A demonstration tool for the relationship between the diameter and circumference of a circle

Abstract

The utility model discloses a diameter and circumference relation demonstration teaching aid of circle relates to mathematical teaching instrument technical field. The teaching aid mainly includes L type support, drawer slide rail, rolling disc and scale ruler. The L type support is formed by the bottom plate of horizontal arrangement and the vertical plate of vertical arrangement, the drawer slide rail is horizontally installed on the vertical plate, and its sliding direction is parallel with the bottom plate, the rolling disc is fixedly installed through a rotating shaft on the right -hand end of slide rail, and its disc surface is parallel with the vertical plate, and the disc bottom is contacted with the flexible pad of bottom plate surface, the scale ruler is vertically fixed in front of vertical plate, and its zero scale line is aligned with the mark initial position on the disc. When using, push the slide rail and drive the disc to do pure rolling on the bottom plate for a week, and the distance of disc rolling is the circumference through the scale ruler, and the ratio of the circumference value and disc diameter value can directly show the circumference ratio pi. The utility model discloses simple structure, convenient operation, and the demonstration phenomenon is intuitive and accurate, can effectively help student to understand the concept of circumference ratio.

Description

Technical Field

[0001] This utility model relates to the field of teaching instrument technology, and in particular to a demonstration teaching aid for teaching the value of pi in elementary school mathematics geometry. Background Technology

[0002] Pi (π) is the ratio of a circle's circumference to its diameter, and it is an important mathematical constant. For beginners, understanding the abstract concept that the circumference is π times the diameter can be challenging. Current methods typically involve wrapping a soft string around the circle and then straightening it to compare with the diameter. This method is cumbersome, prone to error, and lacks the dynamic demonstration of rolling, making it neither intuitive nor engaging. Therefore, there is an urgent need for a teaching aid that can accurately and intuitively demonstrate the relationship between a circle's circumference and diameter. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a simple, accurate, and intuitive teaching aid for demonstrating the relationship between the diameter and circumference of a circle.

[0004] To achieve the above objectives, the present invention adopts the following technical solution: The system includes an L-shaped bracket, a sliding mechanism, a rolling disc, and a ruler. The L-shaped bracket consists of a horizontally positioned base plate and a vertically fixed plate. The sliding mechanism includes a drawer slide horizontally mounted on the vertical plate, with the sliding direction of the drawer slide parallel to the base plate. The rolling disc is rotatably mounted on the sliding mechanism via a pivot, specifically located at the right end of the drawer slide. The surface of the rolling disc is parallel to the plane of the vertical plate, and its bottom contacts the upper surface of the base plate. The ruler is a long, transparent strip, vertically fixed in front of the vertical plate, with a gap between it and the surface of the rolling disc. A flexible pad, either a plush pad or a rubber pad, is adhered to the upper surface of the base plate to increase friction with the rolling disc, ensuring pure rolling. The rolling disc has a radius of 5 centimeters, and its surface has a diameter mark penetrating the center, with an arrow pointing outward from one end of the diameter mark. The total length of the ruler is not less than 50 cm, and its zero mark coincides with the position indicated by the arrow mark on the rolling disc in the initial state. The installation height of the drawer slide is such that the bottom of the rolling disc on it just contacts the base plate, and the effective sliding stroke of the drawer slide is greater than 35 cm. The base plate and the vertical plate are both made of wood or acrylic board, with dimensions of 30 cm wide and 100 cm long. A teaching aid for demonstrating the relationship between the diameter and circumference of a circle includes an L-shaped bracket, a sliding mechanism, a rolling disc, and a ruler. The L-shaped bracket consists of a horizontally set base plate and a vertical plate fixedly connected to the base plate vertically, and is used horizontally as a whole. The sliding mechanism uses a drawer slide, which is horizontally installed on the left side of the vertical plate by screws. The installation height ensures that the components on the slide can contact the base plate, and the sliding direction is parallel to the long side of the base plate. The rolling disc is rotatably fixed to the right end of the sliding block of the drawer slide by a pivot (such as a screw), so that the disc can rotate freely and its surface is parallel to the vertical plate. The bottom of the disc contacts the surface of the base plate. A layer of plush pad is adhered to the surface of the base plate to increase friction and ensure that the disc rolls without slippage as it moves along the slide rail. The radius of the rolling disc is 5 cm (i.e., 10 cm in diameter), and a diameter line passing through the center of the disc is drawn on its surface, with a triangular arrow mark at one end of the diameter line. Initially, the arrow points vertically upwards. The ruler is a transparent plastic ruler, 50 cm in length, vertically fixed to the front of the vertical plate by a bracket, maintaining a gap of approximately 0.2 cm between it and the disc surface to prevent friction. The ruler is positioned so that the "0" mark is precisely aligned with the tip of the arrow mark on the disc in the initial state.

[0005] The beneficial effects of this invention are as follows: by pushing the slide rail, the disc rolls purely on the base plate, transforming the measurement of the circumference of a circle into an intuitive measurement of linear distance. After one revolution, the reading on the ruler indicated by the arrow is the circumference of the circle (approximately 31.4 cm). The ratio of this value to the known diameter (10 cm) (3.14) is an approximation of pi (π). The entire demonstration process is dynamic, intuitive, and accurate, greatly enhancing the teaching effect and helping students deeply understand the meaning of pi. Attached Figure Description

[0006] Figure 1 is a front view of the overall structure of the teaching aid of this utility model.

[0007] Figure 2 is a side view of the teaching aid of this utility model.

[0008] In the picture: 1. Base plate; 2. Vertical plate; 3. Drawer slide; 4. Rolling disc; 5. Diameter and arrow markings; 6. Ruler; 7. Plush pad. Detailed Implementation

[0009] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0010] As shown in Figures 1 and 2, the demonstration teaching aid of this utility model mainly consists of a base plate 1, a vertical plate 2, a drawer slide 3, a rolling disc 4, and a ruler 6. The base plate 1 and vertical plate 2 are made of 1.5 cm thick wooden boards, measuring 30 cm × 100 cm, and are fixed together in an L-shape using wood glue and corner brackets. The drawer slide 3 is a three-section slide with a travel of at least 35 cm, horizontally installed on the left end of the vertical plate 2 with screws, its installation height being 5 cm from the center line of the slide to the upper surface of the base plate 1. The rolling disc 4 is made of a 1 cm thick acrylic disc with a radius of 5 cm, its center connected to the right end of the sliding block of the slide 3 with screws, allowing for flexible rotation. A diameter is marked on the surface of the disc 4 with a red engraving, and a triangular arrow 5 is drawn at one end. A layer of short-pile plush cloth is pasted onto the entire rolling area of ​​the base plate 1 as a plush pad 7. The transparent plastic ruler 6 is fixed to the front of the disc 4 by two L-shaped acrylic brackets, with a spacing of about 0.3 cm. The ruler body is parallel to the vertical plate 2. During installation, first push the slide rail 3 to the leftmost end, adjust the position of the ruler 6 so that its "0" mark is precisely aligned with the tip of the arrow 5 on the disc 4, and then tighten the brackets.

[0011] During the demonstration, the teacher slowly pushes the slide rail 3 from left to right, causing the disc 4 to roll purely under the friction of the plush pad 7. When the disc 4 has rolled exactly one revolution, the teacher stops pushing. At this point, the arrow 5 on the disc 4 points vertically upwards again, and the reading on the ruler 6 it points to is the circumference C (31.4 cm). Students can intuitively read C = 31.4 cm. Given that the diameter D = 10 cm, π = C / D = 31.4 / 10 = 3.14, thus gaining a deeper understanding that pi is a multiple of the circumference and diameter.

Claims

1. A teaching aid demonstrating the relationship between the diameter and circumference of a circle, characterized in that: The device includes an L-shaped bracket, a sliding mechanism, a rolling disc, and a scale. The L-shaped bracket consists of a horizontally positioned base plate and a vertical plate fixed perpendicularly to the base plate. The sliding mechanism includes a drawer slide horizontally mounted on the vertical plate, with the sliding direction of the drawer slide parallel to the base plate. The rolling disc is rotatably mounted on the sliding mechanism via a pivot, specifically located at the right end of the drawer slide. The surface of the rolling disc is parallel to the plane of the vertical plate, and its bottom contacts the upper surface of the base plate. The scale is a long, transparent strip-shaped ruler, vertically fixed in front of the vertical plate, with a gap between it and the surface of the rolling disc.

2. The teaching aid demonstrating the relationship between the diameter and circumference of a circle according to claim 1, characterized in that: A flexible pad, which can be a plush pad or a rubber pad, is attached to the upper surface of the base plate to increase the friction between the base plate and the rolling disc, ensuring that the base plate rolls purely.

3. A teaching aid demonstrating the relationship between the diameter and circumference of a circle according to claim 1 or 2, characterized in that: The rolling disc has a radius of 5 centimeters, and its surface has a diameter mark that runs through the center of the disc. One end of the diameter mark has an arrow pointing outward from the disc.

4. The teaching aid demonstrating the relationship between the diameter and circumference of a circle according to claim 3, characterized in that: The total length of the ruler is not less than 50 centimeters, and its zero mark coincides with the position pointed to by the arrow mark on the rolling disk in the initial state.

5. The teaching aid demonstrating the relationship between the diameter and circumference of a circle according to claim 1, characterized in that: The drawer slide is installed at a height such that the bottom of the rolling disc on it is in contact with the base plate, and the effective sliding stroke of the drawer slide is greater than 35 cm.

6. The teaching aid demonstrating the relationship between the diameter and circumference of a circle according to claim 1, characterized in that: Both the base plate and the vertical plate are made of wood or acrylic sheets, and are 30 cm wide and 100 cm long.

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