Space rectangular coordinate system drawing ruler for mathematics
By designing a mathematical spatial rectangular coordinate system drawing ruler with rotatable Z, Y, and X rods, the problem of difficulty in displaying dynamic changes of vectors and spatial positional relationships was solved, realizing an intuitive display from two-dimensional to three-dimensional, and improving students' spatial understanding ability.
Patent Information
- Application Number
- CN202520385424.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Utility models(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-06
- Publication Date
- 2026-03-20
- Estimated Expiration
- 2035-03-06
AI Technical Summary
Existing technologies struggle to intuitively demonstrate the dynamic changes and spatial relationships of vectors to students, especially the difficulty in understanding them in three-dimensional space.
A mathematical drawing ruler based on a spatial rectangular coordinate system was designed. By setting Z-bars, Y-bars, and X-bars and using the rotation of the bars and the connection of sliding grooves, the ruler can switch from a two-dimensional plane to a three-dimensional space. The ruler also uses spotlights to display the dynamic changes and positional relationships of vectors.
By using an intuitive approach, students can understand the concept of vectors in three-dimensional space, thus improving their spatial imagination and comprehension abilities.
Smart Images
Figure CN224013287U_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The utility model relates to the field of teaching aids, and particularly relates to a space rectangular coordinate system drawing ruler for mathematics. BACKGROUND
[0002] The space rectangular coordinate system is an important tool for studying three-dimensional space in higher mathematics. It establishes an x-axis, a y-axis and a z-axis by selecting a point O as an origin and along three mutually perpendicular directions, thereby constructing a three-dimensional coordinate system. This system can uniquely determine any point in space and express the direction and size of a space vector through coordinates. When drawing the space rectangular coordinate system drawing ruler for higher mathematics teaching, it is necessary to ensure that the coordinate axes are mutually perpendicular and have appropriate length proportions, so as to accurately reflect the spatial relationship.
[0003] However, in actual teaching, it is difficult to intuitively show students the dynamic changes and spatial position relationship of vectors by relying only on the plane space rectangular coordinate system drawing ruler. For example, the parallel, perpendicular, modulus and included angle of vectors are difficult to intuitively display through the static drawing ruler. In addition, students often feel abstract and difficult when understanding the operation and geometric meaning of vectors in three-dimensional space.
[0004] Therefore, we improve it and propose a space rectangular coordinate system drawing ruler for mathematics. CONTENT OF THE UTILITY MODEL
[0005] The utility model aims at the existing problem that it is difficult to intuitively show students the dynamic changes and spatial position relationship of vectors.
[0006] In order to realize the above utility model purposes, the utility model provides a space rectangular coordinate system drawing ruler for mathematics to improve the above problems.
[0007] The application is as follows:
[0008] The Z rod and the Y rod are fixed and arranged at 90 degrees, the X rod is rotatably connected to the fixed point of the Z rod and the Y rod, and the plane formed by the rotation track of the X rod is coincident with the symmetry plane of the Z rod and the Y rod;
[0009] When the X rod is coplanar with the Z rod and the Y rod, the X rod and the Z rod and the Y rod form an included angle of 135 degrees;
[0010] When the X rod rotates 90 degrees around the rotation point, the three rods form an included angle of 90 degrees.
[0011] Preferably, the Z rod, the Y rod and the X rod are slidably connected with the clamping groove half circular ring through the sliding groove.
[0012] Preferably, the two sliding grooves on the Z bar and the Y bar are in the same vertical plane, and the two sliding grooves on the X bar are arranged at right angles.
[0013] Preferably, the half circular ring is formed by a half circular ring and sliding blocks at two ends of the half circular ring, a moving block is slidably connected to the half circular ring along an arc surface of the half circular ring, and the moving block is inserted into a slot of the half circular ring through a pin.
[0014] Preferably, a telescopic rod is fixedly connected to a midpoint of the moving block, and a spotlight is rotatably connected to the telescopic rod, and a rotation track surface of the spotlight is perpendicular to a rotation track surface of the moving block.
[0015] Preferably, a scale groove is formed in the sliding groove, and the sliding block of the half circular ring is clamped in the scale groove.
[0016] Compared with the prior art, the mathematical space rectangular coordinate system drawing ruler has the following beneficial effects:
[0017] In the scheme of the present application:
[0018] In order to solve the problem that the existing plane rectangular coordinate system is difficult for students with weak spatial imagination to understand, the present application sets three coplanar rods to assist drawing a two-dimensional rectangular coordinate system on a plane blackboard or drawing position, and through rotating one of the rods, the three rods form three axes simulating a rectangular coordinate system, so that the switching between the drawing ruler and the display teaching aid is completed through simple rotation, and the nature of mathematical concepts such as vectors in the coordinate system is helped to be understood by students through the intuitive display teaching aid. BRIEF DESCRIPTION OF DRAWINGS
[0019] Figure 1 A front view of a mathematical space rectangular coordinate system drawing ruler is provided in the present application;
[0020] Figure 2 A structure schematic view of an X rod of a mathematical space rectangular coordinate system drawing ruler is provided in the present application;
[0021] Figure 3 A connection relationship schematic view of a half circular ring slot and an X rod of a mathematical space rectangular coordinate system drawing ruler is provided in the present application;
[0022] Figure 4 A connection relationship schematic view of a half circular ring slot and a sliding groove of a mathematical space rectangular coordinate system drawing ruler is provided in the present application;
[0023] Figure 5 A comparison schematic view of before and after bending of an X rod of a mathematical space rectangular coordinate system drawing ruler is provided in the present application.
[0024] Indications in the drawings:
[0025] 1, Z bar; 2, Y bar; 3, X bar; 4, card slot half ring; 5, moving block; 6, telescopic rod; 7, spotlight; 10, sliding groove; 11, scale groove. DETAILED DESCRIPTION
[0026] In order to make the person skilled in the art better understand the technical scheme of the present application, the technical scheme in the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by the person skilled in the art without creative labor should belong to the scope of protection of the present application.
[0027] As described in the background, it is difficult to intuitively show students the dynamic changes and spatial position relationship of vectors.
[0028] In order to solve this technical problem, the present application provides a mathematical space rectangular coordinate system drawing ruler, which is applied to the switching between the drawing ruler and the demonstration mold, and is convenient for the observer to switch between two-dimensional and three-dimensional thinking.
[0029] Specifically, please refer to Figure 1 、 Figure 2 、 Figure 3 、 Figure 4 and Figure 5 , a mathematical space rectangular coordinate system drawing ruler specifically comprises:
[0030] The Z bar 1 and the Y bar 2, which are fixed to each other and arranged at ninety degrees, are rotatably connected to the X bar 3 at the fixed point, the rotation track of the X bar 3 forms a plane coinciding with the symmetry plane of the Z bar 1 and the Y bar 2, and the rotation of the X bar 3 around the fixed point enables the three bars to change from the two-dimensional drawing ruler state to the three-dimensional right-angle coordinate system demonstration structure, and cooperate with the last position three-line intersection formed by the light beam emission of the spotlight 7 to form a fixed point;
[0031] When the X bar 3 is coplanar with the Z bar 1 and the Y bar 2, the X bar 3 and the Z bar 1 and the Y bar 2 form a one hundred and thirty-five degree angle, at this time, when the teacher draws with chalk, the three bars are used as a ruler to draw the two-dimensional space rectangular coordinate system, and ensure that the drawn space rectangular coordinate system meets the two-dimensional drawing specification, and the spotlight 7 is clamped in the scale groove 11 at different positions, and the scale drawing accuracy is ensured by the spotlight 7;
[0032] When the X rod 3 rotates 90 degrees around the rotation point, the three rods are mutually at an angle of 90 degrees, when the three rods are mutually at an angle of 90 degrees, the X rod 3 is separated from the plane formed by the Z rod 1 and the Y rod 2, so that the whole becomes a three-dimensional structure, and meets the constituting specification of the three-dimensional space rectangular coordinate system, at this time, the teacher can use the spotlight 7 on the different rods to cooperate with the extension rod 6 to extend to different heights on different planes, in the form of rays, to show the meaning of the concept of vector.
[0033] In order to enable the personnel in the technical field to better understand the scheme of the present application, the technical scheme in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings.
[0034] It should be noted that the embodiments in the present application and the features and technical solutions in the embodiments can be combined with each other without conflict.
[0035] It should be noted that: similar reference numbers and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.
[0036] Embodiments, please refer to Figure 1 , Figure 2 , Figure 3 , Figure 4 and Figure 5 , a space rectangular coordinate system drawing ruler for mathematics, the Z rod 1, the Y rod 2 and the X rod 3 are slidably connected with the clamping groove half circular ring 4 through the sliding groove 10, the clamping groove half circular ring 4 can move on different rods to indicate the change of corresponding coordinate values, and the change of values and position is displayed by using the sliding mode.
[0037] The two sliding grooves 10 on the Z rod 1 and the Y rod 2 are in the same vertical plane, and the two sliding grooves 10 on the X rod 3 are arranged at right angles, the position of the clamping groove half circular ring 4 on the X rod 3 is different from that on the Z rod 1 and the Y rod 2 through the change of the position of the sliding groove 10 of the clamping groove half circular ring 4 on the X rod 3, so that the clamping groove half circular ring 4 cannot be in contact with the bottom drawing board or blackboard plane when the X rod 3 is coplanar with the Z rod 1 and the Y rod 2, so that the clamping groove half circular ring 4 cannot slide.
[0038] The clamping groove half circular ring 4 is composed of a half circular ring and sliding blocks at both ends thereof, the moving block 5 is slidably connected to the clamping groove half circular ring 4 along the arc surface of the clamping groove half circular ring 4, the moving block 5 is inserted into the clamping groove of the clamping groove half circular ring 4 through the bayonet, the orientation of the spotlight 7 can be changed through the change of the orientation of the moving block 5 towards the clamping groove half circular ring 4, so that the spotlight 7 can change the angle and represent more directional vectors.
[0039] The middle point of the moving block 5 is fixedly connected with an extension rod 6, and the extension rod 6 is rotatably connected with a spotlight 7, and the rotation track surface of the spotlight 7 is perpendicular to the rotation track surface of the moving block 5, the rotation range of the spotlight 7 is expanded by the spotlight 7 with different rotation directions, and the extension rod 6 further expands the range of the representable vector.
[0040] The sliding groove 10 is provided with a scale groove 11, and the sliding block of the clamping groove semi-ring 4 is clamped in the scale groove 11, and the clamping groove semi-ring 4 arranged in a sliding mode enables the observer to more intuitively observe the process of length change leading to three-dimensional value change, and provides a demonstration effect for students with weak spatial imagination.
[0041] In the present application, unless otherwise clearly specified and limited, the terms "mounting", "connecting", "connecting", "fixing" and the like should be understood in a broad sense, for example, it can be fixedly connected, or it can be detachably connected, or it can be integrated; it can be mechanically connected, or it can be electrically connected or in communication with each other; it can be directly connected, or it can be indirectly connected through an intermediate medium, it can be the internal communication of two elements or the interaction relationship of two elements, unless otherwise clearly limited. For ordinary skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.
[0042] Obviously, the above-described embodiments are only part of the embodiments of the present application, not all the embodiments, and the preferred embodiments of the present application are given in the drawings, but do not limit the patent scope of the present application. The present application can be realized in many different forms, and conversely, the purpose of providing these embodiments is to make the disclosure of the present application more thorough and comprehensive. Although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions recorded in the foregoing specific embodiments, or make equivalent substitutions for part of the technical features. Any equivalent structure made by using the contents of the present application specification and drawings, directly or indirectly applied to other related technical fields, is also within the patent protection scope of the present application.
Claims
1. A mathematical drawing ruler using a spatial rectangular coordinate system, characterized in that, It includes a Z-bar (1) and a Y-bar (2) whose endpoints are fixed to each other and set at a 90-degree angle. The Z-bar (1) and the Y-bar (2) are rotatably connected to an X-bar (3) at their fixed points. The plane formed by the rotation trajectory of the X-bar (3) coincides with the plane of symmetry of the Z-bar (1) and the Y-bar (2). When the X rod (3) is coplanar with the Z rod (1) and the Y rod (2), the X rod (3) forms a 135-degree angle with the Z rod (1) and the Y rod (2); When the X rod (3) rotates 90 degrees around the rotation point, the three rods form a 90-degree angle with each other.
2. A mathematical spatial rectangular coordinate system drawing ruler according to claim 1, characterized in that, Each of the Z rod (1), Y rod (2) and X rod (3) is slidably connected to a slotted semi-circular ring (4) via a sliding groove (10).
3. A mathematical spatial rectangular coordinate system drawing ruler according to claim 2, characterized in that, The two sliding grooves (10) on the Z rod (1) and Y rod (2) are on the same vertical plane, and the two sliding grooves (10) on the X rod (3) are set at right angles.
4. A mathematical spatial rectangular coordinate system drawing ruler according to claim 3, characterized in that, The slot semicircular ring (4) is composed of a semicircular ring and sliding blocks at both ends. A moving block (5) is slidably connected along the arc surface of the slot semicircular ring (4). The moving block (5) is inserted into the slot of the slot semicircular ring (4) by a pin.
5. A mathematical spatial rectangular coordinate system drawing ruler according to claim 4, characterized in that, A telescopic rod (6) is fixedly connected to the midpoint of the movable block (5), and a spotlight (7) is rotatably connected to the telescopic rod (6). The rotation trajectory plane of the spotlight (7) is perpendicular to the rotation trajectory plane of the movable block (5).
6. A mathematical spatial rectangular coordinate system drawing ruler according to claim 5, characterized in that, The sliding groove (10) is provided with a scale groove (11), and the sliding block of the slot semicircular ring (4) is engaged in the scale groove (11).