 nd  type of visual teaching tool and 3 rd  type of visual teaching tool, respectively. Remember the digits location. 
     (2). Determine Multiplier: 
     Follow the transition path on the 1 st  layer of the decided visual teaching tool from above step to determine multiplier. 
     As noted above, it is bridging node-to-node through the transition path. The 1 st  node is 1 for multiplier. Then, the multiplier increases 1 for every node it proceeding one transition path. The multiplier increases 1 through one transition path. Thus, the multiplier is equal to the proceeding number of the transition path plus 1 (PN+1). For 1 st  type of visual teaching tool and 2 nd  type of visual teaching tool, the multiplier is also equal to the node number (N) from the initial node to the object node. For example, when hits digit 4 of 2 nd  type of visual teaching tool (4 appearing on the node) as the multiplicand is 6 (shown in  FIGS. 9   a  and  9   b ), the proceeding number of the transition path is 3, and the node number from the initial node (2, 1) to the object node (1, 2) is 4. The object node is the fourth node and obtained through three transition paths. So, the multiplier is 4. 
     (3). Determine “Units” Place (the Second Digit of Result): 
     As described on above step, once the multiplicand and the multiplier are determined, the result (product value) may be obtained. 
     Unit place of the result is the digit as it appears in the selected node. The unit place is the second digit of the result if the product value is two-digits number. 
     For example, as the multiplicand is 3, shown in the  FIG. 5 ; for 1 st  node (three times one) the unit place is 3; for proceeding to 2 nd  node (three times two) the unit place is 6; for proceeding to 3 rd  node (three times three) the unit place is 9; for proceeding to 4 th  node (three times four) the unit place is 2; for proceeding to 5 th  node (three times five) the unit place is 5; for proceeding to 6 th  node (three times six) the unit place is 8; for proceeding to 7 th  node (three times seven) the unit place is 1; for proceeding to 8 th  node (three times eight) the unit place is 4; for proceeding to 9 th  node (three times nine) the unit place is 7; for proceeding to the tenth node (three times ten) the unit place is 0. The digits (3, 6, 9, 2, 5, 8, 1, 4, 7, 0) appearing in the object nodes are unit place of ten product values, respectively. Based-on the  FIG. 6 , digits (7, 4, 1, 8, 5, 2, 9, 6, 3, 0) appearing in the object nodes are unit place of product, respectively. Similarly, according to the  FIG. 7 , digits (9, 8, 7, 6, 5, 4, 3, 2, 1, 0) appearing in the object nodes are unit place of product, respectively. 
     For example, as the multiplicand is 4, shown in the  FIGS. 8   a  and  8   b ; for 1 st  node (four times one) the unit place is 4; for proceeding to 2 nd  node (four times two) the unit place is 8; for proceeding to 3 rd  node (four times three) the unit place is 2; for proceeding to 4 th  node (four times four) the unit place is 6; for proceeding to 5 th  node (four times five) the unit place is 0; for proceeding to 6 th  node (four times six) the unit place is 4; for proceeding to 7 th  node (four times seven) the unit place is 8; for proceeding to 8 th  node (four times eight) the unit place is 2; for proceeding to 9 th  node (four times nine) the unit place is 6; for proceeding to tenth node (four times ten) the unit place is 0. The digits (4, 8, 2, 6, 0, 4, 8, 2, 6, 0) appearing in the object nodes are unit place of ten product values, respectively. Based-on the  FIGS. 9   a  and  9   b , digits (6, 2, 8, 4, 0, 6, 2, 8, 4, 0) appearing in the object nodes are unit place of product, respectively. Similarly, according to the  FIGS. 10   a  and  10   b , digits (8, 6, 4, 2, 0, 8, 6, 4, 2, 0) appearing in the object nodes are unit place of product, respectively. 
     For example, as the multiplicand is 5, shown in the  FIG. 4 ; through 1 st  transition path to the center node (five times two) the unit place is 0; through 2 nd  transition path to 2 nd  node (five times three) the unit place is 5; through 3 rd  transition path back to the center node (five times four) the unit place is 0; through 4 th  transition path to 3 rd  node (five times five) the unit place is 5; through 5 th  transition path back to the center node (five times six) the unit place is 0; through 6 th  transition path to 4 th  node (five times seven) the unit place is 5; through 7 th  transition path back to the center node (five times eight) the unit place is 0; through 8 th  transition path back to 1 st  node (five times nine) the unit place is 5; through 9 th  transition path to 6 th  node (five times ten) the unit place is 0. The center node is 5 th  node. The digits (5, 0, 5, 0, 5, 0, 5, 0, 5, 0) appearing in the object nodes are unit place of product, respectively. 
     (4). Determine “Tens” Place (the First Digit of Result): 
     As described on above step, once the multiplicand and the multiplier are determined, the result (product value) may be obtained. 
     The multiplicand and the multiplier are determined based-on the diagram rotation and the transition paths. The transition paths in the visual teaching tool are divided into two types. The first type of transition paths are for carrying, and the second type of transition paths are for NOT-carry. 
     Tens place is the number of the first type of transition path for carrying. The tens place is the first digit of the result if the product value is two-digits number. 
     For example, as the multiplicand is 3, shown in the  FIG. 5 ; it should be noted that the number of the first type of transition path for carrying is 3. In this example, the first type of transition path for carrying is indicated by bold line, and the second type of transition path for NOT-carry is indicated by non-bold line. The bold line may be at the locations between adjacent nodes, changing column or row nodes, or reaching to the digit “0” node. The number of the bold lines is equal to multiplicand. As the multiplicand is 3, the three bold lines locate between 3 rd  node and 4 th  node (changing column nodes), 6 th  node and 7 th  node (changing column nodes), 9 th  node and tenth node (reaching to the digit “0” node), respectively. Thus, when hit “2”, it is passing through the first bold line, the result is 12, with unit place 2; when hit “1”, it is passing through the first and second bold lines, the result is 21, with unit place 1; when hit “0”, it is passing through the first, second and third bold lines, the result is 30, with unit place 0. Based-on the  FIG. 6 , as the multiplicand is 7, the number of the first type of transition path for carrying is 7. The seven bold lines (locate between adjacent nodes, and reaching to the digit “0” node) are the first type of transition paths for carrying, and the two non-bold lines are the second type of transition paths for NOT-carry. Similarly, according to the  FIG. 7 , as the multiplicand is 9, the number of the first type of transition path for carrying is 9. All of nine bold lines are the first type of transition paths for carrying, and the second type of transition path is zero. 
     For example, as the multiplicand is 4, shown in the  FIGS. 8   a  and  8   b ; it should be noted that the number of the first type of transition path for carrying is 4. The four bold lines are the first type of transition path for carrying, and the four non-bold lines are the second type of transition path for NOT-carry. The four bold lines locate between 2 nd  node and 3 rd  node, 4 th  node and 5 th  node, 7 th  node and 8 th  node, 9 th  node and tenth node, respectively. Thus, when hit 1 st  “2” it is passing through the first bold line, the result is 12, with unit place 2; when hit 1 st  “0”, it is passing through the first and second bold lines, the result is 20, with unit place 0; when hit 2 nd  it is passing through the first, second and third bold lines, the result is 32, with unit place 2 when hit 2 nd  “0”, it is passing through the first, second, third and fourth bold lines, the result is 40, with unit place 0. Based-on the  FIGS. 9   a  and  9   b , as the multiplicand is 6, the number of the first type of transition path for carrying is 6. The six bold lines are the first type of transition path for carrying, and the two non-bold lines are the second type of transition path for NOT-carry. Similarly, according to the  FIGS. 10   a  and  10   b , as the multiplicand is 8, the number of the first type of transition path for carrying is 8. All of eight bold lines are the first type of transition path for carrying, and the second type of transition path is zero. 
     Besides, based-on the  FIG. 4 , as the multiplicand is 5, the number of the first type of transition path for carrying is 5. The five bold lines are the first type of transition paths for carrying, and the five non-bold lines are the second type of transition paths for NOT-carry. 
     As noted above, the invention proposes a method for digit multiplication based-on diagram rotation and transition path combining with the fixed digits configuration to provide an intuition, visualization approach to determine the product of digit multiplication. 
     For a person skilled in the art, the preferred embodiments described above are illustrations rather than limitations of the applications of the invention. The invention is intended to enable various modifications, and similar arrangements are included within the spirit and scope of the appended claims, the scope of which should be accorded the broadest interpretation so as to encompass all such modifications and similar structures.